A Preliminary Report

     I have been reading the book Why Beauty is Truth by Ian Stewart. As the subtitle tells us, it is "A History of Symmetry". This is a key thing to remember in reading this book. Having not completed the book yet, I do not yet know what is yet to come, but thus far the story is not only about the history of symmetry, but rather the history of all mathematics.

     As most stories about the history of something start, this one starts at the beginning. In this case, we start with the Babylonian time. Stewart describes the different eras that follow, describing both the major players and the important findings they had made. These are not just stories about solely the mathematics that they found, Stewart tends to delve into their personal lives as well giving a background to who they were. Another great part about this book is that when describing the mathematical findings, there is also a description of the why. Knowing why the breakthrough was important or why the proof failed but still had a big impact are just as important as what these things were because it allows us as the readers to understand more of the time period and what was important to them and how it has effected each time period following.

     One drawback to this book is the daunting task that it has taken on. To be able to share the history of Mathematics and that of symmetry, it is tough work to do in the 280 pages that the book has. While mostly everything needed to understand the mathematics found within the pages, it is introduced only briefly. Also, Stewart mentions that he will stray away from listing equations, which results in lengthy narratives that describe the equation. This isn't all bad though, as reading about the equation allows you to see more of the "why" and "how" opposed to just knowing you can plug in numbers and have it worked. This shows more of the process involved rather than the end product.

     I hope as I continue to read this book that it talks more about symmetry in general. Whether it be how the ideas came about or the process of using it. As the book is about the history of symmetry, one would hope for a little more focus on the topic. Although learning about the history of mathematics does entail this concept of symmetry, so I can't be too disappointed by this.

Teachings of Old & New

While reading through a discussion board post from a Liberal Studies course that I am taking, I came across the quote "Are textbooks printed in order to teach children, or are the contents of these textbooks to be controlled by the Southern oligarchy and the commercial health of publishing houses?" from Report From Occupied Territory, page 733. This excerpt is found in a book of Collected Essays by James Baldwin. This brought me to thinking about how students were taught previously and how they are being taught today. As per most of my homework experience from elementary school, my parents could help me if it was something they learned. That is, if it followed an algorithm that they learned from their schooling, they could show me how to do it. Now, however, students are not encouraged to memorize a formula or algorithm, but rather understand how the formula works and where it comes from. Students are still (normally) taught the algorithm in the end, but work through it to understand. Mathematics seems to have transitioned from just doing a problem to get an answer to understanding how to solve a problem. More than likely those who only learned the algorithm at one time knew the underlying mechanics, but that part doesn't stick with you very easily. Now students are even more encouraged to understand those mechanics so that they can apply that knowledge to a problem that may look slightly different.

To Win or Not To Win

Playing games in Math classes can be fun and enjoyable, but also can be a way of learning. In class the other day we played a game much like master mind in the sense that you have to try to match your sequence to your opponents. This game differs from master mind by the way you play. Player 1 is given a 6x6 array in which to start the game, Player 1 chooses a sequence of 1's and 0's to fill in the first row of the 6x6 array. After this is done, Player 2, in their 1x6 array, fills in a single 1 or 0. This process continues until Player 1 fills in the 6th row of their array and Player 2 fills in their last square. The goal, much like master mind, is for Player 1 to end with the same sequence that Player 2 creates, allowing Player 1 to win. For Player 2 to win, they must ensure that Player 1 does not match their sequence.

The Book of Choice