Sunday, April 02, 2006

Non-fiction - "Abel's Proof"

After reading "The Equation that Couldn't Be Solved" I wanted to read more about the problem of solving equations, but wanted to read a book that had more math in it. Peter Pesic's book "Abel's Proof" was it. This book covered similar ground as "The Equation the Couldn't Be Solved", but got deeper into the actual mathematics.

In the history of equation solving the author explains the methods that Babylonians used to solve quadratic equations. Using the basic geometrical idea of the Babylonians method it is very easy to derive the standard formula for the roots of the quadratic equation.

One interesting part of the history of mathematics is the rise of algebra The modern notation of using variables in formulars was invented by Francois Viete in the 16th century. Imagine trying to solve equations without using variables.

The main section of the book discusses Abel' proof that equations of degree five or greater cannot be solved with radicals. Reading the proof I can understand the basic idea, but not all the details yet.

Final section of the book includes discussion of Galois theory and implications of symetries.

Finally, the text of Abel's actual paper, with annotations, is included as an appendix.


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