Roaming and Rambling

Daring Cooks: Soufflé

2010-11-17T19:23:00.001-08:00

Dave and Linda from Monkeyshines in the Kitchen chose Soufflés as our November 2010 Daring Cooks’ Challenge! Dave and Linda provided many of their own delicious recipes plus a sinfully decadent chocolate soufflé recipe adapted from Gordon Ramsay’s recipe found at the BBC Good Food website. You can find the recipes we were given here.

The last daring baker's challenge was doughnuts, which did not actually involve baking. This daring cooks challenge was soufflé, which most definitely does. I'm not sure why I find this amusing, but I do.

One of my friends and I made two varieties of soufflé for this challenge. The first was an adaptation of the watercress soufflé found in the above link and the second was the chocolate soufflé.

Now, we did not actually manage to find watercress, so we used spinach instead. We also used cheddar cheese instead of Parmesan and added some finely chopped onion. As is typical with me, we did not bother carefully measuring these out, but this picture should give you some idea of the ratio. The quantity of onion is half of a small onion.

Mixing spinach into the egg mixture turned it a lovely shade of green. Here we have the soufflés shortly after putting them in the oven and then again when they are almost done.

Here are the finished souffle's right after pulling them out of the oven. They both gorgeous and were absolutely fantastic. It is more work than I am likely to put in a meal often (especially since they do not keep particularly well), but definitely something to keep in mind if I am ever trying to make a "nice" meal for something.

Now the chocolate soufflés on the other hand... Folding the chocolate custardy mixture into into the egg whites made pretty swirls.

It did not hold up as well in the oven though. They started to rise and then a couple of them decided that they should clearly be volcanoes. We were glad they were on a cookie sheet.

The ones that didn't explode ended up pretty enough, but I did not find them as impressive visually as the spinach variety. Furthermore, while they were certainly tasty, I do not think they were any more impressive than many of the other chocolate desserts I make. I might try an interesting variation sometime, but I don't really see myself making basic chocolate soufflés in the future. Brownies are a whole lot less work and at least as tasty.

PS. Taking pictures through the oven door is interesting. Some of my attempts clearly came out better than others. Perhaps I should experiment with this.

Tastes like fall :-)

2010-11-02T09:23:00.000-07:00

Fall must be here, because I have been being enticed by winter squash, apples and sweet potatoes instead of zucchini, eggplant and tomatoes. Poking around the internet looking for inspiration on what to do with the current set of produce, I have come across a large number of recipes that call for maple syrup and thyme. This is not a combination I would have thought to put together, but it turns out to be quite good.

Ingredients:

1 buttercup squash (acorn or butternut would probably work just as well)
2 apples (I used fuji)
1 large sweet onion
~1 lb chicken
2 Tbsp butter
1/3 cup maple syrup
1 tsp dry thyme
pinch salt

Instructions:
Preheat the oven to 400. Dice squash, apples, onion and chicken and mix together in a 9x13 pan. Melt the butter and mix with the maple syrup, thyme and salt. Drizzle the syrup mixture over the vegetables and chicken, and toss to coat. Bake covered for 45 min, uncover, stir and bake for another 15 or so (until the chicken is cooked and the squash is soft.) I ate it with couscous, though it would also go well with cornbread or biscuits.

Daring Bakers: Doughnuts!

2010-10-27T13:32:00.000-07:00

The October 2010 Daring Bakers challenge was hosted by Lori of Butter Me Up.
Lori chose to challenge DBers to make doughnuts. She used several sources for her recipes including Alton Brown, Nancy Silverton, Kate Neumann and Epicurious. The recipes we were given can be found here.

I worked from the yeast doughnuts recipe we were given.

Ingredients:
1.5 cup milk
1/3 cup butter
4.5 teaspoon active dry yeast (I have a jar, but this is about 2 pkgs. if you don't)
1/3 cup warm water (95°F to 105°F / 35°C to 41°C)
2 eggs
1⁄4 cup sugar (plus extra to roll them in)
1.5 tsp salt
1 heaping tsp cinnamon
4 2/3 cup flour
oil for frying (I used corn oil) amount depends on size of vessel you are frying in – the original recipe said you need 3 in, I used 1 and was fine.

Instructions:
Heat the milk until it is warm enough to melt the butter. Combine the milk and butter in a large bowl. While it is cooling to lukewarm, mix the yeast and warm water in a small bowl and let it sit for 5 min or so that it gets thick and foamy. Once the yeast mixture is foamy and the milk has cooled enough that it won't kill the yeast, mix the yeast, sugar, eggs, salt and cinnamon into the milk and butter. Add half the flour and mix well. Add the remaining flour, mix well, and then kneed the dough until it is smooth and not very sticky. If you live in a humid place (like I do), you may have to work more flour in as you kneed in order to get it non-sticky. Transfer the dough to an oiled bowl that is large enough for it to more than double, cover with a towel and let it rise for an hour or so. For me it had well more than doubled at that point - I was glad I had ended up with it in my largest bowl. Roll it out to 3/8 in thick on a well floured surface and cut out the doughnuts. The hole cut out of the center actually seems to help it cook more evenly with this recipe, so I would either make them quite small or find something to cut holes with. As you cut them out, place them on cookie sheets or the like so that you can take them close to where you will be frying them. Let them rise for another 30 min or so.

Heat the oil to 365 F (I used my 6 qt soup pot). My stove is terrible at maintaining constant temperatures, and I found that it worked reasonably well anywhere between 360 and 370. Any cooler and they had to stay in long enough that they started soaking up the oil (yech), much hotter and it was hard not to burn them. There were several times I had to take the oil off the heat and let it cool down for a bit before continuing. At any rate, you gently pick up the doughnut and set it in the oil. When the bottom is golden, flip it and cook until the whole thing is golden (this takes about 30 sec per side if the oil is a good temperature - long enough that you can keep it from burning, fast enough that it doesn't end up greasy). I set them on paper towels as they came out. Once they were cool enough to handle I dipped them in granulated sugar. Ideally you should let them cool a little more so you don't burn your tongue, but they are best warm :-)

Daring Bakers: Leaf Cookies

2010-09-27T09:21:00.000-07:00

The September 2010 Daring Bakers’ challenge was hosted by Mandy of “What the Fruitcake?!” Mandy challenged everyone to make Decorated Sugar Cookies based on recipes from Peggy Porschen and The Joy of Baking. She told us to make sugar cookies that represent September. You can find the recipes she gave us to work with here.

I make cookies all the time. Roll-out cookies (including sugar cookies) require more effort (and counter space) than drop cookies, so they get made less often, but there are still several slightly stained recipe cards for them in my recipe box. One of the two go-to cookies if we needed to take cookies to an even when I was little were my mom's butter cookies. When these cookies were taken somewhere they were almost always decorated - although essentially never with frosting. The mess that comes with frosting was reserved for birthday cakes and the the construction and decoration of gingerbread houses. Thus this challenge was essentially asking me to take two things I was familiar with and put them together.

The theme for the cookies was easy - fall leaves. I have a couple of leaf cookie cutters (and an acorn!) that I picked up in the dollar bin at Target one time and have been looking for an excuse to use. We split the dough in half so that we could make some plain (and thus see what exactly the recipe gives us) and added orange zest and a dash of cloves to the other half. I would give you measurements, but we didn't actually measure the flavorings. They came out well, but I have to admit that this particular cookie recipe is not one I am likely to be going back to. I have others that fill the same kind of role that I like better.

With decorating, we tried putting veins in the leaves before and after flooding. Our conclusion was that it was more effective to add the detail after. One of the pictures below shows the difference.

2010-09-23T10:37:00.000-07:00

I have been posting pretty butterflies and such lately. I would not have expected to find butterflies in the city, but they are here anyway. They serve as a reminder to look for the little spots of unexpected beauty in life. On the other hand, when you are chasing butterflies it is easy to miss the beauty in the bigger picture. Sunset and sunrise are bright enough to catch my attention and remind me to not get lost in the details.

On a less philosophical note, I'm trying to learn to use things like traffic lights and power lines instead of always fighting them.

Butterfly collection part 2

2010-09-19T12:37:00.000-07:00

This first one is a little beat up, but pretty anyway.

This one is also black and blue, but less beat up (though it really did not want to sit still).

Then there is a lovely yellow one. Maybe I will eventually learn their names. For now though I am happy to just admire them.

In addition to all of these big showy butterflies there are a whole host of small ones that are easy to overlook.

This last guy isn't a butterfly, but I thought it was a nifty picture anyway :-).

Butterfly collection

2010-09-18T19:12:00.000-07:00

For something completely different, here is some of the gorgeous produce I have acquired from the farmer's market. The three purpley ones are eggplants, the rest are various squashes.

This batch was mixed with some beans and a can of tomatoes and turned into a thick tasty stew. It goes well both with couscous and with biscuits and was even good mixed with scrambled eggs. I am a big fan of foods that lend themselves to lots of variations as leftovers.

Oh, one other thing:

Red leaves! Fall is coming earlier this year than it did last year. I am pretty ok with this.

Daring Cooks: Canning!

2010-09-17T04:33:00.000-07:00

Once again I am running late on posting this... life has been doing far too good a job of keeping me busy, especially in the middle of the week.

The September 2010 Daring Cooks’ challenge was hosted by John of Eat4Fun. John chose to challenge The Daring Cooks to learn about food preservation, mainly in the form of canning and freezing. He challenged everyone to make a recipe and preserve it. John’s source for food preservation information was from The National Center for Home Food Preservation. The instructions they gave us can be found here.

Now, the first part of this challenge was gathering all of the supplies. I already had a wonderful large stock pot and the size of my kitchen dictates that one very large pot is enough. This meant that getting an actual canning pot was out of the question. The only problem with my pot is that it is about an inch less in diameter than the typical canning pot and thus the standard canning racks are not going to fit in it. On labor day (since I actually had time...) I set out for the local Ace Hardware to track down jars and figured there was a decent chance that a hardware store would have something I could repurpose as a canning rack. Apparently I was wrong on that second count. While I was looking around I was approached by an employee who asked what I was looking for. I explained and was informed that they did not have anything that would work as a canning rack and was further given a lecture on how dangerous canning is. I smiled, assured him I would be careful, bought my jars and set out for the walk home.

Walking to Ace took me somewhat farther east than my normal errands do. Whenever I find myself in a part of the city that I do not know as well I try to be observant and learn where things are. In this case I discovered that the Trader Joe's shopping center also has a Richard's Variety Store. Since I had a few fairly odd things I was looking for (something to act as a canning rack and jar tongs) I figured it would be worth stopping to check it out. Not only did it have the tongs and a cooling rack that would work as a canning rack, it has all sorts of other entertaining things. This includes a nice selection of cookie cutters (and some silly ones like gingerbread men missing a bite), unusual note cards, a lovely selection of jigsaw puzzles and stick candy. Overall it was a very good find :-)

Ok, now onto the food. I was very bad about taking pictures this month, so I only have a picture of the finished products:

As you can see, I made peach jam and apple butter. The peach jam was made from the last of my farmer's market peaches from this summer. They had gotten to the point of needing to be used, so jam seemed like a good bet. To make the jam, I blanched the peaches so that I could peal them, and chopped them up. At this point I had a little over 5 cups of peaches. I stirred in about 4 cups of sugar and a splash of lemon juice and let it hang out for a while so that the juice would come out of the peaches and mingle with the sugar. Once it was nice and mixed I transfered it to a large pot (you want one larger than you think you need, as it boils it fills a rather larger volume) and cooked it until it reached 220 F. At this point it went into the preheated jars and then into the stock pot of boiling water for processing. The texture isn't quite ideal, but it isn't bad either and is quite tasty, so I'm calling it a success.

For the apple butter my friend and I got three bags of apples from the grocery store (gala, granny smith and McIntosh) and more or less followed the challenge recipe in the above link. Our only major deviation is that we don't believe in Splenda, and so used a mix of honey and brown sugar to taste instead. The result was fantastic. We now have grand plans to make the Flying Biscuit's cranberry apple butter at some point later this fall when cranberries become available.

Overall this challenge was fantastic :-)

A Beautiful Day

2010-09-04T17:06:00.000-07:00

The weather today was gorgeous. I went to the farmer's market at Piedmont Park (and got an exciting collection of squash) and then wandered around the park for a bit before finding a nice shady spot under a tree to sit and do some math. It was lovely. I also remembered to grab my camera when I left the house this morning.

You can click on the panorama (or any of them for that matter) to see it larger :-)

Pictures!

2010-08-27T18:28:00.000-07:00

Here is the view from my the living room in my new apartment. I unfortunately can not open the windows here, so I'm having to figure out how to take pictures through the glass. Right now this means that camera usually ends up reflected in it...

Of course, in the down in my room also has a screen (despite the fact that it does not open...), which makes things even trickier.

Here we have different sort of sunrise shot than the ones I usually go for. I rather like it though. It is a little hard to see at this size (you can click it to see it bigger), but the next three traffic lights are all different colors!

Then later that morning

Daring Bakers: Baked Alaska

2010-08-27T16:36:00.000-07:00

The August 2010 Daring Bakers’ challenge was hosted by Elissa of 17 and Baking. For the first time, The Daring Bakers partnered with Sugar High Fridays for a co-event and Elissa was the gracious hostess of both. Using the theme of beurre noisette, or browned butter, Elissa chose to challenge Daring Bakers to make a pound cake to be used in either a Baked Alasa or in Ice Cream Petit Fours. The sources for Elissa’s challenge were Gourmet magazine and David Lebovitz’s “The Perfect Scoop”. The recipes can be found here.

This challenge turned out to be quite the adventure. The concept behind baked Alaska is that you start with some sort of cake, generously top it with ice cream, cover it with meringue, freeze the whole thing and then manage to cook the meringue without melting the ice cream.

For the cake we were asked to make brown butter pound cake. I mixed up a half batch of the batter and baked two small cakes in the 1 cup pyrex dishes I have with a little bit of batter left over. In retrospect I think it would have baked more evenly if I had split that amount of batter between three cakes that size (or, you know, followed the instructions - but where's the fun in that). Despite the slight issues with baking, the brown butter pound cake was absolutely fantastic.

I started with my mom's recipe for vanilla ice cream and froze it using the stir-every-hour method. It does not not come out as wonderfully smooth as it does in an ice cream maker, but it is still delicious. Once it was frozen, I chopped up a peach and mixed it in. I prefer this version of peach ice cream to the one I made last month.

Then there is the meringue... My meringue skills need work. It was delicious, but even with freezing did not want to actually stay on. The result was a tasty mess, but nothing so impressive looking as baked Alaska is supposed to be.

Daring Cooks: Pierogi!

2010-08-16T12:42:00.000-07:00

This should have gone up a couple days ago, but life got busy :-)

The August 2010 Daring Cooks‟ Challenge was hosted by LizG of Bits n' Bites and Anula of Anula's Kitchen. They chose to challenge Daring Cooks to make pierogi from scratch and an optional challenge to provide one filling that best represents their locale. You can find the pdf with the recipes here.

I started with the Russian Style Pierogi recipe and replaced the bacon with Kielbasa sausage. I used red potatoes and apparently didn't cook them long enough because they really didn't want to mash. When I got the filling mixed up (minus the egg, which I simply forgot) I realized that what I had was a lovely potato salad, not something I could stuff in pierogies.

I fixed this problem by running the mixture through the food processor. This approach worked quite well.

The dough was lovely to work with (although I will admit that I was skeptical before it got to sit for 20 minutes - that step is important). I ate them with sour cream - they were quite tasty.

I've been playing with peaches all summer, so the logical choice for a local pierogi was something peach. I chopped up a peach and mixed it with some of my left over cottage cheese and a little sugar and stuffed that in the dough (and ate it with sweetened sour cream).

In the future I would add a bit of flour or cornstarch to any kind of peach filling since the peaches release a lot of juice as they cook. The result wasn't bad but it wasn't anything special either. I think I might try it with a creamier cheese and possibly with the addition of cinnamon and/or cardamom.

A Three Course Farmer's Market Brunch

2010-07-31T09:44:00.000-07:00

The Piedmont Park farmer's market has a pastry stand that always looks wonderful and that I usually resist. This morning I decided that I wanted a pastry, dang it, and so didn't eat breakfast before going and decided I would find brunch there.

The first course consisted of a blueberry danish (they were out of blackberry) from the pastry stand, a fresh peach from my usual bag of peaches, and a cup of locally made yogurt (because the peach and blueberries were screaming for something cool and creamy to go with them and the yogurt stand was right next to the peach stand). I sat on the grass and ate this course while listening to the live music they always have and people watching. It was lovely.

At 11 they have a cooking demonstration where a local chef comes, makes something, explains how it works, and then lets everyone try it. Today we had Chef Jeff from SoHo. He made a salad with mixed greens, watermelon and cherry tomatoes, topped it with citrus cured and then grilled salmon and garnished it with a Benne Wafer (a crunchy sesame cookie). It was absolutely fantastic. This was course 2.

Before he started preparing the salad, Chef Jeff mixed up a peach cobbler. It ended up needing to bake slightly longer than he expected, but it was still done not too long after the salad. The concoction wasn't quite what I would usually call a cobbler, but I'm not sure what I would call it other than delicious, so I guess the term cobbler will do.

