Pumpkin and Spice and Everything Nice

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

1. Preheat the oven to 350.
   
2. 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.
3. Cream the butter and the sugar. Once they are completely blended, add the egg and pumpkin and mix well.
4. 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.
   
5. 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.
   
6. Stir in the chocolate chips.
7. Scoop the dough out in cookie sized dollops on your cookie sheet.
8. Bake at 350 until they have started to brown and bounce back when you touch them.
   
9. Enjoy!

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

Cookies with Flowers

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

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?

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

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

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

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: