Math Games

Back when I was in sixth grade, we had a warm up everyday on the whiteboard when we came into class. For a few months in the middle of the year, our project was the "Four 4s," where we had to make every number from 1 to 100 with the combination of four 4s in any mathematical sequence. I had a dream last night which involved switching math games with a friend. I eventually suggested the "Four 4s." I got stumped at 13; I am a lot better at math when awake. I wrote a few down and added a couple of alternatives.

 At the doctor's office today I started working on them while I was waiting and I am now stumped at 31.

Gore, Fire, and Random Updates: A Collection of Thoughts

For politicians in the United States, Friday is affectionately known as "take out the trash day." The reason for this is that media outlets have some number X column inches to fill and if you give them one story on Friday (as less people read the headlines over the weekend) they will fill it with that, but if you give them five stories, each story is only X/5 column inches. So, in general, politicians dump their negative stories in the Friday trash.

In that tradition, I thought I would jumble a bunch of stories together for today's post. This is just because I have a couple of things on which to follow-up as well as some general thoughts and I have been rather busy in the last few days as there is now a deadline for transition in my life: I am going back to school in the Fall. I now am trying to prioritize what i need to do before beginning school.

Gore: By "gore" I mean the noun version of "gory" rather than the former vice-president. Last night I spent a while typing up a preliminary version of my reading list for my graduate school applications. Many of the grad schools require that applicants send a list of all of the texts that they have read in the original classical languages. As I was hunting down syllibi and typing up my list, I realized that I have little memory of any of the texts that I read for my Latin Civil War class. I was stressed and tired during my final semester in college and poured myself into my thesis more than anything else. I also had terrible insomnia because of all the stress and my memory became very poor. I almost think it's insincere to write down the whole number of pages I read in this class. My original solution was to reread it. But then I remembered: I also really did not enjoy the reading. The class itself was ok. The teacher was great and I remember loving her military diagrams. However, we read Caesar and Lucan's account of the civil war in Rome. Caesar's account is a complete bore and the battle plans are often hard to follow (hence the military diagrams). Lucan's account is interesting for about the first 200 lines until he starts talking about the civil war. At that point it becomes so melodramatic and gory that it's just completely joyless to read. For context, Lucan the nephew of Seneca the Stoic philosopher, and a writer in Nero's court. Lucan was one of Nero's contemporary and rumor has it that Nero sentenced Lucan to death because Lucan was a better writer than the emperor. To be fair, Lucan was probably involved in an attempt to depose Nero. Furthermore, Lucan's Latin is tough: he writes Silver Epic and the commentaries are almost completely useless except for intertextual references. This is partially because no one likes Lucan: his content is overblown and his hexameter is boring. I may reread excerpts or read them in English so I don't babble like an idiot when asked about them.

 

Fire: There was an interesting article about Mercury today in the New York Times.

Random Updates: If you have been following my blog, you probably remember that last semester I took a Calculus class at a local community college for fun. I enjoyed most of the class, but I found some of the relearning more difficult than I had expected. Worse, when I showed up for the final, half of it was completely foreign and I left feeling dejected, as I had spent a long time studying. To my great surprise, I actually did well on the final and got fairly good grade in the class. Woohoo! I am even considering taking the next calculus class when I get the chance.

One of Those Days...

It's just been one of those days where nothing goes as planned. It seems to be some kind of math curse. I studied for the exam for the whole weekend. I made a study guide and did practice problems of each of the ypes that my professor enumerated were on the exam. Unfortunately, I was deceived. At least three of of the 13 questions on the exam were of a sort I had never seen. It was one of those days.

I think I will go back over the math. I have books that will take me up through multivariable calculus. It may be harder to teach myself, but at least I will know when I know the information and I cannot get blindsided by an exam that makes no sense. Ultimately, I am learning for my own sake anyway, so there is little downside to teaching myself.

I had a lovely dinner of samosa's my mother bought. I will resume bread baking tomorrow...

General Thoughts...

I'm taking my math final on Tuesday and I just finished up my latest SAT prep class so I will not resume posting in depth for a few days. I am spending my time writing a study guide for the class.

I took the leftover pancake batter from the other day and made apple and cheese crepes for dinner and dark chocolate crepes for dessert. They were great, except I think that next time I will simply used the sourdough for crepes instead of adding the baking soda. Also, I noticed that the slight sour flavor of the crepes requires something with a strong flavor inside-- e.g. the crepes with sharp cheddar and apples were better than those with brie and apples. I forgot to take a photo, but this was the first time I ever made crepes (Servia makes great ones) so they were perhaps not as photogenic as another attempt might be.