Visiting the Northeast

2010-07-28T16:52:00.000-07:00

I thought my plan was to hang out with friends in the Boston area and then go to Mt. Holyoke to visit MathCamp. In reality I also went hiking in New Hampshire and swam in a gorge in Ithaca, New York. MathCamp was full of math and fun and silliness and good people as usual. The whole trip was fantastic.

New Hampshire

Ithaca, New York

Mt. Holyoke

Daring Bakers: Swiss Swirl Ice Cream Cake

2010-07-27T16:05:00.001-07:00

Sorry for disappearing like that. The last couple of weeks have been fun - I'll post something about them once I have sorted through the pictures.

For now though, it is post day for the Daring Bakers again. The July 2010 Daring Bakers’ challenge was hosted by Sunita of Sunita’s world – life and food. Sunita challenged everyone to make an ice-cream filled Swiss roll that’s then used to make a bombe with hot fudge. Her recipe is based on an ice cream cake recipe from Taste of Home. The recipe can be found here.

My birthday is in July but I knew I was going to be out of town for it, so we took on this challenge as an early birthday party. We also, predictably, got somewhat carried away.

The first part of the challenge was to pick flavors. Unfortunately (or perhaps fortunately in this case?) the friend I was brainstorming with and I are both horribly indecisive. This lead to the idea that we should clearly create something like the cupcake version of the challenge so that we could make lots of different flavors. Initially we thought this meant making them in muffin tins. When we were ready to assemble them we decided it actually meant making them in mini-muffin tins. This produced ice cream cake bombs that were about 2 bites each. It was fantastic.

Step 1 was to shrink the swiss rolls. To accomplish this we scaled the cake recipe back to 2 eggs and baked it in a 10x15in pan (mostly because that was the size we had). We made a chocolate batch, a cinnamon batch, and a plain batch. We think we slightly overcooked the chocolate and slightly undercooked the plain, but we managed to get mini swiss rolls made from all three. For fillings we made mint-lime whipped cream, almond whipped cream,chocolate whipped cream, and chocolate-cayenne whipped cream. Trying to cut reasonably thin slices of these tiny guys with a knife was a mess, but dental floss worked nicely.

For the ice cream we made chocolate following the challenge recipe and then made the rest as custard based. The custard flavors were cinnamon (Note that milk, sugar and ground cinnamon produce a somewhat stringy mixture which is, unsurprisingly, reminiscent of cinnamon roll filling. It still freezes up reasonably nicely), cayenne (which was really interesting and turned out to be a friend's favorite), lime (like frozen key-lime pie filling, mmmm...), blueberry (I love berries so much...), and peach (obviously, given that I am in Atlanta). All came out delicious, though the chocolate never quite got hard (though it did thicken somewhat). For sauces we made butterscotch, fudge, and mango.

We made a cinnamon-almond swiss roll with peach and blueberry icecream and butterscotch sauce version in the muffin tin before switching to the mini muffin tin. The extra tiny ones were small enough we didn't want to take up space in the cup with the sauce, so we served them with the sauces. This meant that people got to choose their own sauce and was generally a wonderful time.

Daring Cooks: Nut Butter!

2010-07-13T21:31:00.000-07:00

I mentioned a few weeks ago (when I posted about the chocolate pavlova) that I have joined the Daring Kitchen community.

The July 2010 Daring Cooks’ Challenge was hosted by Margie of More Please and Natashya of Living in the Kitchen with Puppies. They chose to challenge Daring Cooks to make their own nut butter from scratch, and use the nut butter in a recipe. Their sources include Better with Nut Butter by Cooking Light Magazine, Asian Noodles by Nina Simonds, and Food Network online.

This means that I have been eating rather more nuts than usual. The recipes they gave us to work with can be found here. There are four recipes - I have made (variations on) three of them:

Asian Cashew Salad
I followed the recipe for the cashew dressing almost exactly (I added a jalapeno instead of hot sauce) and it was amazing. For the rest of that recipe, I kept the spirit of rice noodles, meat and raw veggies, but didn't pay much attention to the specifics. I used chicken as the meat and red bell pepper, zucchini, and bean sprouts as the vegetables. It is good cold and makes for a very refreshing meal in the summer heat!

Chicken with Pecan Cream & Mushrooms
I debated for quite a while whether or not I was going to try this one since I'm not generally big on mushrooms. However, I have been getting better about that and figure that part of the point of joining the daring cooks is to convince me to try things I would not otherwise decide to go for. My conclusion is that this is not something that I am likely to make if I am just cooking for myself, but it was not bad and I would be happy to eat it again. I will certainly keep it in mind as a way to make something strongly reminiscent of stroganoff that manages to be completely dairy free. Personally, I think the sour cream in stroganoff is amazing, but there are times when it would be nice to be able to avoid it (and the pecan sauce really is wonderfully creamy).

Tomato Almond Curry
This dinner was inspired by the fact that I realized I had a couple of potatoes that really ought to be used soon. I finely diced an onion and pealed and chopped the potatoes and put them in my frying pan with some butter to start cooking and started a pot of rice. While they were cooking I made the almond butter. The cashew and pecan butters both came out beautifully, but the almonds seemed to want to remain as finely ground almond rather than as as butter. I went ahead and added the 1/3 cup of milk that the recipe called for and continued processing. The result was a thick but smooth almond cream. By the time I got that sorted out the potatoes and onions were cooked, so I added the spices (increasing the quantities of everything but the cinnamon and adding a dash of cayenne) and garlic and then went to find the tomato sauce. I had thought I had a large can, but it turned out that I had 14.5 oz cans of diced tomatoes and one 8 oz can of tomato sauce... I decided to just add one can of tomatoes and the can of sauce (and enough water to rinse the cans). Once everything came to a gentle boil I dumped in the almond cream and added about half of a 16 oz bag of frozen chopped spinach. The result was fantastic. I am afraid I do not have any pictures of this one for you - I was hungry and wanted dinner, so I was focused on cooking rather than taking pictures. It really does come together quite quickly though!

On a non-food-related note, the Phantom of the Opera is currently at the Fox Theater! Photography is naturally not allowed during the performance, but I got this picture of the chandelier and part of the beautiful Paris Oprah House set during intermission :-)

From Sea to Shining Sea...

2010-07-04T20:23:00.000-07:00

...almost. I was at a conference at Stanford last week. The campus there is lovely, as are the nearby bay lands.

Today I was back in Atlanta for the 4th and went down to Centennial Olympic Park to listen to the concerts and watch fireworks.

I don't think the show topped the Szt. Istvan show I watched from the banks of the Duna in Budapest, but they nevertheless made impressive use of the space they had to work with. I think this was the first time I have watched a fireworks show that was coming from 3 sides. Adding to the effect is that this building

was on my right. You will note that there are light fluffy clouds reflected in the windows at the moment. Those windows are also quite good at reflecting fireworks. Before we get to the fireworks though you may remember the giant CocaCola bottle I posted a picture of a while back. Its lights are usually programmed to "empty" and "refill" the bottle tonight something different happened when it got dark

Ok, now you can have fireworks. The pictures don't come close to doing it justice, but I got some that are better than most of my previous attempts at fireworks shots. I took pictures the first few minutes and then decided that I would rather just enjoy the show than take lots of pictures, so I don't have too many.

Chocolate Pavlova

2010-06-27T01:03:00.000-07:00

I recently joined the Daring Kitchen community. It is a group of people who like to cook and bake and every month challenge each other to make something that people are likely to find unusual and/or challenging.

The June 2010 Daring Bakers’ challenge was hosted by Dawn of Doable and Delicious. Dawn challenged the Daring Bakers’ to make Chocolate Pavlovas and Chocolate Mascarpone Mousse. The challenge recipe is based on a recipe from the book Chocolate Epiphany by Francois Payard.

Pavlova is a dessert from Australia and New Zealand. The particular recipe we were told to use is apparently slightly non-traditional, but it is delicious regardless.

Step 1: Chocolate Meringues

3 large egg whites
½ cup plus 1 tbsp white granulated sugar
¼ cup confectioner’s (icing) sugar
1/3 cup cocoa powder

Place a rack in the center of the oven and preheat to 200º F (95º C) degrees. Line a baking sheet with parchment and set aside. Put the egg whites in a bowl and whip until soft peaks form. Increase speed to high and gradually add granulated sugar about 1 tbsp at a time until stiff peaks form. (The whites should be firm but moist.) Add the confectioner’s sugar and cocoa powder to the egg whites and fold the dry ingredients into the white. (This looks like it will not happen. Fold gently and it will eventually come together.) Fill a pastry bag with the meringue. Pipe the meringue into whatever shapes you desire. Alternatively, you could just free form your shapes and level them a bit with the back of a spoon.

Bake for 2-3 hours until the meringues become dry and crisp. Cool and store in an airtight container for up to 3 days. If you make them thick or bake them for less time, the middles come out kind of marshmallowy, which I think is pretty fantastic.

Step 2: Chocolate Mascarpone Mousse:

1 ½ cups heavy cream (cream with a milk fat content of between 36 and 40 percent)
grated zest of 1 average sized lemon
9 ounces very dark chocolate, chopped
1 2/3 cups mascarpone
pinch of nutmeg
2 tbsp orange juice

Now, mascarpone cheese is somewhat hard to find and expensive, but you can make your own from cream without much trouble. That site says not to use ultra-pasteurized cream. Ultra-pasteurized was all I could find. It works just fine.

Put ½ cup of the heavy cream and the lemon zest in a saucepan over medium high heat. Once warm, add the chocolate and whisk until melted and smooth. Transfer the mixture to a bowl and let sit at room temperature until cool. Place the mascarpone, the remaining cup of cream and nutmeg in a bowl. Whip on low for a minute until the mascarpone is loose. Add the Grand Marnier and whip on medium speed until it holds soft peaks. (DO NOT OVERBEAT AS THE MASCARPONE WILL BREAK.) Mix about ¼ of the mascarpone mixture into the chocolate to lighten. Fold in the remaining mascarpone until well incorporated. Fill a pastry bag with the mousse. Again, you could just free form mousse on top of the meringue.

Step 3: Mascarpone Cream

1 cup whole milk
1 cup heavy cream
1 vanilla bean, split or 1 tsp pure vanilla extract
6 large egg yolks
6 tbsp sugar
½ cup (120 mls) mascarpone

In a bowl, whisk together the egg yolks and sugar until the mixture turns pale yellow. Combine the milk, cream and vanilla in a saucepan over medium high heat, bringing the mixture to a boil. Take off the heat. Pour about ½ cup of the hot liquid into the yolk mixture, whisking constantly to keep from making scrambled eggs. Pour the yolk mixture into the pan with the remaining cream mixture and put the heat back on medium. Stir constantly with a wooden spoon until the mixture thickens enough to lightly coat the back of a wooden spoon. DO NOT OVERCOOK. Remove the mixture from the heat and strain it through a fine mesh sieve into a bowl. Cover and refrigerate until the mixture is thoroughly chilled, about 2 hours or overnight. Gently fold in mascarpone (the recipe called for more heavy cream at this point, I decided that was not needed). Drizzle over the mousse.

And then I got peaches and realized that they would go well with the chocolate

And on a completely different note, mushroom update:

I'm guessing this is what they look like before they open. Either that or I have two kinds of mushrooms in my planter now...

Well, THAT was unexpected...

2010-06-26T06:12:00.000-07:00

A few days ago I found a lady bug sitting on a chive in my little window sill herb garden. Given that I live on the fifth floor I was not expecting that. I'm guessing someone had opened the window for a bit and it flew in.

This morning I went to check on my herbs and was in for a bigger surprise.

Little mushrooms?! Sure enough...

Apparently I get to weed my indoor planter.

Dogs, etc

2010-06-19T19:35:00.000-07:00

Every Saturday morning there is a farmer's market at Piedmont park. It has absolutely fantastic peaches. Today I got there reasonably early and then stuck around for the cooking demonstration (where they talked about how to make your own yogurt). While waiting for it to be time for the cooking demonstration I found a shady place to sit, eat a peach and just watch. There are a very impressive variety of dogs that get to visit the market. Here are just a few

That last guy was sitting near me and kept trying to come over. His owner explained that he really likes peaches :-).

After the cooking demonstration I walked across the park and came across a lovely butterfly.

Around the City

2010-06-15T16:14:00.000-07:00

Cauliflower and Chickpeas with Basil Pesto

2010-06-08T20:55:00.000-07:00

My basil needed to be cut back and I wanted something other than pasta. I also had a head of cauliflower in the fridge. This was the result. A friend and I had it on its own for dinner and finished it, but I think it would also work well as a side for roasted or grilled chicken (or you could chop the chicken up and mix it in too).

Recipe:
1/2 head cauliflower, cut into bite size pieces
1 can chickpeas, drained
~1/2 cup pesto

Saute cauliflower in a little bit of olive oil until it starts to get tender. Add chickpeas and cook until cauliflower is done and peas are warm. Toss the cauliflower and chickpeas with the pesto and enjoy :-)

2010-05-26T15:53:00.000-07:00

Here we have a stately blue jay who can't figure out why I don't just leave him alone, and a young cardinal (I think) who seemed as curious about me as he was wary.

A variety of lovely flowers

The most prevalent flower right now is the magnolia - the flowers are huge and are also unusual and fascinating if you stop and really look at them. They also smell nice :-)

Then there is that ever present aspect of life at Tech...construction. I think the fraction of campus that is fenced off for construction is growing daily.

2010-05-12T18:32:00.000-07:00

I went to Alumni Weekend at Mudd. You would never come across this at Tech:

I got to see the Shakespeare play

and a hummingbird nest

among a variety of other things. Visiting felt like going home, but this

is home now too, so life is good.

Pretty flowers:

Oh! I have a new herb garden! It smells delicious and is full of tasty things :-) It also has a pretty silhouette.

Smile!

2010-05-04T16:58:00.001-07:00

2010-04-26T16:26:00.000-07:00

"SO…that's why I tell you to keep your eyes wide.
Keep them wide open…at least on one side."

You never know what you might find if you do.

And sometimes it pays to take a closer look, this

could turn out to be
.

Oh, and yes, I /am/ looking at you

Eggs!

2010-04-20T18:25:00.000-07:00

But not the kind you tend to eat....

Here is mamma (I assume) robin sitting on her nest

Some lovely flowers from the courtyard of my building

Earth week art

A ridiculous fish

And a reminder that I do still live in the middle of a city

More Flowers!

2010-04-13T18:41:00.000-07:00

The flowers make for pretty pictures, so I am going to let them speak for themselves rather than ramble about them.

And now for something completely different. I wish I had gotten a slightly sharper shot, but this will have to do:

Birds!

2010-04-07T20:25:00.000-07:00

Birds are as much a sign of spring as flowers. They are, however, much harder to get good pictures of than flowers as they are much less willing to sit still while I take piles of pictures of them. I'm trying to get the hang of it. Until I do, here are a few half decent ones:

Happy Easter!

2010-04-04T12:27:00.000-07:00

Trees!

2010-03-29T16:55:00.000-07:00

Spring is slowly arriving. We've had daffodils for a while and now the trees are taking turns blooming.

Even the trees that are not in full flower are pretty :-) I love the curly baby leaves on this one!

Lemon Rosemary Cupcakes

2010-03-24T07:13:00.000-07:00

I went to my grandparents' home for Thanksgiving last year. While there I found the "Let them eat cake!" issue of Taste of Home and it was sent home with me. It has been sitting next to my cookbooks begging to have something made from it. Usually my baking urges take the form "mmmm...cookies!" but yesterday I got an inexplicable urge to make cake (and huzzah for spring break making it reasonable to actually do so!) - and not just any cake, something fruity and springy. Flipping through the cakes in the magazine, I came across a Lemon-Rosemary Layer Cake. It sounded fantastic, but for the fact that I don't have 9in round cake pans. After thinking about it a bit, I realized that it is easier to take cake around to share in cupcake form anyway. This recipe produced 19 regular sized cupcakes and 24 mini cupcakes.

Recipe

Ingredients for cake:
1 cup plus 2 Tbsp butter, softened
2.5 cups sugar
4 eggs plus a yolk
4 cups all purpose flour
3 tsp baking powder
1.5 tsp salt
3/8 tsp baking soda
1.5 cups sour cream
6 Tbsp lemon juice
3 tsp grated lemon zest
3 tsp minced rosemary

Ingredients for Frosting:
8 oz cream cheese, softened
4 + cups powdered sugar
1 Tbsp grated lemon zest
1 tsp lemon juice

Instructions:
Cream butter and sugar until light and fluffy. Add eggs and yolk and beat well. Combine flour, baking powder, salt and baking soda in a separate bowl. Alternately add flour mixture and sour cream to butter mixture, beating well after each addition (don't worry if it seems a little dry, you are getting ready to add lemon juice.) Beat in the lemon juice, peel and rosemary.

Scoop into paper lined cupcake pans and bake at 350. The mini cupcakes were done in about 15 minutes. The normal sized cupcakes baked for 20-25 minutes. Let them cool completely before frosting.

For the frosting, beat cream cheese until fluffy. Beat in the lemon juice and zest. Add powdered sugar about a cup at at time, beating well after each addition, until you like the consistancy.

The friend I was baking with dislikes cream cheese, so she concocted a glaze from butter, milk, and brown sugar. It was tasty and looks quite pretty, but I think these guys really want the cream cheese frosting.

Rainbow!

