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:

## Saturday, July 26, 2008

## Sunday, July 20, 2008

### 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:

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.

## Sunday, July 13, 2008

### 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:

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

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

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:

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:

## Sunday, July 6, 2008

### Well, That Was Different...

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 :-)

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 :-)

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