Math: An Experiment in Relearning

Retaking calculus after six years has proved an odd experience. Concepts that came to me so easily back in high school are much more difficult now. On the other hand, those concepts that I did not learn then or that I did not understand fully come much more easily. I am spending the next four days studying for my final. I am using my old technique of creating a comprehensive study guide.

Concerning math, I listened to a pretty cool podcast from In Our Time with Melvyn Bragg which discusses imaginary numbers. Enjoy.

More Math...

I have a math exam and I have realized that even though I took calculus before, I actually need to study for exams. Anyway, in a scientific vein, enjoy this article about orphaned giant planets as food for thought until I post again tomorrow...

The Return

I have returned from my Alma Mater (a few days ago). I now have a math test I need to crash study for. I will be on hiatus until Friday night. In the meantime, there is a great "In Our Time" piece on Unicorns that I listened to while I was visiting Cerinthus. I highly recommend it and will discuss in in greater detail when I get back.

Chocolate Cake and Cockaleeky Soup

I was watching an episodes of Jeeves and Wooster in which Tuppy Glossop wanted to sell his grandmother's recipe for cockaleeky soup to a soup company. He is convinced that it is the best soup in the world. The soup company begins marketing the soup because it turns out the his favorite soup is not a secret recipe but in pretty much every cookbook.

A similar thing happened with the chocolate cake from my childhood. A lovely woman who worked as a housekeeper and took care of me. Every year for my birthday, she made the most amazing chocolate cake that I thought was the food of the gods. So did all of my friends. Eventually, when I had a chemistry assignment to do a chemical analysis of a food, I asked for the recipe and analyzed the interactions. About two weeks back, I found almost the exact same recipe on One Perfect Bite. Still the best cake in the world, but not a secret recipe. If you ever want to make a chocolate cake, this is the one you should try.

Speaking of things that are not like I remember, I took my first math exam today. Although it was not awful and I certainly understand things in class, it is much more difficult to deal with the exams than I remember. I am rusty even after a few weeks. I thought this class was going to be a cakewalk, but it may be a bit of a challenge. What it really demonstrates is that I need to keep my brain engaged.

Bureaucratic Nightmare

I had one of those days where I couldn't do anything right. Many things went wrong, but suffice it to say that I realized I ordered my used copy of Hammer's German Grammar and Usage in German instead of English (i.e. all of the notes on how the language works are in German) and it just got worse from there. I was really excited to go to my math class, until I wandered into a bureaucratic nightmare.

It turns out, at this particular Community College, if you make a mistake on a form, you have to get an entirely new form and fill the whole thing out again, instead of just crossing it out and rewriting it. Perhaps there is some reason for it that I do not know, but this policy seems absolutely insane. Anyway, having a visual processing issue, I often mix up numbers and letters when I write them down. I reversed two of the numbers in one of the pieces on the form. So, I was told very snootily, that I had to go back and get a new "add form" and it was unlikely that I would be able to get into the class. Seriously? Anyway, I talked to the professor who was very nice and said he was happy to get me a new "add form" but this still does not explain the "no cross-outs" policy. Bureaucracy sucks.

Update 02/11/11: I woke up this morning (after sleeping in) and the world looked a little brighter. Even better, when I went down to check the mail for my math book (which has not yet arrived), I found that my German book arrived-- and it's in English! Apparently the words "German Edition" (I bought a cheap used copy) just meant that the book was a descriptive German grammar, and all of the explanations are in English. I breathed a sigh of relief and cackled gleefully at having purchased a perfectly clean used edition for less than a quarter of the new price.

Circumnavegating the Wall #2: Calculus

By the time I took calculus in high school, I was quite a good math student. I loved calculus and I could not wait to take more math in college. As I mentioned in "Cicumnavegating the Wall" in multivariable calculus I hit a wall and had to drop the course. It just did not make any sense. Consequently I pursued my other great passion, classics, and graduated with a BA. Math was no longer in the direct path to my future.

Being out of school made me realize that while institutions may organize education in order to place their students on particular paths, there is no reason that self-education must follow those same paths. So there was noting barring me from taking more math. As I promised in "New Year, New Possibilities," I registered at my local community college. Realizing that I needed a math refresher (and because of timing commitments) I decided to take Calculus I and I will move up through the math classes from there (they offer three semesters of calculus followed by linear algebra and differential equations). I took a big step and went to my first class today.

The past week, I have been nervous and annoyed about my decision to start the classes. There was no need. Calculus (at least the evening class I am taking) is a decently paced introduction taught by a middle aged man with a thick Indian accent and an efficient, clipped style. The class is entirely lecture, although after every few sentences he asks "is this ok?" which seems to translate to "understand?" and then he moves on without waiting for a reply. If a hand is raised he will eventually call on the person and he seems happy enough to answer genuine questions, but my best guess would be that he has taught this class for many years and simply wants to get the material to the students in the most expedient manner possible.