2010-03-21T19:13:00.000-07:00

There was a gorgeous rainbow today and I had a great view of the full half circle from my apartment. Unfortunately I could not figure out to get a good shot of the whole thing even using the panoramic thing. Here are a couple of partial views:

Seeing a rainbow today was fitting given the veritable rainbow of flowers around.

My favorite picture from the last week, however, was neither of the rainbow nor of a flower. I love the contrast between the old redish leaf that is doggedly hanging on next to the soft green of the new leaves.

Happy Pi Day!

2010-03-14T14:17:00.000-07:00

The math department had a pi day potluck! I was asked to bring not-pie... What they really meant was that I should bring not-dessert. I concluded that the right compromise between wanting to bring pie and being asked to bring something savory was quiche.

The crusts both came out beautifully:

I made one with bacon and one vegetarian. For the vegetarian one I borrowed my friend's pi-plate (since she was making something that was distinctly not-pi and it needed to be used) :-)

Quiche Recipe (for one quiche):
1 medium onion
~8oz chopped spinach (aka, about half of one of the 1lb bags of frozen spinach)
bacon and/or mushrooms (or, really, anything else you think would go well)
2 large handfuls grated cheese (I used mozzarella this time, cheddar works well too)
3 eggs
~1/2 cup milk

Dice the onion and saute until soft. Add the spinach and cook until thawed. Remove from heat and mix in cheese and bacon crumbles/chopped mushrooms. Dump this mixture into the pie crust. Beat the eggs with the milk and add salt and pepper to taste. Pour the egg mixture over the spinach mixture. Bake at 350 for ~45 minutes or until set. Let it cool for about 10 minutes before eating.

If you end up with more filling than will fit in your pie pan, it goes well in scrambled eggs :-)

Yesterday, that friend and I made dessert. Chocolate souffle cupcakes with white chocolate mint cream may have joined my list of favorite kinds of desserts.

Hey look, its acting like spring!

2010-03-11T17:02:00.000-08:00

At least this week... Whether or not it stays that way is another matter entirely. The temperatures have been consistently above 60 and I'm pretty sure we have even topped 70. The trees are budding and blooming, the lawns are thinking about greening up and there are daffodils popping up in a fairly sporadic fashion around campus.

On a completely different note, there was a mini math conference here on Saturday. We ended up with far more bagels than necessary for breakfast and they were left sitting in the corner of the room where we had lunch. There was more time alloted for lunch than we ended up needing to eat. Thus there were a bunch of mathematicians with nothing in particular to do and a pile of bagels...

That is a bagel that has been cut so that it forms two linked halves. Now I just need to learn how to cut a bagel into a trefoil knot :-)

Om nom nom: Squash Bread

2010-03-05T18:29:00.001-08:00

Yes, squash bread. Butternut squash to be more precise.

Last weekend I made a butternut squash and sweet potato tagine, based on a recipe from A Veggie Venture, though I seem to be incapable of following a recipe exactly. I altered the ratio of squash to sweet potatoes so that they were close to even and stirred in some shredded chicken I had left over from a different cooking project before adding the raisins. It was delicious and went well with both tortillas and couscous (huzzah for slight variations for leftovers).

In the process of altering the recipe, I realized that using the whole squash would have produced a rather larger batch than was reasonable (and might not have fit in my casserole dish). Instead of making a giant batch, I left ~1/3 of the squash unchopped and put it in a separate dish to bake while the tagine baked. I then ran the squash through the food processor to produce squash puree and stuck it in the fridge to determine what to do with later. During the semester I spent in Budapest I learned that I could make "pumpkin" pie from the Hungarian winter squash that I have yet to come across in the US, so I figured I could probably make some sort of "pumpkin" X from the squash puree. I was right. As a base recipe, I used Kitchen Parade's Autumn Pumpkin Bread (and bah to anyone who points out that it isn't autumn). I roughly halved the recipe (roughly, because I cut both kinds of sugar to 1/4 cup) and added a couple dashes of cloves. Oh, I also replaced 1/2 cup of the flour with whole wheat flour (since I happen to have it around). With my small (but wonderful) loaf pans, the half recipe made two loaves. They both came out as gorgeous as they are delicious.

Snow!

2010-02-22T18:59:00.000-08:00

This past weekend the temperatures were in the mid 60's at least. The previous weekend, however, we got approximately 3 inches of snow! This first picture is looking up the stairs right outside the math department

I have a tendency to find streetlights intriguing anyway (you have probably noticed this), but they are especially cool when shining on snowy trees!

The only logical way to spend Friday evening was to go out and play in it :-) Here is a snowman that my roommate and I created

Here are a couple of other snowmen that I ran into that weekend. The first is standing by the gate to Tech's president's house and the second is at a restaurant I pass on the way to church.

My view of snowy Atlanta on Saturday morning

And to finish off, a few lovely flowers peeking out above the layer of snow

2010-02-11T06:33:00.000-08:00

Someone has apparently been hanging chains of light around the city... I'm not quite sure what to make of it.

Maybe the chains of light are what holds up the cables in the sculpture in the next picture.

Now a story about Tech. If you click on this next picture to see it bigger, you will notice that the letter "T" is missing from the word "Amphitheater". Last week I gave you a picture of Tech Tower. A traditional prank is to steal the letter T from that tower - and there are all sorts of traditions about how that should be carried out. However, the administration decided some number of years ago that it very strongly does not approve of this prank and implemented a variety of security features that sound as though they would be quite effective at thwarting attempts to steal the T's on the tower. The response was that people have been stealing T's from other signs around campus instead. If you are ever on campus and a sign seems to be missing a letter, you can practically guarantee that it was a T.

2010-01-30T10:20:00.000-08:00

We actually had a non-white sky for part of the week! This is Tech Tower, one of the more iconic buildings on campus:

Atlanta under the full moon:

One of my cousins got married last weekend. This is where the reception was held:

And we will finish with a picture that captures part of why I am perfectly happy to not have a car in Atlanta:

The light is green - the cars are not moving. I frequently find myself walking past cars that are either creeping or not moving at all. In addition to not being caught in traffic, walking means I can better appreciate the beautiful sunset.

2010-01-22T20:11:00.000-08:00

It has been overcast a lot lately. The only part of this that I find frustrating is that it makes it hard to get pictures where the sky is anything but just white.

The clouds parted slightly for a short while. I was intrigued by the fact that I saw the break in the clouds reflected in the building before I saw it in the sky.

Those first two were from last Sunday. The next one is from Wednesday, when it was just as overcast.

It did decide to clear up this afternoon though - and I found a new window to take pictures from :-)

Snow!

2010-01-12T06:42:00.000-08:00

The closest it got to snowing while I was in Coquitlam was a heavy frost. The pictures I have posted of Canada so far have all been nature shots, but I'm supposed to be trying to get better at urban photography, so here is a shot of part of the Coquitlam skyline before we go back to Atlanta.

The day after I got back to Atlanta the temperature dropped below freezing and we got snow. Not a lot of snow, but enough to be pretty (at least where it didn't promptly melt and refreeze into ice sheets...).
The sign in front of my building:

A light post near the industrial engineering building:

Birds! The cold seemed to make them more willing to sit still than usual.

Merry Christmas from Canada

2009-12-24T22:59:00.001-08:00

Greetings from Coquitlam! These first three pictures are from a local park.

We also took a drive up the Sea to Sky Highway towards Whistler and stopped at several points along the way:

A couple of attempts at panoramic pictures (I'm having trouble getting them to format any bigger without getting blurry on this page. You can click them to get a bigger version):

It's Christmas time in the city...

2009-12-09T21:50:00.000-08:00

While my sister was here visiting, we got Christmas decorations put up!

That combined with baking lots of cookies has helped it feel like it might be getting close to Christmas time :-)

There are some decorations up around the city, but it doesn't even come close to Budapest...

Thanksgiving

2009-12-06T18:53:00.000-08:00

I went to Tallahassee for Thanksgiving. Normally I would have had my camera out taking tons of pictures of the food, but there were two other people with cameras out and I decided that three would be going overboard. However, I can't not have any pictures of food in a Thanksgiving post, so here are two that my sister Karen took:

While we were down in Tallahassee, my grandparents took us to Wakula Springs - and I did have my camera for that. There were lots of cool critters hanging out - alligators, turtles, a whole host of birds...and manatees!

The swamp is also pretty in its own right.

Catching up on November...

2009-12-06T18:05:00.000-08:00

Yay for fall!

The trees here do a much better job of knowing that it is fall than the trees in Claremont did, but they still had trouble agreeing exactly when they were supposed to start changing colors/shedding their leaves. One tree was particularly confused and seems to think that since it has almost lost all of its previous leaves, it must be time to start making new ones...

Now, part of my goal with reviving this blog was to work on finding beauty in my urban setting. Focusing on trees makes for pretty pictures, but feels more like finding ways to avoid the city than finding beauty in it. Some of my earlier pictures reflect (hah) the fact that there are a lot of reflections in the city - having lots of windows will do that. This next picture shows that there are reflections beyond the ones in windows:

Night

2009-11-05T17:28:00.000-08:00

The end of daylight savings time means that it is essentially dark out by 6pm. At least it means that it is less dark in the morning when I am trying to wake up.

Color

2009-10-25T14:29:00.000-07:00

I have missed fall... It is nice to finally have it again.

Last night the buildings all appeared rather red as they reflected the sunset. This morning it was almost as though the buildings were trying to camouflage as they reflected the blue sky and fluffy white clouds.

Playing with Light

2009-10-18T12:17:00.000-07:00

The sky cleared last night. This meant that the temperature dropped nicely so that it was rather on the chilly side this morning. In response, I got out one of my Budapest scarves for walking to church. Since the sky had cleared, the sun was out and making fun shadows. I was particularly entertained by the shadows formed by the fringe of my scarf. The sun being out also resulted in lots of interesting reflections.

Hello Again!

2009-10-11T19:26:00.000-07:00

A lot has happened since I last posted. Most notably, I graduated from HMC and have moved on to grad school at Georgia Tech. I've been adjusting to living in a city again (and Atlanta is very different from Budapest). I have been working on learning to see the beauty in my new urban setting and, as part of this goal, I have been trying to figure out how to take pictures of cityscapes. To make sure this keeps happening, I'm going to try posting pictures here on some kind of regular schedule - I haven't decided exactly how often yet. To start off:
A sunset picture taken from the window in my apartment

I have also been discovering that there is natural beauty to be found in the city, you just have to be paying more attention:

Pumpkin and Spice and Everything Nice

2008-11-02T14:15:00.000-08:00

I greatly enjoy Halloween at Mudd - it means getting to carve pumpkins, try all sorts of tasty cheese (we go trick-or-cheesing at East), and generally serves as a good excuse for everyone to come out of their rooms and hang out.

Now, being a mathematician that happens to also enjoy crafty/artsy type projects, I am never content to just carve a face in my pumpkin. This year I carved two iterations of Sierpinski's pentagon - oh, and I cut the lid of the pumpkin out using two iterations of the Koch Snowflake. Math is pretty :-)

Two of my friends also carved pumpkins and we set the three up outside our suite:

Now, the pumpkins that we got had rather thick walls - far too thick for the sorts of things we wanted to carve. We dealt with this by scraping down the flesh of the pumpkin on the inside until it was a more reasonable thickness. In the process, we ended up with a rather large bowl full of pumpkin shavings. It seemed silly to let these go to waste, so I adapted a recipe for

Pumpkin Chocolate Chip Cookies

Ingredients:

~1 cup mashed pumpkin
~1.5 cups brown sugar
1 stick butter
1 egg
1/2 tsp each of baking soda and baking powder
1/2 tsp salt
Spices. I just dumped them in until it smelled and tasted delicious, if I had to guess at amounts: heaping teaspoon cinnamon, shy teaspoon each of ginger and nutmeg, half teaspoon cloves
enough flour to make a nice dough, probably around 3 cups, but it will depend on how much liquid the pumpkin adds
1 bag chocolate chips

Instructions

Preheat the oven to 350.
Cook the pumpkin. I took the bowl full of pumpkin shavings (note that I mean that actual flesh of the pumpkin, not the slimy part that holds the seeds) and microwaved it for ~5 minutes, If you have a solid chunk of pumpkin, baking it works well too. Once it is cooked it should be soft enough for you to mash it up with a fork.
Cream the butter and the sugar. Once they are completely blended, add the egg and pumpkin and mix well.
I tend to not want to get any more bowls messy than necessary, so I then dump ~two cups of the flour on top of the pumpkin mixture and then stir in the baking powder and soda, salt and spices on top before mixing the whole business together. If you don't get the dry ingredients mixed at least partially together before you blend in the wet ingredients it is easy to not do a good job of, say, getting the salt well distributed.
At this point the dough is probably still really, really sticky. Mix in more flour. How much more you need will depend on the moisture content of your mashed pumpkin. As it turns out, there is not just one perfect consistency for the dough, so just mix in flour until it feels manageable. My guess is that adding another 1/2 to 1 cup should be reasonable.
Stir in the chocolate chips.
Scoop the dough out in cookie sized dollops on your cookie sheet.
Bake at 350 until they have started to brown and bounce back when you touch them.
Enjoy!

Oh, and you might enjoy checking out the pictures from Mudd's Study Abroad photo competition

Cookies with Flowers

2008-09-28T00:46:00.000-07:00

One of my friends is particularly fond of both the scent and flavor of lavender and has begun to incorporate it into her cooking. Most relevantly, she has discovered that it goes extremely well in shortbread. The only problem with this is that lavender is not quite a typical cooking ingredient, and so is not carried by grocery stores. It is, however, used in landscaping. Thus, we went on a lavender hunt and successfully brought back plenty of lavender flowers to stir into shortbread batter. I agreed with her that the result was quite tasty. Incidentally, I am starting to add various herb type things to my mental map of where I can gather foodstuffs around the campuses. It is really amazing just how much rosemary is used for landscaping...

Some pictures from around Mudd (and one from Pomona). As always, you can click on them to see them larger.

More bugs

Blue

Lines (at Pomona)

Greetings from Mudd

2008-09-05T11:07:00.000-07:00

I was hanging out in Hixon Court between classes yesterday and noticed that there were several dragon flies flitting around the pond. I managed to have my camera with me, so you get pictures:

If you click on a picture you can get a larger version where you can see more detail on the dragon flies!

I have been to all of my classes at least once at this point and it looks like it should be a fun semester :-) I will try to update on a somewhat regular basis.

How many airlines does it take to get from Missouri to Oregon?

2008-08-04T11:59:00.000-07:00

Air travel is ridiculous, but overall life is good.

Friday Aug 1
I get an email in the morning from Delta reminding me to check in online. I follow the link and am informed that my first flight is actually on Pinnacle (who?) and so I can't check in online. Right.
Around 11 pm I get a phone message from Northwest (Pinnacle flights are apparently operated by Northwest) informing me that my first flight has been canceled and that I am now scheduled on a US Air flight that leaves rather later in the day *sigh*.

Sat Aug 2
I arrive at the airport. I booked my flight through Delta originally, got a call from Northwest and was taking a US Air flight. Who was I supposed to check in with? I could not find a US Air desk, so I went to ask the people at Northwest... who sent me to United. I go talk to United and am informed that I am booked on their flight but that somehow Northwest still has control of my ticket, so their computer system will not let them check me in. The Northwest and United people talk for a while and get things sorted out.

After hanging out in the airport for a while, I had a relatively uneventful flight to Denver - arriving at the far end of Concourse B. The departure boards in Concourse B only have departure info for flights leaving from Concourse B, ie only flights on United and their affiliates. I was supposed to be connecting to a Delta flight... I eventually found someone who could tell me that Delta flights are all on Concourse C. I go to Concourse C and find that my Delta flight is not appearing on the departures board. There is however an Alaska flight with the same time and destination, so I go talk to the Alaska people. After a few tries they manage to find me in their system and then manage to trick it into letting them check me in (I think they had the same problem the United guy had had in the morning).

Anyway, I am at camp now (though the bag I checked is not). The puzzle hunt was fantastic :-)!

In which I pretend this is a photo blog

2008-07-26T18:55:00.000-07:00

I was in an artistic sort of mood this week, so I did a better job than usual of carrying (and remembering to use) my camera. Today the REU group went on a hike. Thus you get lots of pictures :-)

First off, my birthday was this week. My birthday cake:
I enjoy decorating birthday cakes, but when I get to choose the cake I go for a jam cake that does not lend itself to decoration. Go figure. It was delicious though :-)

Around campus:
My view from the bench where I sit to eat lunch every day.

A couple of pictures of different angles of the same flower. I'm not usually attracted to the red ones, but for some reason this one caught my eye.

I have no idea what these are, but they are really cool!

Squirrels!

And one from the construction site near the math building... The names that some companies decide to take never fail to amaze me.

Busiek State Forrest:
Not very far along the trail we came across a pretty butterfly. Shortly after that we reached a stream where the bridge was out...

And then we found the bridge...

The rest of the hike was very pretty, but not terribly eventful.

