Pressing Toward the Prize

Archive for September 2010

As part of our Senior Capstone, each of us who is majoring in math will be writing a research paper that will involve mathematical notation and formatting. In anticipation of this, we are currently learning to use LaTeX, a mathematical typesetting language that will allow us to produce academically sound, professional-looking documents. Our first assignment in the learning process was to re-create a document crafted by our professor in order to give us exposure to the various aspects of LaTeX.

After attending an introductory LaTeX session, printing off a sample document with accompanying code, and finding an online tutorial, I set out on my adventure. The process of writing the code to reproduce the professor’s document was a bit cumbersome, because I had to stop and look up how to do nearly every component!! Of course, not every command was readily available, and I had to learn how to “tweak” the examples to write code that would produce the specifics I needed. I discovered that many of the commands are fairly intuitive in that they are often a simple description of the symbol or function you want to create, which is nice. For example, to produce the symbol “is an element of” you type “\in,” for “greater than or equal to” you type “\geq,” or to center something, you type “\begin{center}…\end{center},” and so on. But like other computer programs, LaTeX wants what it wants when it wants it, and part of the trick is finding out what that is in any given situation!!

LaTeX does have some interesting idiosyncrasies, however, that I found quite humorous. To make something print larger than normal, one would use the command “\big,” for larger one would type “\Big,” and “\Bigg” would produce something larger still. But to go very huge, one could type “\Huge.” Isn’t that a hoot?!

All in all, I feel much better about learning and using LaTeX since I have “battled through” creating (or re-creating, if you will) a document myself. It was a very momentous occasion when I compiled the code and it actually produced the document exactly as it should have been. I couldn’t have been more proud (and thrilled) if I had just finished writing my first novel!

In Capstone Seminar today we were introduced to the faculty members of the math department at PLU. Each professor gave a brief presentation of his or her areas of expertise, as well as some ideas for interesting Capstone projects. I was impressed by the wide array of mathematical fields represented by the nine professors, as well as the variation among the professors themselves. One works almost exclusively with probability and statistics, and another prefers topology and geometry, having declared statistics “boring.” There was so much information given that it was hard to take it all in, but many wonderful ideas were presented. With so much variety, I cannot imagine any of my fellow students not finding at least one topic that sparked his or her interest.

I am not very spatial in my thinking, so topology and geometry may not be the best for me, although I find them both quite interesting. I struggled a bit with multivariate calculus for that reason: I could do the math with no problem, but I sometimes had trouble “seeing” what was going on. At first blush, there were two topics that caught my attention. One had to do with educational assessments, involving both theory and development, and the other was number theory. I checked out some websites to investigate exactly what number theory entails, and I discovered that it is a very large branch of mathematics. Something that caught my eye, however, is the study of Diophantine equations, or equations that have only integer solutions, of which Fermat’s last theorem is one. I am not sure if either one of these topics will lead to my Capstone project, but they are possibilities to explore.

While perusing the website Teaching College Math, I came upon a blog entitled Mathematics of Coercion. I was immediately intrigued, and discovered it was actually a review of a video on TED Talk called “Bruce Bueno de Mesquita Predicts Iran’s Future.” Apparently Mr. Bueno de Mesquita has created a model using mathematical analysis to make predictions about complicated issues involving negotiations, such as war and politics.

After watching the video, I was a bit disappointed that even though there are a couple of references to mathematics, nothing of substance is offered. He mentions game theory, and that the factorial is used in determining the number of interactions of n people influencing an issue, but he never explains how he quantifies the various characteristics of the “influencers,” or how math is used in his simulation computer program. He does state that his predictions are based on estimations of future behavior, not statistics of past behavior. So even though we don’t really know what he does use, he makes it clear what he doesn’t, and no statistics are needed!

I was recently discussing with my math professor and a fellow student the relevance, or lack thereof, of current math courses to high school students. When I commented I wasn’t sure if it was the relevance of the courses, or the marketing of those courses, that was the problem, my professor directed me to a video of a talk given by another math professor, Arthur Benjamin. In it he explains why he feels that making calculus the pinnacle of the high school math curriculum is not the best, and that students (and society) would be better served if learning probability and statistics was the zenith. He does not minimize the value of calculus for certain students, but he feels it is not relevant to our everyday lives in the way that probability and statistics are.