The students also surprised me. In the discussion before class, I ascertained that most of the students were at the college with the hopes of transferring into the local university. Many were in the class because they want to pursue degrees in engineering. I found them to be engaged with the class and intelligent. Although first impression are often misleading, I believe that these students will probably continue to be good classmates. I was really nervous about fitting in, but a few students asked me questions about the nature of the class during the break so I guess I must have looked like just another student. Luckily I fit the profile of the typical girl in the class (interestingly the class is a 50-50 gender split): skinny jeans, t-shirt, and boots (although I had knee-high instead of the ankle-height boots sported by the rest of the women).

Any of you who read my new year post noticed that I was also supposed to be taking German because it is one of the classes necessary to pursue a more advanced degree in classics. As it turned out, the class was based on conversational German and used a textbook reputed for avoiding tricky things like grammar. As much as it would be nice to be able to talk to people, what I need is academic German, and specifically German for reading. I realized that the money that I would be spending on the class itself could be spent instead on approximately 34 nonfat lattes which, if I could find a coffee shop, could allow me to spend that time more effectively trying to teach myself reading German. So my thought is that I will compare a few different textbooks. At the moment I am leaning toward Jannach's German for Reading Knowledge, which I have put on hold at the local library. If anyone has a recommendation, I would greatly appreciate it.

Fun with Math

Wandering around New York Times site this morning, I stumbled upon a math column. The column was a short run-- a fifteen part series-- by a professor of applied mathematics from Cornell University. I have not read much of the series so far, but I read the piece on the integral and I found it to be engaging.

Note: I am going up to my Alma Mater tomorrow for a week to see Cerinthus. I will try to keep up with my posting.

New Year, New Possibilities

I decided to take more math. It is a New Year and I think that means that it is time for me to start something new.

One thing that I hear a lot from college and post-college female friends is that they miss science or math. This seems to break stereotype. Going to an all-girls high school, I had always heard that single-gender education and tailoring classes to "the way that girls learn best" allows girls to feel comfortable in math or science (or any field) and should help confidence and begin to rectify the gender gap in the sciences. Yet, there seems to be something wrong with that theory. A number of girls who enjoyed science in high school but went into humanities, art, or social sciences instead.

Some of them probably had issues in their math or science classes like I did (as I mentioned in "Circumnavigating the Wall"). Some of them just decided another path was better, and now have changed their minds, or wish they could reincorporate math and science back into their life. The real problem seems to be that the sciences require constant devotion. To finish as a physics major in four years at my alma mater, you had to start immediately as a freshman, otherwise you could not graduate in time. However, students often changed their majors to the humanities or social sciences after the first year. The problem was not that there were less requirements-- it was that classes in the humanities and social sciences can be taken concurrently. For example, one could take a 200-level Shakespeare class, a 300-level Chaucer class and a 400-level Literary theory class all at the same time, provided instructor consent and student devotion to the subject. With math and science, there is much more of an order of things; each level builds on the previous one and requires a rigid line throughout. Most of my female friends have a large variety of interests [1], and either did not want to sacrifice most of their other interests to science or were not sure that was the path they wanted to venture down.

So what should this group of girls do, who like science but have BAs or are working toward BAs in other fields? Taking science classes after a BA is regarded by other people as "useless," "inefficiant," or "a waste of time and money." I decided that I don't care. Today I registered at a local college and when my registration is processed I am going to sign up for a calculus class. I will probably never need advanced mathematics in my life, just as I will probably never need to know the philosophical standpoint of Pierre Bourdieu, which I studied in my Lit Theory class, but I think that it will enrich me as a person.

I picked the college because it was nearby, but also because it decided to offer German. None of the programs in my area had been offering it. I guess it's because German is primarily useful for classicists and students of philosophy, neither of which really exist at the local colleges [2]. German will help me get into graduate school and will also allow me (hopefully) to eventually read the German philosophers and writer's I like in their original language.

I hope the classes are not so full that I cannot get into them. Wish me luck!

Endnotes

1. There are probably males in this position as well, I just do not know any of them. Most of the guys I know who have varied interests seem to have varied interests within the humanities, or are science majors who take a few classes in other disciplines but have never wavered in their devotion to science.
2. There is a big university near me (which has great programs in both classics and philosophy), but unfortunately one cannot take many classes there unless one is an actual student at the university.

A Humanities-Based Discussion of Mathematics

I love math. I realized this when I took geometry and again when I took calculus. After calculus the love never dissipated, even when I decided to go into classics instead of math. Since I have been out of school, I have been looking for interesting lectures and tutorials in math.