And of course we have flowers from along the trail:

Looks like Red, Tastes like Cake

2008-07-20T20:53:00.000-07:00

This past Friday was Charlie's birthday (one of the other REU students). He wanted red velvet cake. Red Velvet cake is red simply because of ridiculous quantities of food coloring. As in, we dumped two one ounce bottles of red food coloring into the cake batter (well, first just into the buttermilk)

With the bright red batter mixed, we dumped it into the one casserole dish we have that is almost the right dimensions for a cake pan. You can see the two empty food coloring boxes behind it. In the process of baking, the red got darker - but no less red. We frosted it with cream cheese frosting and I used the few drops of red food coloring that did not make it into the cake itself to dye a little of the frosting red for decoration:

It is a tasty cake (delicious and moist with a hint of chocolate), but in the future I am going to be inclined to replace the food coloring with water or more buttermilk unless there is a good reason to need a red (or for that matter any brightly colored) cake. There will be more cake baking this week. This time it will not involve the dumping in of food coloring...

Friday night several of us met one of the professors for dinner at Hickok's Bar and Grill (their website is rather entertaining). It is themed after the old west and in particular after the shootout between Wild Bill Hickok and Davis Tutt. In fact, they were going to be doing a reenactment of the shootout later that night, but we decided we did not want to wait around that long. I was overall amused. Oh, and they had tasty fried okra :-) .

It was determined that the REU group ought to visit Branson at some point. One of the professors discovered that Yakov Smirnoff (a Russian comedian) has decided that he wants a talk show and so was giving out free tickets to the taping of a pilot episode. When we arrived at the theater one of the ushers that was catching everyone at the door realized that we were a group of mainly college students and as a result pulled us aside and took us in early to pre-seat us near the front.

It was an interesting experience. I can't say that it made me have any desire to watch the talk show if it actually becomes one, but then again I would be amazed if there were a talk show that I would consider worth watching. He had interesting ideas about the importance of laughter in relationships. I was amazed at how disorganized it all seemed to be. I would have thought that they would have figured out things like how they were going to get the right camera angle to film objects on the table ahead of time...

I finished both Hardy's Tess of the D'Urbervilles and Dickens's Oliver Twist this week. I am greatly enjoying reading both authors, but I think I have a slight preference for Dickens. Dickens likes to have a narrator that is not afraid of breaking away from the story for a moment to directly address the reader and for me this seems very natural (when I am relating a story to my friends I am very prone to going off on side tangents). Dickens also uses amazing analogies, for instance, in Oliver Twist the narrator is justifying jumping back to the countryside when Oliver has found himself in quite a mess in London and starts out his explanation with:

It is the custom on the stage, in all good murderous melodramas, to present the tragic and the comic scenes, in as regular alternation, as the layers of red and white in a side of streaky bacon.

Down the River

2008-07-13T19:33:00.000-07:00

This week's baking adventure was the result of having two overripe bananas but neither a loaf pan nor muffin tins (or, for that matter, my banana bread recipe). I creamed half a stick of butter with a handful of sugar and then mixed in an egg and the two mashed bananas. I then mixed in a pinch of salt, a little baking soda, some cinnamon and enough flour to make a reasonable batter (thicker than I would usually make banana bread batter but not as thick as I usually make cookie dough). I divided the resulting batter into six blobs on a cookie sheet and baked it at what my oven calls 325. This was the result :

They were a little spongier than I was expecting, but were deemed a tasty success. :-)

Two weeks ago a group of us decided to make pancakes for Sunday brunch. Last week we made pancakes, scrambled eggs and home fries. This week the group was larger and we had pancakes, scrambled eggs, home fries, bacon, and cinnamon rolls. I wonder if it will continue to grow next week...

While we were cooking this morning we got a call from one of our professors asking if we wanted to go canoing. The response was a resounding "yes!", so we arranged to meet the professors after we had our giant brunch. We went out to Lake Springfield Park and spent about an hour and half canoing on the James River. It was gorgeous, but I unfortunately don't have any pictures since I figured taking my camera on the canoe might not be the most brilliant idea in the world.

A couple of other interesting incidents from this last week:

Scene 1: My self and a girl and guy I don't know happen to arrive back at the dorm at the same time and get on the elevator. I'm wearing my blueberry pi shirt.

girl: *looks at my shirt* Is that a Hebrew letter?
me: *smiles* It's actually the Greek letter pi.
girl: *giggles and looks really embarrassed*
guy: *to girl* Well, you're on a college campus...
me: ...

At this point the elevator thankfully reached the 8th floor and I got off and I managed to get to my room before breaking down laughing. That was a new one.
___________________
Scene 2: I've gone to the library to pick up a couple of books on Gröbner bases so that I can understand a math article I am supposed to be reading and went ahead and picked up Oliver Twist and Hardy's Return of the Native while I was there.

kid running the circulation desk: What's a Gröbner base?
me: *recalls that I am not at Mudd and thus cannot assume that people know linear algebra* Um, do you know any linear algebra.
him: Not really, but I have a lin al book!
me: Ok... Well, its sort of like a generalization of the kind of basis you will encounter in linear algebra...you can sort of think of it giving us a way to represent a generalization of numbers...
him: So it has something to do with area?
me: ... not quite.
______________

Since then I have been trying to think how I would convey the idea of a Gröbner basis without using at least linear algebra. I think I've figured out how to get the general idea across without using anything more complicated than polynomials:

The degree of a polynomial is the highest power of the variable, say x , that appears in the polynomial. For example:

5x^2+3x+2 has degree 2.

Now, suppose we wanted to think about the collection of all polynomials that have degree at most two. Any such polynomial can be uniquely written as

ax^2+bx+c

where a, b and c are allowed to be any number, but can not have any x's. So a=42 is fine, a=6x is not allowed. As a mathematician I would then say that { x^2, x ,1} is a basis for the collection of polynomials of degree at most two.

However, it is also possible to write any degree at most two polynomial uniquely as

dx^2+e(x+1)+f

where I again allow d,e and f to be any number. This means that {x^2, x+1, 1} is also a basis for the collection of polynomials of degree at most two.

For a relatively simple collection like the set of polynomials of degree 2, any of the many possible bases (the plural of basis is bases) we choose is going to behave nicely. When we start getting into more complicated sets of polynomials (allowing more variables, allowing the coefficients themselves to contain variables, etc) it is possible to find a set that serves as a basis , but does not behave as nicely as we would like. A Gröbner basis is a basis that also behaves nicely in other ways. They are named after the Austrian mathematician Wolfgang Gröbner and were first introduced in 1965.

What does math research look like?
Lots and lots of paper:

Oh, and we had a couple of spectacular sunsets this week:

Well, That Was Different...

2008-07-06T12:58:00.000-07:00

July 4

I made myself a really tasty breakfast by mixing some left over acorn squash with a handful of oatmeal, a little milk and some cinnamon and then curled up on the couch to read Great Expectations. Pip (the main character) managed to make me so mad that when one of our professors called suggesting that we should all go out to a movie, I actually decided to go. We went to the Moxie - a tiny independent cinema in downtown Springfield. The Fall is a really, really weird movie.

We had planned to go to the Thai restaurant near campus after the movie, but it turned out to be closed for the long weekend. The second Thai restaurant we tried was also closed. Happily, the third Thai place we tried was open. I was surprised to discover mango curry on the menu (I had never considered the idea of mango in curry) but it was delicious, if not deserving of the 5 star spiciness level they claimed...

After dinner, the professors pointed us in the direction of the fireworks show (they did not want to deal with the crowds). We were told that the fireworks were at the intersection of Division and 65. While driving down Division toward 65 we observed that there were a lot of people who were parked in various parking lots and set up there to watch the show. We parked in one of these lots and then decided to walk down Division to get closer. We briefly pondered how bad an idea it would be to walk across the overpass, but decided to go for it (the shoulders were really wide and there were plenty of other people crossing) and managed to get close enough that we could hear the music they were playing to go with the fireworks. Now, in my experience 4th of July fireworks displays are generally accompanied by a variety of patriotic music, but that was not quite what we found. For some reason the Springfield 4th of July fireworks show is organized by one of the local super churches and so we watched fireworks choreographed to the kind of music I would expect from a praise band at a "contemporary" church service. It was fine, but not quite what we were expecting. The fireworks were nice enough.

When the show was over we were rather amused that we were walking faster down Division than the traffic was moving until shortly before we made it back to where we had parked. Upon getting back to the dorm I had an amusing conversation with one of my suite mates:

Her: We should have ice cream!
Me: I'm more in the mood for cookies...
Her: (skeptically) Do we have cookies?
Me: We could.
I pause briefly to glance at the time, decide that 10:30 is not too late to make cookies, and pull a stick of butter out of the fridge.
Her: (excitedly and amazed) Are you going to make cookies?!
Me: Yes...

So we had oatmeal chocolate chip cookies - and managed not to let our oven burn them this time. I'm getting better at identifying how browned the bottoms of cookies are getting by smell...

July 5

The bank is right across the street from the mall and far enough from the dorm that we have not felt like walking. The suite mate who drives uses a different bank, but is a fan of the mall, so she took us to the bank and then we went to the mall. As a result I ended up spending multiple hours on the 4th of July weekend "going shopping" at the mall. Where by shopping I mean following the other girls from store to store and remembering why it is that it has been a while since I have bought anything other than pants at the mall... That said, I was somewhat impressed to discover that while it still contains nothing that I would wear, the junior department actually contains clothing that is not completely hideous. It was also nice to note that there is a pretty teal and purple combination that appears to be "in" this year.

We saw an interesting delivery truck as we were driving to the mall:

ps. I have discovered that my roommate's camera cord works with my camera, so you get pictures again :-)

Pie!

2008-06-29T17:48:00.000-07:00

Last Thursday after dinner a couple of us were sitting and chatting and someone suggested that ice cream would be delicious. It was observed that the nearest ice cream place that is open later than 5pm is about a 40 min walk away. After considering this for a little while, we decided to go anyway :-). It was a very pleasant walk and since it was just getting dark the fireflies (incidentally, I have realized that I alternate randomly between calling them fireflies and lightning bugs... I wonder where I picked up which name...) were all out. I had forgotten how pretty they are! It is really too bad that we don't have them at Mudd... The ice cream was tasty (I had German chocolate with pecans and coconut) . We took a different route back to the dorms - I have to admit that I find residential neighborhoods rather more interesting than walking past used car lot after used car lot, but it was still a reasonably nice walk.

It was observed that yesterday (6/28) could be considered 2pi day and as such was determined that there needed to be pie. We made three pies - apple, strawberry rhubarb, and cherry. Making pie crust when it is extremely humid is quite the adventure (made even more so by the fact that the closest thing we had to a rolling pin was a coffee mug...), but we managed. It was relatively late in the day when we finally got around to baking and one of our professors (Jorge) had invited us all over for lunch today( Sunday) so we decided to save the pies to take with us to lunch.

Jorge and his wife are from Peru, so lunch included ceviche, yucca root and Peruvian corn (in addition to some of the sorts of food you would be more likely to expect at a barbecue). I had heard of ceviche, but never had it, and from what I had heard I was rather skeptical - fish "cooked" by leaving it in lime juice overnight rather than using heat just did not sound terribly appealing, especially as I am not generally a huge fan of seafood. However, I try to make a point out of trying everything at least once - and today reminded me why. It was absolutely delicious, especially with the yucca!

The pies went over well. It is always interesting to note which pies get finished first... Today the strawberry rhubarb was finished and the apple was down to one piece before anyone took the cherry. I had never had strawberry rhubarb before but friends have been telling me for some time that I needed to learn to make it, and I had happened to notice rhubarb at the grocery store, so I figured I might as well try. I was somewhat surprised at how excited people got at the prospect of rhubarb pie - prior to going to college I had never even encountered the idea (or at least had not taken note of the idea)- but it really is quite good.

We then spent the afternoon playing Scattergories and chatting with the professors and their wives (or at least I did, some people watched the soccer Euro 2008 final game and some movie). Overall, it was a very pleasant afternoon. :-)

Math is going well. I'm working on planning out a series of "higher level math for the non-mathematician" posts that will work toward giving you an idea of what it is I am working on this summer.

I have finished Bleak House and will be starting in on Great Expectations (also by Dickens) next. It is really interesting to be reading several of Dickens's novels in succession. I am noticing recurring character types and situations between the novels that I almost certainly would not have noticed if the other novels we not so current in my mind.

"There are dark shadows on the earth, but its lights are stronger in the contrast."

2008-06-22T09:39:00.000-07:00

The above quote from the Pickwick Papers seems particularly apt given the rather dark clouds that have been coming and going all week (and that sent us to the basement Thursday with a tornado warning). I still appreciate actually having weather though :-)

Earlier this week I decided that we needed cookies. Since discovering in Budapest that I could make fine cookies without the bother of carefully measuring things out, I have almost exclusively been making "variations on approximation cookies." Now, given this style of baking I am never quite sure how long the cookies are going to take to bake and I am well aware of the fact that different ovens have different cooking times - but they usually take ~10-12 minutes. Less than 5 minutes after putting the first tray of cookies in the oven the apartment began to smell of popcorn (why the burning bottoms of cookies smells like popcorn I have yet to figure out)... They were definitely still edible, but their bottoms were rather blackened. I turned the oven down from "350" to "300" and gave it time to readjust the temperature before putting in the second tray - 12 minutes later the cookies were still slightly gooey. I took them out anyway and they /mostly/ set up nicely as they cooled and ended up being really soft. I think I need to experiment more with baking cookies longer at a lower temperature. I also need to remember to be really careful when dealing with the oven here...

Friday night a group of us from the REU walked into downtown Springfield (roughly the same distance that it is from Mudd to the Village) to find dinner. After wandering around for a while (which reminded me rather strongly of wandering up and down Raday in Budapest) we finally decided to eat at Trolleys and sat outside so that we had a view of the square. My chicken sandwich was good, though not spectacular, but it was served with sweet potato fries. I was slightly skeptical of the fries when I saw them on the menu (the time Mudd's dining hall tried to make them they seasoned them with salt and pepper, it really didn't work) but decided to try them anyway. I'm really glad I did - they were fantastic. I was through about half of them before I finally figured out that they had sprinkled them with cinnamon :-)

While we were eating dinner we discovered that there were local bands giving a free concert on the square later in the evening, so we ended up hanging out on the square in downtown Springfield listening to the music and people watching.

an old bearded guy sitting right up by the stage who was /really/ into all of the music regardless of the style
a group of three middle aged cowboys complete with cowboy hats and holsters with varied combinations of knives and guns
plenty of little kids climbing on the big geometric sculpture and playing in the fountain
a guy handing out glowsticks to any kid brave enough to go ask for one
a group of students who didn't seem to know how to get clothes that fit and liked baseball caps with spikes
and the list could go on and on

In short there was a rather large spectrum of people all gathered on the square.

When being less social and not doing math I have been doing a lot of reading. Having finished the Pickwick Papers (incidentally, Springfield has consecutive streets named Pickwick and Weller...), I started and have finished a collection of Dickens's Christmas writings and started Bleak House. I'm finding that I really enjoy Dickens. He manages to draw me into the story while maintaining the feeling that I am sitting with the narrator listening to him/her tell me the story. This latter impression is built by the small digressions and comments clearly directed at the reader that do not typically appear in novels. I was especially amused by Dickens's digression on idioms at the beginning of A Christmas Carol:

Old Marley was as dead as a door-nail.
Mind! I don't mean to say that I know, of my own knowledge, what there is particularly dead about a door-nail. I might have been inclined, myself, to regard a coffin-nail as the deadest piece of ironmongery in the trade. But the wisdom of our ancestors is in the simile; and my unhallowed hands shall not disturb it, or the Country's done for. You will therefore permit me to repeat, emphatically, that Marley was dead as a door-nail.

I have also been entertained by all of the allusions to various nursery rhymes in Bleak House and slightly surprised at how many of them I recognize before having them pointed out in the notes (and that I have found at least one that is not in the notes at all).

Now, it has been requested that I explain what exactly one does when doing "Math research." The simplest possible answer I can give is "math", but that is probably not a very satisfying answer. There are a few different kinds of broad things that count as math research (and this list is probably not exhaustive)

Start with a problem that someone else has come up with but that no one knows the answer to and try to find the answer.
Alternately, it is sometimes good to take a problem that we know the answer to and find a new way to get to the solution. This sort of thing is useful in mathematics since it can often give us a new way of looking at mathematical structures and lead to new insights.
There are some areas of math that have been around since ancient times that are fairly well explored and understood. There are also areas of math and mathematical objects where things are named after mathematicians who are still alive today. In these areas it is quite possible to find interesting questions that no one has thought to ask and to then try to answer them.

My particular research this summer falls into some combination of the first and last of the above categories. I spent a good bit of the first week here learning about the theory of Local Rings and looking at the kinds of questions that my adviser for the summer has been interested in. From this we have come up with a vague question for me to attack - and working toward that is producing smaller more manageable problems to understand and solve. In particular, I am trying to understand the relationship between the zero divisor graph of finite local rings and the zero divisor graph of their corresponding graded ring.

I have been thinking about how to explain the general idea of what I am doing without using such technical terms, but I'm not quite there yet. I shall continue working on that :-)

Greetings from Springfield, MO

2008-06-16T20:10:00.000-07:00

My parents and grandparents have complained that they knew what I was up to better when I was on the other side of the world than when I am just across the country and have thus requested that I revive this blog. I must admit that Springfield is somewhat less exciting a city than Budapest and I am not convinced that my life here is going to be quite as interesting to anyone still reading this as it was last fall, but I suppose I may as well give it a shot.