After taking my first statistics course, I was so impressed by the relevance of the material that I began to believe, and still do, that everyone in America should know statistics. If followed, Professor Benjamin’s “formula for changing math education” would make that possible. We are so inundated in our culture with facts, figures, and persuasive techniques involving statistics (think sports, politics, lotteries, advertising), that one needs to be able to sift through the rhetoric in order to recognize the reality. If one more fully understands the data being presented, one can make more informed decisions. It would seem, then, that I have had to re-think my position on high school math in favor of changing the current course offerings and emphasis to bring more relevance to our students. And as Professor Benjamin points out, probability and statistics involve uncertainty and risk, which are clearly relevant to our everyday lives.

On Tanya Khovanova’s Math Blog I encountered a couple of interesting probability puzzles involving a truel. In one, the three men have an infinite number of bullets and they shoot in order until only one man is left alive, and in the other, each truelist has only one bullet. Ms. Khovanova gives the solution for the second one, based on probabilities and basic survival instincts, but leaves the first one to the reader. These puzzles remind me of a problem we were given in Professor Edgar’s M317 Proofs class:

“The five Dukes of Earl are scheduled to arrive at the royal palace on each of the first five days of May. Duke One is scheduled to arrive on the first day of May, Duke Two on the second, etc. Each Duke, upon arrival, can either kill the king or support the king. If he kills the king, he takes the king’s place, becomes the new king, and awaits the next Duke’s arrival. If he supports the king, all subsequent Dukes cancel their visits. A Duke’s first priority is to remain alive, and his second priority is to become king. Who is king on May 6?”

We all tried to solve this, and there was some interesting logic involved in our attempts, but even with the hint that working backwards would help, only one young lady in our class was able to solve it. She also solved it for six Dukes, and discovered a pattern that followed for even and odd numbers of Dukes. I have given a few hints, but I am not going to give the solution in case others might like to try it.

I have noticed that in order to solve any of these three puzzles, not only must probabilities for each action be considered, but one must have a good understanding of human nature as well. These are not merely about numbers, but also involve a fair amount of psychology. Two things I take away from this: 1) sometimes it is necessary to work backwards to find a solution, and 2) math does not exist in a vacuum!

Hi! My name is Linda Nusser, and I am currently pursuing a BS in Mathematics at Pacific Lutheran University for the purpose of one day teaching math at the community college level. Although understanding math can be challenging at times, I thoroughly enjoy the feeling of accomplishment I get when a problem has been solved successfully. I have been very blessed to have teachers throughout my education who were very passionate about math, and they lit the spark of passion within me.

For the most part, math makes perfect sense to me, and I always feel badly for people who think math is too hard. The desire to help people discover that understanding math is well within their reach is what inspired me to become a teacher. I am a math tutor at Pierce College, and seeing a student’s eyes light up as they grasp a math concept for the first time is very gratifying. When being a student feels overwhelming, I remind myself that I am working toward fulfilling my lifelong dream of becoming a teacher. This is one of the prizes I am pressing toward.

I was asked to discuss the most interesting class that I have taken at PLU, and I found this to be a very tall order. Every course I have taken has been enlightening, and the professors are wonderful. To choose the “most” interesting is very difficult, but after much thought I have decided it was the Intro to Computer Science class. Computer programming was new territory for me, and learning the language and how to use it effectively was very time-consuming. But I liked the mix of learning a “foreign language” and then using that language to perform procedures and solve problems that included math. I was amazed at how much is involved in creating and running even the simplest programs, and I felt euphoric every time a program worked the way it was supposed to. As a result of my own experience, I found myself in awe of the amazing things that programmers do.

Last, but certainly not least, is the Capstone project. At this point, I really don’t have a clue what I would like to do.  I have taken three different classes on statistics and probability, and I find these topics intriguing and relevant to our world. The application of statistics concepts can be found in nearly every aspect of life. Perhaps performing a hypothesis test on a claim, or using probabilities in some way, would be interesting. I don’t know what I want to do with this, though, and I will definitely need some ideas and direction.



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  • gramsonjanessa: I can't wait to listen to your capstone presentation in the spring! Your proposal was really interesting and I'm interested to see how the linear alge
  • dewittda: This is impressive! I thought I was good because I solved a rubik’s cube once in an hour. I served with a guy in the Air Force who could solve a r
  • ZeroSum Ruler: The Euclidean algorithm should me the mainstream way we teach students how to find the GCF. Why isn't it? A mystery.

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