Earlier today I happened upon this discussion between Eva Brann, Brian Greene, Mario Livio, Barry Mazur, and Elaine Scarry. It is a lecture called "Mathematics and Beauty" from something called the Philoctetes Organization. I have not listened to it yet (internet problems) but it looks great. I had some trouble getting the video on the Philoctetes site, so I found it on youtube. I seem to be having trouble with my internet so I cannot embed it into the webpage.

Great College Stunts

Back when I was in applying to colleges, I heard a lot of stories about various pranks that the students took part in at each institution. The science and technology schools are especially proud of their heritage of practical jokes. However, on these college tours, one never hears about my favorite type of prank: jokes on the students by the professors for the sake of some greater educational purpose.

I was listening today to the sixth lecture from the History 5 class (Fall 2010). Even in the video, one cannot see the lecturer but only the slideshow. So, listening to it, this practical joke (and I use this in a loose sense) might have been funnier than in person. Thomas Laqueur (the lecturer) is speaking about the divisions in the early protestant church. He stops; there are some rustling noises. Then he says "is that a Berkeley homeless person?" Another long pause ensues in which presumably some unknown person moves through the audience. Then he says, no, it's Ulrich Zwingli (and the slide changed to a portrait of Ζwingli). I presume, again, that the "homeless person" is dressed like the portrait of Zwingli that Laqueur shows in the slideshow at this moment. Everyone laughs. Zwingli, played by emeritus professor Thomas Brady [1]. "Zwingli" explains the theological contention he has with Luther and the connection between religion and politics of the period. Laqueur interjects frequently with after jokes about Zwingle's death and the protestant conception of the afterlife. Finally, the stunt ends and Laqueur returns to his lecture, now focusing on the Catholics.

 

This reminded me of an instance at my own university in which a math professor played my number theory class. And I know it sounds totally weird, but this is a true story. So it was 11am and I was standing in the vestibule outside my number theory class. I had been up late the night before working on my qualifying paper, and I was very tired. The door opened to the lecture hall and a thin man with scruffy brown hair, wearing-- I thought-- round spectacles and pushing a cart full of pineapple. I blinked for a moment, just to make sure, and then stepped aside to let the outpouring of Linear Algebra students exit the classroom.

Our lesson that day was on the mathematics of the Fibonacci sequence. The lecture was interesting and fun (and, as it turned out, very similar to the Linear Algebra lecture from earlier that day). At some point, my professor, whom I will call James for the sake of convenience, stopped the class for a moment, explain that he forgot something. He proceeded to call 411 on his cell phone and ask for the number of Quimby and Dimby's Singing Pineapple Delivery Service.

This bizarre moment may need some context. In most classes, a stately math professor doing something like this might seem like it would require the Infinite Improbability Drive from Hitchhiker's Guide to the Galaxy. However, James was a little different. A specialist in surreal numbers and the coauthor of a textbook that included fake biographies of the Ancient Greeks and cartoons, James was stick skinny, gangly, sporting a full beard, and often covered head-to-toe in magenta chalk. He was brilliant and exuberant, but also comical in, among other things, his obsession with brightly colored chalk. So the mid-class cell phone call was certainly unusual and pushing the boundaries of his usual eccentricities.

So he finished his 411 call and told the class that he had to make just one more call before he got back to teaching. He called Quimby and Dimby's Singing Pineapple Delivery Service and appeared to have some difficulty explaining to the person on the other end of the line that his class was in the same room as before in order to have them do the show. At this point, my morning already appeared very strange and I was open to almost anything to happen next.

About ten minutes before the lesson ended, a man entered the room with a cart full of pineapples and something that resembled a violin case. Although he looked like the same guy as before, he was not wearing glasses. He greeted the class cheerfully. James said to him, "aren't you going to sing the song and show them how to count the pineapple [2]." The man, who was presumably Dimby, explained that his brother, Quimby, had come to the previous class, but was unable to return due to "too much Maui Wowi." He said he would show us how to count the pineapple, which he did, but he told James (who looked rather concerned and dishearted at the news) that he could not sing. He explained that he could accompany James if James wanted to sing, and he handed James a untidy pile of papers that were presumably the lyrics to the song. He then proceeded opened the violin case, which turned out to be a ukulele case, and the two of them put on a rather strange performance of a song. I don't remember any part of the song except the chorus, which was made up of the list of the Fibonacci numbers up through around 6000. It was pretty funny. We all joined in on the last chorus.

That evening when I got home, I googled Quimby and Dimby's Singing Pineapple Delivery Service. There were no results matching that phrase. The whole thing was an elaborate prank.

Endnotes

1. Brady is credited in a slide at the end of the stunt. According to Laqueur, Brady wrote a book on this splintering in the protestant movement.
2. The pattern of growth on a pineapple matches the Fibonacci sequence, as does the pattern of growth on many plants.