After a spring semester involving rather less math and rather more non-technical courses than I have grown accustomed to (but which was nevertheless enjoyable) I have taken off to Missouri to spend my summer doing math research. For those of you who understand the language of math, I am exploring the zero divisor graphs of local rings and in particular am analyzing the relationship between the zero divisor graph of a local ring and the corresponding graph of its associated graded ring. Other than math I have been doing quite a bit of reading and have finished the Pickwick Papers - next semester I am taking a class on Dickens and Hardy, so my summer reading is going to be largely centered around these two authors.

I'm not exactly sure what else to talk about, so I am going to turn to the weather. I remembered from back when we lived in Cape Girardeau that Missourians are fond of the saying "Don't like the weather? Wait a couple hours." but I had forgotten just how true it is. As an example, Sunday morning dawned bright and sunny. By noon we had light fluffy clouds and by mid afternoon we were in the midst of a thunderstorm that decided briefly to hail. Before sunset it had cleared up again...so that it could cloud over by morning and sprinkle on us as we walked from our dorm (Sunvilla, I'm on the 8th floor) to the math building. Since the forecast (hah) was predicting thunderstorms I packed a lunch. At noon I sat on a bench outside in the shade and watched the fluffy white clouds move across the bright blue sky. By 5pm it was completely overcast and threatening to rain again. The variability seems to be bothering some people, but I consider it a welcome change from the, shall we say, more stable climate of southern California.

(As a side note, I think spending a semester reading Shakespeare and the last week reading Dickens may have slightly altered my writing style...)

The Long Delayed Summary Post

2008-01-02T19:15:00.000-08:00

[Edit: this seems to think that it is being posted January 2...It is actually currently June 16]

I seem to have done a very good job of failing to give a concluding post. This has been due in large part to that fact that there is far too much that I should say but that I have figured out very little of what comprises said large amount. A full semester later I am still trying to sort out just how my semester abroad has affected me, but I am convinced that going abroad was definitely an amazing opportunity. It seems that I uploaded pictures in a previous attempt at writing a post to conclude my experience abroad, so despite the fact that I currently have no means of getting pictures off of my camera (and no access to the large number of pictures that I had previously extracted to my laptop) you still get pictures. :-)

Vienna was extremely cold - we found a thermometer in the park that informed us that it was -2 degrees Centigrade (and that was not taking into account the fact that it was somewhat windy). As we were looking at the thermometer a relatively old Austrian man came up to look at it and made some comment that was clearly about how cold it was. Without thinking we replied "igen!" (rather than "yes!") and then had to try to explain that no, we weren't actually Hungarian, we were actually American. This was made more difficult that Christina and I both momentarily seemed to have forgotten the word "yes"... Eventually we managed to explain that we were American and he though that it was "Wunderbar!" that Christina was from California. When we decided that we needed to get out of the cold for a bit we visited the Belvedere - a Baroque palace turned art museum that was amazingly gorgeous and contained really cool art. It made me glad that I had taken that art history class back the summer after my freshman year of high school so that I could recognize some of the artists...

Once the sun had set (so it was even colder) we went back out to see the lights and visit the Christmas markets. I thought Budapest had gone all out with the lights...I was wrong.

One of the stands at the Christmas market had chocolate covered just about everything for sale. We shared one of the skewers of chocolate covered strawberries. They were delicious :-)

And we will finish with a picture of Budapest that I took from the castle the morning I left...

All Things Come to an End Eventually

2007-12-18T00:21:00.000-08:00

It is currently Tuesday. I took my last final of the semester this morning. Christina and Tom and I are most likely going to take a day trip to Vienna tomorrow. Thursday is the BSM farewell party. On Friday I fly home. As usual with this sort of thing, none of it seems real. It still has not completely sunk in that within 3 days I will be back in the United States. The next few days are going to be crazy. This is most likely the last post from Budapest, but I will update at least once after I get back to the US.

I've been working on Christmas shopping, so I have spent a lot of time bouncing between the Christmas markets that have sprung up at nearly every metro stop looking for gifts for everyone. The markets can be a bit overwhelming at times because of the sheer number of people, but they also have a wonderfully happy Christmasy atmosphere and are certainly much more fun than shopping in any American mall.

Saturday it snowed - not a lot, but enough to coat the hill behind the apartment in a blanket of white. I was inside most of the time that the snow was falling. My host mom and I spent all morning cooking and then had a HUGE lunch with her two daughters and son-in-law and two grandsons and Jessie. We then spent most of the afternoon chatting and snacking on some of the extra food. After everyone had left and we got things reasonably cleaned up, I met up with people to go look at some of the Christmas lights that are all over the city. I tried to take pictures, but they are the sort of thing that it is impossible to really capture.

Az Allatkert!

2007-12-10T02:08:00.000-08:00

Csütörtökön, Christina en is az állatkert városligetben mentek. Sok, sok állat az allatkertben.

It was very interesting to compare the Hungarian and English names of the animals. For example, the nilius víziló, which would literally translate as the "water horse of the Nile" is the hippo. The mosomedve, literally "washing bear" is the raccoon. The vörös macskamedve, literally "red cat-bear", is the red panda.

In addition, they also had rhinos (somewhat slower than the ones Mudd had me used to)

and a super cute kisoroszlán

There were turkeys roaming around instead of peacocks

a pretty wolf

pelikanok that were trying to eat fish too big to fit in their bills

And penguins which only eat sea fish

On Friday we tracked down the honey festival. It which was much smaller than it was made out to be and thus slightly disappointing, but it was still nice. Afterwards we went to a slightly nicer restaurant than usual since we wanted to try something new and it looked interesting. As we walked, the greeter asked us, in Hungarian, if we wanted the smoking or non-smoking section. I responded in Hungarian without really thinking about it and only afterwards realized that I had understood and responded without consciously translating into English and back.

On Saturday, Jessie organized a "talent-no talent" show which was held at Christina's apartment since hers is one of the few with a piano (though it is painfully out of tune). My talent was making cookies without measuring anything. I mixed up several stages of dough for oatmeal chocolate chunk cookies and held something like a cooking show on fast forward. It was fun and everyone got to eat cookies. The whole show was quite entertaining.

Sunday largely ended up being a HW day. In the evening I went to the California Coffee Company for the first time to find the other people that were working on Geometric Graph Theory (apparently it is a favorite place for some people to work). It was ridiculously American - and thus felt very strange. Coming back to America and realizing just how used to living in Hungary I have become and having to re-acclimate myself to living in the US is going to be very odd...

A Karácsonyi Fa

2007-12-03T01:55:00.000-08:00

First a brief note. Sunset is now before 4 pm. On Monday, Tuesday and Wednesday I get out of class around 4:30. On Thursday and Friday I get out at 10 and noon respectively. Given that there is no daylight after class on the first half of the week, I figure it is good for me to get outside after class on Thursday and Friday. This means that I am not spending as much time in the computer lab on those days and is the cause of there not being end of the week math posts. The math is still fun and exciting :-)

On Thursday, Christina and I met up with Blair and the three of us went off to explore the Christmas Market. The atmosphere of the market is amazing. There are stands selling various wooden crafts, and all sort of fabric crafts and several kinds of traditional Hungarian food. There is even a stand where a blacksmith is set up and with several candle holders and cute dragonfly corkscrews for sale. In addition, one of the buildings bordering the square where the market is set up has its windows set up as an Advent Calendar. Oh, and naturally there is a giant Karácsonyi fa - a Christmas tree.

On Friday we celebrated Christina's birthday (it was actually Sunday, but there were some people traveling this weekend. I made and decorated a chocolate cake and we had mulled wine and played our homemade version of apples to apples. It was great fun.

Saturday I spent the morning at home learning to make paprikas krumpli (paprika potatoes) - which is very tasty, but I suspect is going to be tricky to get right at home where I don't have a bowl where I save the oil from frying the chicken for csirke paprikas... In the evening I took the Putnam. It was strange to be starting it at sunset and to finish at midnight. I think I prefer having it in the morning.

After church on Sunday, Christina and I went to the flea market (which was highly entertaining, but there was way to much stuff for me to actually try to decide to buy anything) and then to Tesco to obtain Christmas goodies. Her apartment now has a decorated Christmas tree, an advent wreath and a poinsettia. It feels like Christmas :-)

A Musical Weekend

2007-11-28T02:32:00.001-08:00

Friday afternoon, Christina, Kyle, Tom and I went out to Gellert Hill to watch the sunset (at 4pm). On the way up the hill we stopped at the giant slides! It had been so long since I have been on slides...These are the sorts of slides that would probably be considered safety hazards in the US, but they are great. I even saw a grandpa going down one of the slides with his grandson.

It was cold, but nice out. The sunset was pretty, and the full moon was rising just as the sun was setting. Overall, it made for a very pleasant evening.

Saturday I stayed home in the morning and one of my host mom's daughters came over for lunch. I still have not quite gotten used to the Budapesti notion of lunch... We started with soup, then had homemade french fries and some sort of fried meat patties (I think they were made from ground turkey mixed with spices, egg, and bread crumbs) and after that my host mom brought out a large pot of spaghetti. Needless to say, I was stuffed. In the evening a group of 7 of us gathered at Christina's to make American style pancakes for dinner and then to go to a piano concert. I really enjoyed the concert. Making time to just go listen to music is a very good thing and the Liszt Ferenc Zeneakadémia where the concert was held is absolutely gorgeous.

Sunday I went to church in the morning (and recognized all but one of the tunes for the hymns!), worked on HW with Christina in the afternoon, went to the organ concert at the Lutheran church in the evening, and then met up with Kyle to go to the pancake place for dinner (yes, pancakes two nights in a row, but they were very different kinds of pancakes).

The weather has decided that it is going to be clear and cold for a while. Oh, and windy - quite windy (20-40 km/hr windy). I am glad my coat is good a blocking wind. The wind chill factor has been keeping the temperature below 0 C and Monday I woke up to find the hill behind my apartment dusted with snow. It is exciting. I love having actual weather :-)

Happy Thanksgiving!

2007-11-23T03:55:00.000-08:00

This marks the third year that I have not made it home for Thanksgiving. My freshman and sophomore years I had Thanksgiving at my dorm back at Mudd with the (23 my frosh year, 40 or so my sophomore year) of my friends that were also on campus. Last year I managed to put myself in charge of the production. Having successfully pulled off organizing Thanksgiving for 40 last year I decided that it would be a good idea to take charge of making sure it happened here in Budapest. As it turns out, organizing Thanksgiving abroad is a somewhat larger project than organizing Thanksgiving at Mudd for 2 main reasons:

1) Here we are spread all over the city rather instead of being concentrated in a small area.

2) Foods that count as traditional in America and thus show up in larger than usual quantities near Thanksgiving are not necessarily foods that are common in Magyarorszag.

The first one is not that big of a deal, it just requires a bit more logistical planning. The second...
Sweet Potatoes I love sweet potatoes. They are delicious baked and my mom's sweet potato casserole is one of my favorite foods at Thanksgiving. Hungary on the other hand is not quite so familiar with them. I had been watching for them in the various different grocery stores and at the fruit and vegetable stands and even Tesco (the closest equivalent to Walmart here) for a while and they seemed to be completely non-existent. On Monday I do not have class until noon, so in the morning Christina and I headed to the giant market. The first floor of the market consists of a ridiculous number of fruit and vegetable stands along the sides with various meat stands and baked goods stands in the center. We figured that if there were going to be sweet potatoes anywhere they would be at the market. Sure enough, at the two stands in the far back corner of the market there were unlabeled piles of what looked like sweet potatoes. One of the stand owners knew enough English that with my limited knowledge of Hungarian I was able to confirm that they were in fact sweet potatoes. This worked out fine, the process of finding them was just rather time consuming.

Cranberry Sauce
Another very traditional Thanksgiving food. At Mudd we usually end up with a homemade cranberry sauce and some sort of cranberry relish and possibly also cranberry sauce from a can. When we went to the market I was watching for cranberries, but, unlike the sweet potatoes, we did not have any luck there. Charlie and I went to Tesco to hunt later, thinking that perhaps it was just hiding somewhere strange, but no. The only mention of cranberries we found in the whole store were dried cranberries in a box of granola - not exactly useful for concocting cranberry sauce. We eventually gave up on trying to locate cranberries.

Pecans
This one was especially frustrating since Hungarians seem to like nuts. Walnuts, hazelnuts, peanuts, pistachios and almonds are all very easy to find. Things like cashews and macadamia nuts are rarer but can still be found with minimal searching. Pecans though... nincs. Rumor has it that they can occasionally be found in small quantities at exotic markets, but I did not have any luck. Thus pecan pie and pecan topping on sweet potatoes and such things were out of the question.

Pumpkin Pie
Tesco had pumpkins back about a week prior to Halloween. These days, there are no pumpkins anywhere (this was another thing I had been watching for at the market). There is what seems to be butter nut squash at every small fruit stand and a different winter squash in all of the grocery stores (it intrigues me, none of the grocery stores have the butternut and none of the stands have the other kind). The flesh of the squash in the grocery stores has a similar texture to pumpkin, so I got a chunk of it and decided to see what happened if I turned it into a pie. This involved more improvising since evaporated milk also seems to be hard to come by here - or at least I have been unable to recognize it if does exist. Despite all of the improvising, it came out great, so Christina and Alison looked for another piece of the squash when they went to the store on Thanksgiving morning. Even though they were at the same place I had bought the squash the day before, it seemed to have vanished. Thus we ended up with a single 'pumpkin' pie... such is life.

Despite all of this, the whole production went off amazingly.

As per usual, I made crescent rolls - about 100 of them. I don't know if it was the European flour, or the fresh eggs or if I just managed to do something exactly right, but they came out extremely light and fluffy. I was very pleased.

While I was working on the rolls and baking the pumpkin pie, Chelsey made deviled eggs. When we were done cooking, this meant that we now had 100 rolls, a pie and several plates of deviled eggs that we had to get from Christina's apartment to Kevin and David's apartment (where we were all meeting to actually have dinner). We decided that it would be less awkward to just walk than to try to take it on the metro, so we made quite the procession as we paraded down the sidewalk of one of the largest streets in Budapest carrying a tub-o-rolls, a pie, several plates of deviled eggs and a pot of butternut squash (Kyle had joined us by that point). I was rather amused by all of the double takes we got from the Budapesti that we passed on the way :-)

Dinner ended up starting around 4:30 and, despite the fact that the cranberry sauce was missing, it was a very impressive spread. Even after everyone had been through and taken heaping plates of food there was a LOT of food left on the tables.

All 40 or so of the people who showed up ended up stuffed and happy, so the meal was a resounding success :-)

I hope everyone else had an equally wonderful Thanksgiving!

2007-11-21T09:02:00.000-08:00

I'm doing well, but life is rather busy at the moment. Finding everything for Thanksgiving in Budapest is quite the project - Pecans seem to be non-existant as are pumpkin and cranberries. And things like evaporated milk seem to be unknown here. It is going to be a very improv Thanksgiving dinner :-). I will give a more detailed update after Thanksgiving when I am less busy.

Happy Thanksgiving!

How to approach a math problem...

2007-11-19T02:07:00.002-08:00

Mathy post today. I will try to get a non-mathy one up tomorrow :-)

In Conjecture and Proof:

* Define something that prevents.

* Consider something smallest.

* Consider something largest.

* Find a clever coloring.

* Try using a Hamel basis.

* Try following paths.

* Count things.

In Geometric Graph Theory:

* Turn the edges into rubber bands.

* Triangulate.

* Draw circles around *everything*.

* Apply Euler’s formula.

* Pass a line across it.

* Color the edges red and blue and find the vertex where the red edges are together

* Use physics.

In Set Theory:

* Use the sandwich theorem.

* Use ridiculous seeming approximations.

* Look at the cardinality of the sets.

* Order the sets and compare ordinals.

* Consider a representative set.

* Draw the diagrams.

* Remember that everything is a set - unless it isn’t.

In Topics in Geometry:

* Try stringing definitions together.

* Try looking at equivalent definitions.

* Play with the geometry, convert to algebra, play with the algebra, convert back to geometry, repeat.

* Look for eigenvectors/values.

* Draw pictures.

* Use symmetry.

* Look at subgroups.

Hó hó hó!

2007-11-12T00:51:00.001-08:00

I’ve been learning about the wonders of tejfől. I did not feel like doing HW Thursday evening and my next assignment was not due until Monday, so I decided to experiment with cooking instead. My goal: to try actually making some of the delicious Hungarian food I have been watching my host mother make. I went to Kaiser (one of the local grocery stores) and obtained two large tubs of tejfől (sour cream), a small box of tejszin (really thick heavy cream) and a carton of tojas (eggs). I then obtained ket hagyma, ket alma és ket körte (two each of onions, apples and pears). I decided to start the project with nokedli.

When I asked my host mom what was in the nokedli dough she responded: ket tojas, ket deci viz, fel kilo liszt. Now, when we were making the nokedli it was clear that there was a lot more dough than would come from those proportions (and we had about 3 times as much nokedi as I was hoping to make) so I decided to just hope that she had given me a reasonable sized recipe. I beat the eggs with the water and then attempted to add something close to ½ kilo of flour (my host mom never measures anything, so I figured the exact amounts were not crucial). This resulted in a dough that resembled the dough we had used before, I figured we were off to a good start. I got a pot of water boiling, dug out the cheese grater and found a big metal spoon to force the dough through the grater with. The first blob of dough that I blopped onto the grater was difficult to force through and was resulting in very small noodle/dumplings, so I added a little more water to the dough and this corrected the problem. The only other issue was the grater. My host mom’s grater seems like it was made for making nokedli - the back has raised sides to keep the dough from falling off the grater and otherwise has no unneccesary bumps or grooves. Christina’s grater on the other hand has the raised sides, but also lots of little groves that like to catch the dough and keep it from going through the holes. I am going to see if I can find a proper nokedli grater to bring back to the States with me. Nokedli is a fun alternative to pasta and rice and I rather like the texture.

However, like noodles, nokedli is somewhat bland plain, so my next task was to create something to serve over it. While I was working on the nokedli I had a separate pot on the back burner boiling eggs (I was rather amused that the one thing I had to look up online for this meal of things I had never made on my own before was how long to boil eggs). Cartons come with 10 eggs, and I used two for the nokedli, so I boiled 8. While Christina was pealing the eggs, I diced and sauted the onions. I dumped on of the tubs of tejföl into a bowl and mixed in a largish glob of the tejszin, some flour (for thickening purposes, roughly the same amount I would have used if I had been making the kind of cream sauce I was used to) and a liberal portion of paprika (akin to the quanity of chili powder I might use when making chili). I then added two sour cream tubs worth of water to the pot with the onions and mixed in the cream mixture. While this was heating up, I chopped the eggs and added them to the mix. From this point it just needed to be stirred periodically to keep it from sticking and it came out great. It was really far easier than trying to get a normal cream sauce to the right consistency.

Now, this probably would have been enough for dinner, but I had been wanting to try my hand at fruit soup for a while now. I have not managed to be home when my host mom was making fruit soup yet, but I have asked her about it and as far as I could tell it consisted of boiling fruit until it is mushy and then adding – naturally – tejföl és tejszin és picsit cukor (a little sugar) és fahej és szegfűszeg (cinnamon and cloves). As such, we pealed and chopped the apples and pears and put them in a pot with some water to boil them. A traditional Hungarian meal would start with the fruit soup, but it made more sense to make it last given the selection of pots Christina’s apartment is stocked with (I used all of the large ones twice), so we let them boil while we ate the nokedli and tojas paprikas (I have no idea what it is really called, but that follows the pattern of csirke paprikas so I assume it works as a reasonable name). When the fruit had gotten soft, I scooped some of it out into a bowl, mashed it, and added it back to the pot. I then mixed half of the second tub of tejföl with another glob of the tejszin, a little flour, some sugar, cinnamon and cloves and then dumped it into the pot of fruit. Once I got it all blended together, I took it out and set it on the balcony to get it to cool off (using the balcony as a fridge seems to be common practice here, and when it is at least as cold outside as in the fridge it really makes sense. The concoction was delicious. It was not quite like any fruit soup I have had here, but also was not that different, more of a variation on a theme than something different.

Overall, I deem the whole project an overwhelming success and a much more productive use of a Thursday night than getting ahead on HW. Also, I suspect that sour cream may become a kitchen staple.

Friday was not terribly exciting and this is going to be quite long as it is, so I will just jump to Saturday.

Saturday morning I went over to Christina’s apartment. It felt chillier than it had been being, certainly colder than the 10 C Christina had seen on a sign when she had gone running earlier that morning. We looked up the weather report on line and found that it was 6 C feels like 2 C – that’s quite a wind chill factor. Never mind the cold, it was actually sunny. Or rather, it was about half sunny. There was a distinct line in the sky between blue and some potentially nasty looking grey clouds. Mandi came over to theoretically work on HW, but none of us could focus, so we decided that it was a good day to go up to the top of St. Stephens Basilica to see the view of the city. We collected Kyle on the way and then got to see the results of having both rainy and sunny weather at the same time – a rainbow! Not a very bright one, but still:

The view of the city from the top of the basilica was quite impressive:

After that we went back to Christina’s apartment. Christina and Mandi worked on their combinatorics and I made dinner . Every time I have gone to the zöldseg-gyümölcs recently they have had big squash and I had been wanting to try it, so I finally decided to just get one. I baked it like I would an acorn or butternut squash and then decided that it smelled like it would go really well with nutmeg, cinnamon and cloves, so I scraped it out of the skin and mixed it with some of the leftover tejfől and tejszin, a little bit of brown sugar and a liberal sprinkling of each of the above mentioned spices. It was quite tasty. I served it as a side with the left over tojas paprikas sauce and rice (since we had basically eaten up the nokedli).

After dinner the four of us (Kyle had shown up for dinner) went to a tanchaz – a Hungarian folk dance thing similar in spirit to a contra dance as Kyle and Mandi are in a class that had encouraged them to go. It was quite fun, though also exceedingly exhausting. The Hungarians and seemed to be slightly amused at the presence of American students, but were none the less very helpful and happy to dance with us. It’s really too bad that Mudd does not have any sort of folk dance class. That would be a PE class I could enjoy.

Sunday morning Christina and I went to church. The service made me very happy as I actually knew 3 of the hymns. But anyway, after the service we had tea and sweets as usual and stood around chatting with the other members of congregation. Christina mentioned that she would really like to see it snow and asked what the chances of it snowing while we were still here were. The general consensus was that the forecast is expecting this to be a mild winter and there is not likely to be much snow, if any. We then go back to Christina's apartment to eat leftovers for lunch. After lunch I went out on their balcony to check my email (it is the only place they get wireless) and it started to rain. I went back inside and started helping Christina clean up in the kitchen, watching the rain out the kitchen window and not really looking forward to walking to the busz stop at Deák in the rain. Then the rain started falling funny. At first I just attributed it to the fact that wind does strange things in their courtyard sometimes, and it quickly looked like normal rain again, so I shrugged it off. Pretty soon it had changed back to falling funny...it really did not look like rain, it really looked more like...snow! Christina and Alison and I all crowded at the window and confirmed to each other that, yes, it really was snowing! Within a minute it had changed back to rain again. I figured I should head back to my apartment to get my HW done, so I put on my shoes and collected my jacket. By the time I was ready to leave, it had once again been transformed to snow. Christina and I glanced at each other and exchanged looks that clearly said, "Do you think there is any chance...?" and shook our heads. There was no way it was going to stick. Everything was wet from the earlier rain and it couldn't even make up its mind to stay snow. I walked to the busz stop at Deák, amused by the bewildered looks I saw on the faces of the Hungarians I passed (and the huge grins that little kids had), and sat on the busz watching it snow as I waited the 5 or so minutes before it was time for it to leave.

Mother nature seemed to have decided that yes, it really was going to snow today, not rain. By I got to my stop the benches and the cars parked on the side of the road had started to accumulate snow (as was my jacket and hair).

I went up to my apartment, and by the time I had finished my geometry (which did not take long) the hill behind the house was covered in snow. I realized that it was also starting to accumulate on the street level when a snowball came flying through the grates in the window of the little balcony room and smashed into my window (I then looked out and down to see a group of kids excitedly packing snowballs and throwing them at each other and the building).

Around 4 I decided to take a break from my homework to go see just how snowy it had gotten outside and to see about getting some pictures of snow covered Budapest. Judging by the trees and castle walls we had gotten at least an inch of snow by that point.

Sometime during the night it had switched from hó back to eső, from snow back to rain, so by morning most of the snow had melted. However, I came across this on my way to school

Hó hó hó!

Suppose you have an infinite checkerboard...

2007-11-09T07:42:00.000-08:00

Math can sometimes be frustrating, it is true. It will sometime take hours of playing with equations and theorems and such to crack through and understand how to solve a problem. Occasionally when you solve it the response is "oh, that was dumb" - those problems are annoying. Sometimes the response is "huh, thats cute" or "OH!, thats clever." - those problems are satisfying to solve. Sometimes the response is "Wow...that's...impressive..." which usually happens when the solution really is quite long, complex and/or involved - those problems leave you with a sense of accomplishment. Occasionally you find a particularly beautiful solution to a problem and the response is one of pure joy and excitement. The Conjecture and Proof club problem was one of that last category this week. It was amazing. The only problem was that I was then on such a math high that it was impossible for me to go to sleep at a reasonable hour (though I was impressively productive during that time).

Geometric Graph Theory continues to make me thankful for the Core physics required at Mudd. One of our HW problems on the last set was basically a simple mechanics problem, but really messy if you were not comfortable dealing with balancing torques and forces. We are currently playing with double circuit embeddings which result in chalkboard pictures in at least 4 colors of chalk where it is still hard to keep track of what everything is. It is a great deal of fun.

We have started projective geometry in the topics in Geometry class. It is fun to play with things that can't quite be properly visualized. It was also very interesting to see two different models - one completely algebraic in nature and the other based on adding 'ideal' points to regular Euclidean space (where 'normal' high school geometry occurs). On the surface they look completely different, but we showed that they really are the same. During the 'office hour' portion of class today I got him to give us the formal definition of homeomorphic- a notion that I vaguely understood just from the contexts where I had seen it used but which I had never seen defined. It was quite interesting.

I love set theory. The axiom of choice is very strange. It seems intuitive that it should work and there are things that are equivalent that seem very natural, but it leads to some very strange things. The idea that it is possible to put an ordering on the real numbers so that there is a 'smallest' one and any subset has a 'smallest' element seems very counter intuitive (granted, such an ordering is impossible to describe) .

Food!

2007-11-07T02:32:00.000-08:00

Sorry about the long absence. We had last Thursday and Friday off, so my internet access was very limited over the weekend and then coming back from a long weekend seems to result in life being extra busy!

Thursday was very low key. I spent most of the day alone in the apartment getting little things I had been meaning to do done. Having time completely alone occasionally is really nice, it seems to not happen often. In the evening I went over to a Kyle's apartment (Christina was out of town all weekend) to make dinner and to just hang out and chat.

On Friday, Zoli and Adam, my host mother's grandsons, and her daughter Erika came over. This meant that my host mother had to make a big lunch for everyone, so we spent the morning cooking. The most exciting part was making nokedli - dumpling/noodle things which are formed by running the batter through a cheese grater into a pot of boiling water. We served the nokedli with a sour cream based sauce with boiled eggs.
Here is a picture of me with my host mom and Zoli :-)

On Saturday morning my host mom was cooking all out again to have food to take over to Zoli's house since EVERYONE was coming over to celebrate Zoli's birthday. I learned how Hungarians fry meat and helped make a husi paprikas (meat in a paprika/sour cream sauce) topping for the nokedli. She then got all dressed up and posed for me with one of her Christmas cacti:

When she left, I went over to Kyle's and since it was a beautiful day we headed to Nepliget (a park) to go for a walk. It is fall here - I'm really enjoying actually having seasons.
Pictures from the park:

Sunday morning I finally decided to go to choir practice before the service (I've been toying with the idea and just not getting to it for a while). The choir was desperately in need of altos, so I agreed to attempt to sing alto. It was interesting. The alto line didn't go to low, so it was ok in that regard and given that I had only seen it that morning and was basically carrying it next to a group of very strong sopranos I think it went quite well. I definitely prefer singing higher though.

When I got back from church, Zoli, Adam and their dad were over - as were one of my host mother's nephews and his wife and three little boys. My host mother had gone all out with lunch. It started with cherry soup (fruit soup here is amazing) and then there was fried meat and potatoes, and nokedli with the meat sauce as the main course and a sweet custardy soup with meringue floating in it called madartej (literally bird's milk). All of it was quite tasty. The afternoon was interesting - having 5 little boys running around is loud and exhausting. It was interesting though, and good for my Hungarian.

The little things

2007-10-27T03:48:00.001-07:00

First a little bit of background:
* Apartment buildings in Budapest tend to be nestled in the city, so the door into an apartment building is frequently right next to the door to a shop.

* Locks here are exciting. Sometimes you have to turn the key around 3 full turns to get the lock to open. Sometimes you have to do a half turn in the wrong direction and then a 1 and a 1/2 turn in the right direction. Sometimes you have to have the door handle in a certain position when you put the key in and a different position when you turn the key. Sometimes the door to apartment buildings is so heavy that you can have it unlocked and not realize it if you are not expecting it.

Now for the first story:

One night last week Christina, Kyle, Tom and I went to dinner at the Hummus Bar (a small restaurant with really tasty falafel) . After dinner, we walked back to Christina's apartment and along the way came upon an interesting situation. An old man in a wheel chair was sitting in the middle of the sidewalk and a lady was standing in the door of a shop just staring at him. As we approached he greeted us with "Szép estét kivánok!" and proceded to rattle off a long string of Hungarian that was clearly asking us something. We stopped and tried to explain that we did not understand. The lady standing in the shop door called out to him that we were not Hungarians and I think she was telling him to just not bother, but he was not deterred. He proceeded to continue speaking in Hungarian and gesturing wildly until we understood that he was in front of his apartment, but there was a step that he could not get up, so he could not get back in. Christina and I took his key and figured out how to coax the door to the apartment building open while Kyle and Tom got him up the step. Being able to be helpful makes me happy :-).

***
Friday night, as usual, we decided to go out somewhere for dinner. Christina threw each of us a guidebook and we thumbed through them looking for restaurants. We eventually decided on an Italian place in Buda that was described as being popular with the local college students. The menu was in Italian, Hungarian and English (by the way, I love the attempts at English translations of menu items, it frequently results in such dishes as "crashed potatoes"), but the staff was clearly not as fluent in English as the waiters on Ráday street. We were able to successfully order and communicate, but it was clearly slightly frustrating on both sides. (I had a cold raspberry soup and lasagne - a huge slice served in a ceramic bowl that it appeared to have been baked in. It was amazing). After dinner I caught the man who did not appear to be a waiter, but seemed to be there to wander around the tables and make sure everyone was happy and told him "Kösönöm, nagyon finom volt!", ie "Thank you, it was delicious" and he responded with a huge grin. Even though I am far from fluent in Hungarian, I am glad I have picked up enough to be able to be polite. :-)

"As I told you, I have no idea how to prove theorems, so we will suppose it is not true and hope for the best." - Professor Komjáth

2007-10-26T03:55:00.000-07:00

Midterms have started!

The first was geometric graph theory. Now leading up to this midterm, we all agreed that we had no idea what to expect. After the midterm, we all agreed that it was definitely not what we were expecting, despite the fact that we did not know what to expect. The problems were actually much easier than I was expecting, but because of this it kind of threw me for a loop and had me constantly second guessing myself. Combined with the fact that I feel like I am good at graph theory mostly because I am persistent, not because I see what to do quickly and that writing things up well and quickly is challenging for me, I'm really not sure how I did on it. I'm not really that worried about it, I just feel like I ought to have been able to do better (of course, I still don't have it back yet, so we will see).

Yesterday was the Conjecture and Proof midterm. I'm quite happy with how it went. The problems were fun and the sort of clever that I am coming to expect from this class.

This morning I had the Topics in Geometry midterm. It was another one that really had more questions that I would say a test with its length of time should have, but it also had questions that honestly did have rather short, easy to write up answers, so I am fairly confident about it :-). Class periods here are two hours. We had the test for the first hour and then an introduction to Spherical Geometry for the second half. Since next Thursday is a holiday, they are giving us next Friday off, which means that tomorrow is next Friday. This means that I have two hours of Geometry tomorrow and then another two on Monday. It should be exciting, expecially since we are going to try to cover everything we are doing for spherical by the end of class on Monday!

Set Theory has not had a midterm yet. Set Theory has not scheduled a midterm yet. I have no idea whether Set Theory will have a midterm or not. The class amuses me endlessly. Theoretically, we are supposed to be meeting every Wednesday. We had class on October 3, and then not again until this past Wed, but we also met on Friday this week. On Wednesday, Professor Komjáth started class with "As usual, I will not be here next week. I think we will have class this Friday instead" (the class was originally a 2 days a week class, but got switched to 1 when there were only 4 of us - Friday was originally a normal class day). Thus we had set theory twice this past week, and Bridget and I are planning to meet on Sunday afternoon to go over the handouts he passed out today and make cookies. It should be fun. Aside from the fact that the class has no schedule, Professor Komjáth has a wonderful subtle sense of humor and the material is fun. We spent the last two class periods on Ordinals. We have defined what it means to "add one" to an ordinal (which is defined as the order type of a well ordered set) , proved that the class of all ordinals is not a set, and introduced the concepts of transfinite induction and recursion. Oh, and once we had already done all sorts of stuff with ordinals he decided that we should actually give a formal set theoretic representation of the ordinals... As he put it "I never said my classes are non-contradictory."

Jó reggelt kivánok

2007-10-24T00:51:00.000-07:00

First, a few pictures from the Hungarian dinner party since I never managed to get them added to the relevant post…

Now, for the new stuff :-).

I’m living in a city that actually has seasons. This makes me far more excited than it really has any right to. The leaves have been turning colors, the weather has taken a definite turn towards the colder, and there are people selling roasted chestnuts (which are quite tasty incidentally) and hot wine from carts in the parks. The obvious correct response to this is to spend more time walking around outside enjoying the existence of autumn. On Thursday we went for a walk in Nepliget – a beautiful park that manages to forget that it is in the middle of a city. Here are some pictures from that walk:

On Friday, we decided to go for a walk in the evening before dinner (we had had a late lunch), and since it has been getting dark early, we decided that it would be fun to climb Gellért Hegy (a large hill in Buda) to see the view of the city at night. We walked to Deák Tér, got a couple pictures of the sunset and rode the blue metro line to Kalvin Tér. From there we walked across Szabadság Híd (Liberty Bridge) and then up the side of Gellért we had not previously climbed. We have concluded that some afternoon we need to pack a picnic dinner and take blankets and watch the sunset from the top of the hill and stop to play on the giant slide park on the way up (it was a bit dark when we found the slides on Friday). At any rate, the view from the hill is just as stunning at night as it is during the day.

When we decided we were ready for dinner, we walked back to Kalvin Tér in Pest, wandered down Ráday utca and picked a café for dinner. I had hideg gyümöcs leves (cold fruit soup, in this case strawberry) and gulyas with fresh bread. It was wonderful. We have been cooking dinner most nights, but Friday is our night for going out to dinner and most every week we pick some restraunt or cafe on Ráday. With the exception of when we go to the Pink Cadillac (an amazing pizza place), I usually opt for something that is traditional Hungarian.

Saturday, Christina and I headed to Keleti train station to catch the train to Romania to visit my friend Roxana (a MathCamper from Baia Mare, a city in the Transylvania region of Romania). I love the little tunes that the trains play as they are arriving and leaving from the station – they all sound so happy. We took the train from Budapest to Satu Mare and Roxana’s dad picked us up there. When we got to Roxana’s flat, they had bread, a tray with meat and cheese and delicious eggplant salad waiting for us. On Sunday we had breakfast and then went to the village museum with Roxana. It was a really cool outdoor museum with lots of traditional Romanian houses from different time periods. After the museum we stopped at Roxana’s favorite ice cream place (ice cream is good even when it is cold out) and had big bowls of delicious vanilla/chocolate swirl ice cream with huge mounds of amazing fresh whipped cream topped with fudge sauce. It was heavenly. From the ice cream place we went to the mineralogy museum. Baia Mare is Romanian for “large mine” and the region is known for its gold mines and mining in general. The museum had lots of really shiny crystal formations, most of which had come from mines in the region around Baia Mare. I really enjoyed it. Around 2 we went back to her flat for Sunday dinner. The meal started out with the meat and cheese tray, bread, eggplant salad, a plate of tomatoes and crackers. Roxana warned us not to eat too much as there was more food coming – I don’t think either Christina or I realized just how much more food was coming. The next course was soup – on a cold day there are few things tastier than soup. Then her mom brought out a huge platter piled high with mashed potatoes and topped with fried chicken and roast beef (having roast beef and mashed potatoes was exciting, I have not come across anything resembling roast beef in Hungary). Oh, and a plate of what are best described in English as cheese crepes. All of it was wonderfully delicious. After all of this her mom brought out a cake. Her dad runs some sort of delivery service that includes things for bakeries, so they get all sort of free deserts. The cake had two layers of chocolate cake with a rich cream frosting between them and then it was topped with caramel and chocolate decorations. The whole concoction was tasty, but rich enough that I don’t think I could have eaten a larger slice than I was served (and I usually have a very high tolerance for rich foods.

After dinner (which had taken at least two hours) we hung out with Roxana and her family. We played backgammon with her dad and then she and her dad taught us a fun Romanian card game. We played it twice, first with Roxana and her dad and then with her and her brother. Her brother was very entertaining. He knows just enough English slang to be really funny when he tries to use it (which he was doing constantly). For supper, the meat and cheese tray and eggplant salad came out again, this time accompanied by chocolate filled crepes, large mugs of warm fresh milk that her grandmother had sent and muesli (a granola and fruit cereal).

Monday morning Christina and I worked on HW while Roxana’s family was all at school/work. Around 2:30, they came home and we had “lunch” which was just as involved a meal as Sunday dinner, and just as delicious. We went for another walk to see more of the city itself and then came back and looked at pictures Roxana had of things like the chestnut festival and the region at other times of year. It was a fun and relaxing evening. For supper we had pizza and more milk with muesli, followed, of course, by dessert.

The train station at Keleti and pictures taken from the train:

Pictures from the village museum:

Wait...that's not a European license plate... We saw it while walking around in Baia Mare

Her family (minus her mom who was taking the picture) and the cake we had on Sunday

Tuesday morning we caught the train back to Budapest. Overall it was a wonderful trip. Visiting a friend and staying with their family is also definitely a wonderful way to travel. We got a very different view of Romania (and one that is probably much better at portraying it accurately) than we could have gotten visiting it any other way.

Interestingly, the trip also made me realize just how much Hungarian I have learned and how used to Hungary (and Budapest in particular) I have gotten. I could understand and read bits of Romanian because of my Latin background, but I was very aware of the fact that I did not know how to say even simple things like good morning. It was almost disconcerting to see the blue, yellow and red vertical stripes of the Romanian flag everywhere rather than the red, white and green horizontal stripes of the Hungarian flag and when we walked by a bank that had flags from several nations flying I noticed the Hungarian flag before noticing the American flag (which always looks so out of place amongst the European tricolors…). When we were getting the seat reservations (separate from the train ticket, it is an interesting system) for the train back to Budapest I automatically responded “igen”, Hungarian for yes, when the ticket lady asked, in Romanian, if there were two of us. I also never thought it would be so nice to be greeted “Jó reggelt kivánok”, Hungarian for “Good morning,” by the boarder guards when we crossed back over the boarder into Hungary and realized that I actually understood (and not just from the context) when he asked to see our passports and commented that I have the new version of the US passport while Christina’s is older (Speaking of which, I now have several stamps in my passport – it is exciting). It is going to be interesting to see what sorts of little things like these stand out when I come back to the US at the end of the semester.

Hideg van

2007-10-19T08:25:00.000-07:00

The internet at school is broken, so I am typing this from Christina's balcony where we get a spotty, insecure wireless connection. And feels like it is definitely below 10 degrees C. Yeah. Oh, and I am going to Romania to visit a MathCamp friend this weekend, so I will probably be away from the internet until Wed. I will update properly when I get back and actually have internet access somewhere that my fingers don't start get stiff when I try to type.

Szia!

szilva túró süti

2007-10-15T01:56:00.000-07:00

Has it really been two months? It doesn't seem possible, but my current (second) 30 day metro pass expires today (so I need to remember to get a new one tomorrow morning), so it must be true. It is strange how fast I manage to settle into a place. Budapest really does feel like home. It feels natural to catch the bus to the metro to get to school in the morning. Signs in Hungarian no longer inherently look strange. I still can't read most of them (though the number I can is ever increasing), but they at least look as though they have reasonable words on them. I know my way around the city well enough that I am frequently able to give directions to tourists and only have to pull out my map if I am trying to find some place in a part of the city I have not yet explored. Life is definitely good.

This past weekend Chelsey threw another dinner party - this time with our attempt at creating traditional Hungarian food. She made a vegetable stew called lecso that we served with rice as the main dish, which was quite tasty. For appetizers we served lots of bread with a Hungarian cheese spread called körözött and "egg foam" (fried whipped egg whites with yolk spooned over them and then baked) as toppings. And then there was desert... Tom made cookies, which were quite tasty, though it was questionable whether they counted as traditional Hungarian, and I decided to go crazy...

My host mother had made a delicious curd cheese and plum cake as part of the huge lunch she made on St. Stephen's day, so I decided that would be a good candidate to make for desert for the party. But I needed a recipe. I asked google for a plum and curd cheese cake...and it did not come up with the correct recipe...so I googled the phrase "szilva túró süti" and was directed to a recipe. A most definitely Hungarian recipe and the picture is definitely what I was looking for. The only thing on the ingredient list I did not recognize was "darált mandula" (which I now know means ground almonds) and I figured that I know enough about baking that I could probably pull something off, so I saved the recipe to my computer and attacked it with the dictionary. It took quite a while and some amount of guess work, but I eventually extracted something that looked like a reasonable set of instructions. Now just this was crazy enough, but we add to it the fact that the only measuring implements I have access to is a set of three funnels labeled 8oz, 4oz, and 2oz. The whole process was quite exciting, but the end product came out quite amazing, it slightly over browned on top. I have to admit that successfully baking a cake from a recipe in Hungarian is very satisfying. I got no HW done on Saturday - but I definitely practiced my Hungarian.

I will add pictures later when I remember to extract them from my camera...

"It's true anyway, it does not matter why." - Prof Elekes

2007-10-12T04:08:00.000-07:00

This week's C&P set was...interesting. It decided to throw a bunch of problems at me that did not exactly fit with my normal approach to attacking math problems. It's good for me, but can be frustrating when I am not allowed to discuss them with people. Despite this I still found myself presenting a solution (despite having told myself that I was not going to this week). The set that is currently out seems to fit my style (which I would have no idea how to characterize) better.

The set theory prof is out of town, so we did not have class this week.

Geometric graph theory never fails to amaze me. This week we talked about rigidity of graphs and why infinitesimal motions (not just physical) motions are important to engineers. We had proofs in terms of engineering concepts. Prior to this class I knew math had applications in physics and engineering, but I would not have guessed that physics and engineering had applications in math.

I absolutely love Topics in Geometry. The material in the class itself is fascinating to me and is making me look at algebra differently...there is a lot more of algebra that can be visualized than I thought there was. I think my favorite part though is the "office hour". Every Friday we have class as normal for the first hour and then have an hour where we can get questions answered and such. We never have enough questions to fill a whole hour, so Gábor tells us about all kinds of cool geometric things that we are not going to get to in class. This morning he explained how you can use geometry to analyze topological properties of some algebras and how number theory can be used in geometric arguments. Seeing all of the connections is both exciting and frustrating. It is amazing that they exist and you can prove really cool things by drawing the connections, but at the same time it means you never know what kind of math will be used in the nicest proof of any given statement and there are currently so many branches of math and so much in each branch that is no way to know if you have the right background and certainly no way to know everything that could possibly be useful.

Szeretek a BKV

2007-10-08T01:59:00.001-07:00

I love Budapest public transportation (if you follow the link you can listen to the amusing little tunes the buses and metro and such play when the doors are closing or we are arriving at a stop, etc) and the magical 30 day metro pass that gives me unlimited usage. Take last Friday as an example:

I left the apartment and caught the 16 busz (which stops almost directly across the street from my apartment). I rode the busz to Déak Tér where I transfered to the red metro line and rode it to the Keleti Pályaudvar station which has an exit onto the street College international is located on. At school I went to class, checked my email, etc and then Christina and I caught the 74 trolley busz to her apartment. We hung out briefly at her apartment and then walked a couple of blocks to Déak Tér where we met up with Mandi and took the red metro line to Batthyány Tér where we transfered to the HEV commuter train which we rode to Obuda (an older region of north Buda. In Obuda we went to an op art museum dedicated to Victor Vasarely. After the museum we wandered around and came across a Roman amphitheater and what appeared to be some sort of gathering of college students. They were clearly in teams (each team had matching shirts) and they had all sorts of random junk (a traffic cone, a vacuum hose, the shell of a lawn mower, an old motherboard, a broken guitar, etc) which they were using as play weapons. It was quite the event. When we got board with watching them, we walked back to the 1A tram stop we had noticed and took the tram to a blue line metro station . We rode the blue line back to Déak Tér where we met up with Kyle and then continued along the blue line to Kalvin Tér, which is near Raday street (a street known for its restaurants). We had dinner at the Soul Cafe (I had a cold raspberry soup with lemon sorbet and then csirke paprikas, it was delicious. The only problem is that I am not overly fond of having to pick my chicken off the bone, but it is not a big deal. ) and then caught the blue line back to Déak. We walked back to Christina's and hung out for a while before I caught the 16 busz back home. I am really going to miss having this kind of public transportation when I get back to the US.

It was Chelsey's birthday this past week, so we made her a cake. It turns out that raspberry jam works reasonably well for coloring butter cream frosting and that even though it makes it slightly runny, I can still successfully use a plastic bag with the corner snipped off to write with it.

While wandering around Obuda, we found this statue. It is surrounded by pansies. I have lots of pictures of the pansies, but I will spare you that.

A restaurant we passed called csaszarkert, literally, Caesar Garden. It turned out to be interesting forshadowing.

A street in Obuda. They have the same green signs with white writing that we have in the US.

The amphitheater

Another view of the amphitheater

One of the crazy college students arriving

Sunset picture taken from the amphitheater

"I can call anything anything I want - this is math."

2007-10-04T01:35:00.000-07:00

The title is a quote from my Set Theory prof.

It is always interesting when classes overlap :-)

Example One:

Conjecture and Proof: Prove that a cube cannot be tiled with smaller cubes of all distinct sizes.
Geometric Graph Theory: We can use graphs with rubber band edges to find ways to tile rectangles with squares. Here are some examples, including one that shows a way of tiling a square with smaller squares of all distinct sizes.
Conjecture and Proof: Passes around a picture of how to tile a square with smaller squares and explains how to create an electrical circuit that represents such a tiling. This electrical circuit is what would result from viewing our rubber band graph in the context of an electric circuit.

Example Two:

Set Theory: Lets play with cardinalities and different kinds of infinities and such!
Conjecture and Proof: Which of the following sets are countable?

Example Three:
Topics in Geometry: We are looking at affine spaces instead of just linear spaces, so we need generalizations of things like "independent vectors" and "basis". Some of these generalizations involve a configuration known as general position, so we are going to explore it.
Conjecture and Proof: Consider a set of half planes in general position that cover the plane...

I guess by classes overlapping, I mostly mean that conjecture and proof keeps being related to my other classes... But at any rate, I am still very much enjoying my classes. They are providing a nice balance of challenging me and yet not sucking all of my time. Set theory is particularly nice in this regard as it is constantly making me think in new ways, but once I figure out how I am supposed to think, the HW does not take that long.

And now Christina and Mandi and I are going to go find a part of the city we have not yet been to to explore, so I will leave it at that for now.

2007-10-01T01:59:00.000-07:00

There are somethings that are present everywhere in the US, some of them are just as prevalent here...one of these things is road construction

I had another conversation with an old Hungarian woman on the bus. This one started when she commented on the fact that the plants by the bus stop that are usually just greenery suddenly had little flowers. I understood just enough words that with her gesturing I knew what she was talking about. She asked if I knew what kind of flowers they were. I responded that I did not. My "nem tudom" must have sounded less that confident because she then asked "Magyarul?", I responded "Tudom kiscit magyarul." She pondered this for a second and then asked if I was from Slovakia. When I responded "nem" she asked if I was from Romania before I could add that I was American. When I told her I was American she looked shocked. She asked if I was visiting a sibling here, and I responded that no, I am just here to study. She asked what I am studying and when I responded math she told me that she has a sibling who does math and physics. These conversations are nothing very deep, but it is nice to know that I can at least understand and answer basic questions.

One day last week Christina, Kyle and I went to a gyros place for lunch. Incidentally, there are as many gyros places here as there are burger places in the US. I have to admit that the gyros are better than fast food hamburgers though... Anyway, I mentioned this because while we were eating Kyle suddenly sat up alert and asked incredulously "Is that...csipp csepp...?" We listened for a minute, and sure enough, the music playing in the gyros shop seemed to be a techno-remix of the Csipp Csepp song. This would be roughly the equivalent of a techno remix of the eensie weensie spider playing at a fast food place. It was interesting to say the least.

Friday night a group of us decided to go to a classical concert at the Palace of the Arts. The concert hall is incredible. We were sitting in the very last row of the top balcony and could still hear everything perfectly. The only thing that was at all out of balance was the organ, and even that was not badly out of balance. We also experienced an interesting cultural phenomenon. After the last scheduled piece in the concert, the applause did not die down and instead everyone started clapping in unison, apparently calling for an encore. This happened 3 times! None of us had ever seen anything like it and it was all we could do not to burst out laughing when it happened the third time. It makes me wonder if this is normal here.
Here is the view from where we were sitting

and the outside of the Palace of the Arts

On Saturday, Christina, Bridget, Leslie and I took a train out to Lake Balaton and a thermal spring that is near it. It was amazing to get out of the city. I am enjoying Budapest immensely, but I really don't think I am a city girl. The best anecdote from the trip occurred when we were getting on a bus to go between two small towns near Lake Balaton. The bus driver realized that we did not know much Hungarian and told us that the fare for the four of us would be ein thousand forint. "Ein" sounds an awful lot like "nine", so we were a bit worried for a minute, but we figured out what was actually going on quickly. It make sense that the native Hungarian speakers would be just as likely to mix their foreign languages (German and English) as we are to blend the other languages we know with our meager Hungarian, but it can certainly make for interesting communication issues :-) Here are some of the pictures I took during the Lake Balaton adventure:

"It can be larger than larger than infinite!"

2007-09-28T05:16:00.000-07:00

Geometric Graph Theory

This class is making me glad I have the physics background I do. One of our proofs involved replacing some of the ideal rubber bands connecting the points of our graph with rigid bars so that we could make the "forces" at all of the vertices sum to zero while still forcing them not coincide. All of this is to prove that 3-connected planar graphs can be viewed as the skeleton of a convex polyhedron. I think this class is going to prove to be the most challenging, but it is fun :-). I'm definitely glad for my background with graph theory and knowing what sorts of techniques are useful for approaching graph theory problems. It made the first HW set much more manageable for me than it seemed to be for a lot of my classmates...

Topics in Geometry

It is a great deal of fun to do proofs that effectively involve staring until you understand the geometry of what is going on, translating it into Algebra so that you can actually explain what is going on, working through the Algebra until it gets stuck, translating back into the language of geometry to get past a few sticky parts and then going back to Algebra to finish the proof. I love that math is so wonderfully interconnected! It also highly amuses me that several times questions, such as "Is the empty set an affine subspace?" have gotten the response, "Well, some elementary text books say (that/it is), but I do not think that is a good idea."

Set Theory this week, aka Playing with Infinity

When playing with cardinals, we start out with all of the natural numbers. We say the number of natural numbers is aleph naught. If we add aleph naught copies of 1 together, we get aleph naught. If we add aleph naught copies of 2 together, we get 2*aleph naught, which is just aleph naught. In fact, if we take the sum of all of the natural numbers, then we get Aleph naught. However, if we multiply them all together, we get c (the size of the set of real numbers). Now we have c*c=c and c^(aleph naught)=c and for that matter c^c =c. However, 2^c>c and we call it c_1. In fact we can define countably many c_i's with the formula c_(n+1) = 2^c_n. If we add all of these c_i together, we get a cardinal that is strictly larger than any of the c_n, so we call it d. We can then follow the same procedure with d to create e and so on. Once we have countably many of these countable sets of levels of infinity, we can add all of them together to create an even larger infinity, and so on and so forth. It is exciting.

Conjecture and Proof

The number of different possible approaches to problems often amazes me. We had one this week about tiling a rectangle. Various solutions included counting different kinds of dominoes in certain parts of the board mod n, looking at what happens if you roll a sphere around in the rectangle, and two very different colorings of the board. Over all it continues to be a fun class full of really cool proofs.

Mellow is fun too :-)

2007-09-24T07:28:00.000-07:00

Last Tuesday and Wednesday were not that terribly exciting. I made dinner with Christina (and Kyle on Wed) and did math. It is important to just relax sometimes :-). One day, and I don't remember which so I am just going to talk about it here, I ended up in another conversation with an older Hungarian lady on the bus. This one used to be a translator, so she spoke English. It is really quite interesting - she asked if I was Canadian. I don't know if I really don't come across as American or if people are afraid they will offend me if they assume I am and I happen to not be. Either way, it must not be obvious. I wonder what I do or don't do that makes it less obvious that I am American (several of my classmates have had people frequently identify them as American, sometimes before they say a word).

Thursday

The BSM program set up a showing of the documentary about Erdős Pál, "N is a Number," at the Renyi Institute and were highly encouraging all of us to go, so I went. Erdős was a very interesting person. I have to admit that the idea of not having anywhere in particular that you are expected to be and being able to do math and travel around the world to do math with other people on a whim is somewhat appealing. I don't think I would actually do it though, having some amount of stability is nice. It was also very interesting to see the footage that was filmed in Budapest. War scenes are much more striking when you recognize the buildings and bridges and statues as things you see on the way to school everyday...

Friday
Christina and I threw another dinner party at her apartment. We made a broccoli and pepper stirfry, lots of rice and carrot sticks for dinner. After dinner I made another batch of approximation cookies - this time with a spice cookie variation - the box of random spices had nutmeg and cinnamon and we had obtained fresh ginger for the stirfry. I was very, very pleased with the result :-)

While I was making the cookies, people decided that we should make an Apples to Apples game. Several of us had been wanting to play, but no one brought a set. The homemade game is likely going to be a work in progress for the whole semester. It is rather interesting version of the game: a large set of the cards are in (frequently mispelled) Hungarian, another large set are math terms, and a non-trivial set are inside jokes that have spawned in the time we have been here. Eventually we decided we had enough cards to try playing. It was hilarious, as Apples to Apples should be. I think my favorite play was when the adjective was "countably infinite" and the winning noun card was "Hungarian vowels".

Saturday

Christina, Chelsey and I planned to go to the Hummus Bar for lunch, but it was closed for Yom Kippur so we found lunch at their place instead. After lunch Christina and I went to track down a thrift store she had heard about to find a "classy dress" for the "classy sandwich party" two of our friends were throwing on Sunday. Shopping is not usually my thing, but it was fun :-). You can find interesting clothing in Hungarian thrift stores...

In the evening I went back to my apartment for dinner as one of my host mother's real daughters was coming over. We had fried eggplant with yogurt (which was surprisingly tasty), fried mushrooms, fried turkey, boiled potatoes and corn. Despite being mostly fried, the food was quite good. She also served wine with dinner. About half way through dinner she started refilling the wine glasses...I tried to tell her no thank you but she insisted on refilling it fuller than it was to start with *sigh*. About half a glass of wine had me slightly light headed. I was very glad I was did not have anything that needed to get done that evening...

Sunday

I actually watched my host mother make the Hungarian version of French toast! (usually she has it made before I wake up...) . First beat the egg (not excessively, but like you would for scrambled eggs) - just egg, do not add milk (you only add milk if the bread is dried out and not fresh). Heat (sunflower) oil in a frying pan while you soak the bread in the egg. Fry the egg soaked bread in the hot oil until it is golden brown. She always serves it with a mixture of powdered sugar and cinnamon. I think the biggest difference is using the wonderful fresh Hungarian bread rather than the sandwich loaves we get in the US...

Christina and I met up for church, but when we got to the Lutheran church just before 9, we noticed that the 11:00 service included a Bach Kantata. We glanced at each other and without hardly having to say anything concluded that we should go be productive and come back at 11. It turned out to be really cool, although the sheet they gave us with the German lyrics and Hungarian translation was not that terribly useful...

After church we had lunch and then went to Margit Sziget (the park island) to meet up with a couple of friends and do math outside. By the time we left the island, I had all but one of the problems due Monday done and written up. Christina and I went back to her place and got ready for the Classy Sandwich party. The party was fun, the sandwiches were tasty, and it was nice seeing most people dressed up. :-)
Sandwich assembly line:

Yesterday and today are math days. Tomorrow I am making dinner with Christina and we will have a math party. The theory is that if we can get on top of the HW during the week, then we can actually do bigger exciting things on the weekends. Hopefully this will work out well!

Oh, as a side note, apparently the Duracell bunny is much more adventurous that the Energizer bunny...

0^0 = 1

2007-09-21T04:00:00.000-07:00

I have now been to two weeks worth of all of my classes, and remain excited about all of them, so this is a good sign. This is a math post. I have decided that bringing my laptop to school every day is a little ridiculous, and the keyboards on the computers here are British and thus strange and I don't want to type long things on them, so I should come up with some sort of schedule. My current plan is thus to have a non-mathy post on Monday/Tuesday and a mathy post on Thursday/Friday which of the two days in each case depending on things like what other plans/hw I have ;-).

Geometric Graph Theory
A few days ago we gave three proofs of the same theorem ( If G is a three connected planar graph, S is a nonempty subset of V(G) and f0 is a function that maps elements of S to the real plane, R, then there is a unique function f:V->R, such that f(i) = f0(i) for i in S and it is harmonic at all other vertices. ) The first proof of this involved random walks and probability theory. The second had us view the graph as an electrical circuit and used physics to obtain a proof. The third started out with ideal rubber bands that obey Hookes law from these we defined an energy function such that minimizing it gave the desired configuration. It was very interesting seeing these three very different approaches - and the resulting equivalences between statements about physics, math and probability theory. I really like math that plays in the areas between the defined subjects :-). Also, I want my shelf of textbooks that I have used in former classes. There are not that many on it yet, but it would be really nice to be able to look up the details of theorems I mostly remember...

Topics in Geometry
This class is also very good at getting into the area's between subjects! Proofs have a tendency to start out as a geometry problem, involve using algebra properties to define isometries, manipulating the isometries geometrically - playing with things like distance functions, and then drawing them back in to the group context to use the techniques that became so familiar in Abstract. It is really interesting seeing geometric interpretations of group theoretic ideas that previously did not seem like things to be visualized (granted, when the geometry gets into higher dimensions it also does not really get visualized.) Additionally, when we don't have questions during the "office hour" the prof does cool geometry stuff, like giving a geometric proof of the Cauchy-Schwarz inequality.

Conjecture and Proof
This class is definitely the three credit version of Putnam seminar. On Tuesdays the prof goes over cool proofs and points out various useful ideas and techniques. On Thursdays he collects the HW and then we go over it, having people present the different proofs they have come up with. It is really cool to see the sometimes drastically different approaches people take to problems. Problem solving is not exactly my favorite type of math, but the practice and being exposed to different techniques and ways of thinking is good for me and the proofs are definitely exciting.

Set Theory
We seem to be down to 4 people in Set Theory, which means that it will happen, but that it will be turned into a reading class where we are expected to teach more of it to ourselves and it will only meet once a week. *sigh* Ah well, it will still be fun. It will also teach me to pay very, very close attention to proofs in class. The prof has a tendency to go through a proof, look like he is ready to move on and then say "Oh, as a foot note, that was not a proof and the theorem is false as currently stated" and then we stare at the board for a minute or so until we figure out what the problem is. Today we had to figure out why a0<=a and b0<=b does not imply a0^(b0)<=a^b. In set theory, 0^0 = 1 and 0^a=0 for all a not equal to 1, so if b and b0 are both 0 it is false. We also looked at why the proof of the fact that the countable union of countable sets is countable requires the axiom of choice. It is a fun class :-)

A szep napot van!

2007-09-17T02:08:00.000-07:00

Yesterday morning as I was sitting and waiting for the bus an elderly Hungarian lady came and sat down on the bench next to me. She noted that the weather was beautiful and I smiled and agreed. Then she asked me something that I could not quite figure out... I explained that I only know a little Hungarian. She smiled, nodded and then talked to me using very simple Hungarian. Sometimes she would have to reword things, but there was only one question that I never managed to figure out! Even better, I knew enough Hungarian to answer her questions - my grammar was far from perfect and I did not always use complete sentences, but I could make myself understood. They were simple things, like where I was from and where in Budapest my classes are, but I understood the questions and new how to answer them! Also, I apparently do not have a strong American accent in my broken Hungarian - she asked me if I was German and was genuinely surprised when I explained that I was American. Her stop was before mine and as she got off I wished her "szep napot" - have a beautiful day - and she smiled and waved from the stop as the bus pulled away. I think it made both of our days :-)

Sunday Christina and I tracked down a small Anglican congregation whose service is in English. Their sanctuary looks like it was adapted from the same sort of wine cellar as the bar we went to to listen to live Hungarian music. Their priest was in Austria at some sort of meeting, so they were planning to have a basic morning prayer service but there was a priest who just happened to be visiting from England, so they ended up having a normal service after all. There were only about 20 people there and the 'sanctuary' could not have held more than twice that, but everyone was very friendly and it was really nice to actually understand everything. I also really enjoyed the number of different accents :-) Everyone spoke English, but we were still from all over the world. We will probably go back there frequently, though it is also nice to visit the gorgeous churches that are all over Budapest.

In Budapest there is a phenomenon known as a tanchaz - as best as I can figure out, a tanchaz (literally "dance house") is like a contra dance but with traditional Hungarian Dancing. This past Saturday was the tanchaz ball where all of the different teachers and bands and dancers came together starting at 8pm and there was supposed to be dancing until 5 am. Christina, Chelsey and I decided to check it out. We got there around 8 and discovered that there were 3 different rooms with different kinds of dances in each room and the dancing in any given room changed every half hour or so as teachers familiar with the dances from different regions switched out. We tried dancing some, but my feet and ankles are not cut out for that kind of intense foot work (I realized that part of why I like contra is that the emphasis is not on footwork). Chelsey and Christina were much better. I really enjoyed watching and listening to the live music though. The boot slapping dances that the men do are especially impressive. We left around 10:30 so that we could catch the metro home, but it was definitely a lot of fun :-)

Erzebet Tér has been invaded by cows. Here are a few of the more interesting ones:

And this one even had flies

Last Thursday Christina, Kyle and I climbed Gellert Hill - a hill taller than the one the castle is on and that houses the citadel. It has gorgeous views of the entire city. It also has a pretty garden and a simple playground consisting of swings and concrete dinosaurs. Other than that words really are not useful, so here are pictures
The castle in Buda

The Danube

Pest

Math!

2007-09-13T01:44:00.000-07:00

I have now been to all of the classes I think I am planning to take at least once, so this post is going to be my first impressions. For those of you who are not as interested in the math, at the bottom there are also a few pictures ;-)

Geometric Graph Theory

Last spring I took Mudd's Graph Theory course. Throughout the class, we made a point out of the fact that the specific drawing, embedding, of a graph was not important. We focused on properties inherent to the graph regardless of drawings. Drawing were useful for seeing what was going on and obtaining intuition, but did not tend to play a crucial role in the proofs. I get the feeling that this semester the most important part of most of the proofs is going to be finding the correct embedding of a graph (sometimes in 2-space, sometimes in 3-space). It is going to involve things like observing that every three connected planar graph can be drawn as the skeleton of a convex polytope. In turn, given the skeleton of a convex polytope we can prove that it is a 3-connected planar graph.

We first providing a method of projection that gives us a straight line embedding in the plane with no crossings - pick any face of the polytope and choose a point "close" to that face, where close means that if we extend the plane of any other face of the polytope that point and the polytope are in the same half space, and project onto the plane of the original face via that point. To prove that it is three connected we need to show that removing any two arbitrary points a and b leaves the graph connected. Select any 4 points a,b,c,d in the polytope. Either these 4 points are in a plane or they form a tetrahedron. If they form a tetrahedron, then we can find some plane that will separate a and b from c and d. Consider the portion of the polytope in the half space containing c and d. If c and d are adjacent, then we are done, otherwise follow a path from c and a path from d that always moves away from the dividing plane. Eventually, we will not be able to move farther away (since we are on a convex polytope). At this point, the paths will intersect, the final verticies of the paths will be the endpoints of an edge of the polytope and we can connect paths entirely in that "half" of the polytope, or the final vertices of the paths will be two of the vertices bounding a face of the polytope that is parallel to the dividing plane - in which case they are part of a cycle and we can connect the path. In all of these cases we have shown that c and d must be connected in the "half" of the polytope that does not contain a and b and so removing a and b does not disconnect the graph. If all 4 points are coplanar, we use that plane to divide the polytope and then restrict ourselves to stay on one side of the plane (it does not matter which unless they are all part of the same face, in which case we obviously take the side of the plane that contains the rest of the polytope) and use the same argument.

I find it very exciting that we can use phrases like "always moving away from the specified plane" when proving things about graphs! I am going to learn a completely new way of thinking about graph problems :-). The class is being cotaught. One of the professors is amazing, the other is slightly harder to follow, but the material is exciting enough that it is definitely going to be worth the work.

Topics in Geometry

The first day was mostly just outlining what we are going to be covering and the approach we are going to take, but I am still excitied. We are going to start with Euclidean Geometry, but instead of using the axiomatic approach (which the professor deemed "stupid") we are going to study geometry via transformations. In particular, we are going to spend a lot of time studying the isometry group of R^n. (Anyone know of any nice way to write math in a blog?) I really like seeing the connections between subjects, so studying Geometry via Algebra should be fun :-). After Euclidean, we are going to take a similar approach to studying the spherical, projective, and hyperbolic geometries. It will be nice to formally study them for more than a week long class at Mathcamp.

Conjecture and Proof

The best description I have come up with so far is that that this class looks like it is going to be the equivalent of turning the Putnam Seminar into a 3 credit class (and then forbidding collaboration on most of the problems...). It is full of very shiny proofs - the sort that are wonderfully simple and elegant and make you wonder how on earth anyone every found them. One of the things I really like about it is the same thing I really like about the Putnam Seminar - it is going to make me stop and think about all sorts of different areas of mathematics. It is far too easy to learn material one semester and then let it drift to the back of my brain and get rusty from disuse. I suspect C&P will make me use most of the math I know at some point or other :-). The fact that collaboration is mostly forbidden makes me sad though. Mudd has me very used to sitting with friends and bouncing ideas around...

Set Theory

Everything is a set. For instance, the ordered pair (a,b) can be thought of as the set {{a},{a,b}}. The basic axioms of set theory allow us to easily prove that {{a},{a,b}} = {{c},{c,d}} iff a=c and b=d, so it does indeed act like an ordered pair. Set Theory looks like it is going to be all about looking at familiar things in an unfamiliar way. The professor has a good, though subtle, sense of humor. Overall it looks like it will be a good class. The only problem is that there were exactly 6 of us that went yesterday, at least 2 of which I suspect are not going to actually take the class. If a class drops under 6, they turn it into a reading class rather than a normal class (as long as there are still at least 3 of us, which I think there will be). I would rather have it as a normal class, but a reading class will be fine too if it comes to that.

And now the non-math.

Some of the flowers that are around the building most of our classes are in:

Near the giant hour glass that I posted about earlier, there is a large parking lot. Currently, this parking lot appears to be some sort of advertisement show - it has billboards set up all over it. In addition to the billboards, there are animals made out of trash and oddly decorated phone booths.

Last night several of us hung out at Christina and Chelsey's place and had görögdinnye and tea. It is important to note that this was not organized by either of the mathcampers that are here this semester (though we were both there).

Hey look, the Danube is flooding

2007-09-12T02:13:00.000-07:00

I went to intermediate Hungarian yesterday. The teacher informed us that the class always ends up horrible, but that he has a new crazy plan for this semester. We are going to spend about 3 weeks on grammar and then study Hungarian by translating the song lyrics from a hip hop band that did an album with songs about Hungarian History. My immediate thought was that this would be like learning English by studying School House Rock or that Animaiacs song about the Presidents... It should be interesting.

I will write about the math classes once I have been to all of them. :-)