Tag: Galois Theory

Professor Stewart’s Incredible Numbers

Amazon just informed me of a new book which is the #1 New Release Math Book on Amazon!

The book is titled: Professor Stewart’s Incredible Numbers.

At its heart, mathematics is about numbers, our fundamental tools for understanding the world. In Professor Stewart’s Incredible Numbers, Ian Stewart offers a delightful introduction to the numbers that surround us, from the common (Pi and 2) to the uncommon but no less consequential (1.059463 and 43,252,003,274,489,856,000). Along the way, Stewart takes us through prime numbers, cubic equations, the concept of zero, the possible positions on the Rubik’s Cube, the role of numbers in human history, and beyond! An unfailingly genial guide, Stewart brings his characteristic wit and erudition to bear on these incredible numbers, offering an engaging primer on the principles and power of math.

Previously, I read Galois Theory, Third Edition (Chapman Hall/Crc Mathematics), also by Ian Stewart, and I have to say his style is very accessible to the average reader. Not overly technical or abstract, he actually explains Galois Theory in as concrete a way as possible, which is not easy, since Galois Theory is one of the most abstract topics in mathematics.

I read the Third Edition, featured above, but lately there is a newer and better fourth edition: Galois Theory, Fourth Edition.

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Trisecting an Angle (Possible?) [Very Interesting Videos]

In O Level E Maths, we learn how to bisect an angle using compass and straightedge (ruler). However, is it possible to trisect an angle?

It turns out it is impossible! This took 2000 years to prove, and requires the use of a very difficult theory called Galois Theory.

Check out this interesting video on trisecting angles:

It turns out it is possible to trisect angles using Origami though:

Featured Book:

Galois’ Theory Of Algebraic Equations

Galois’ Theory of Algebraic Equations gives a detailed account of the development of the theory of algebraic equations, from its origins in ancient times to its completion by Galois in the nineteenth century. The main emphasis is placed on equations of at least the third degree, i.e. on the developments during the period from the sixteenth to the nineteenth century. The appropriate parts of works by Cardano, Lagrange, Vandermonde, Gauss, Abel and Galois are reviewed and placed in their historical perspective, with the aim of conveying to the reader a sense of the way in which the theory of algebraic equations has evolved and has led to such basic mathematical notions as “group” and “field”. A brief discussion on the fundamental theorems of modern Galois theory is included. Complete proofs of the quoted results are provided, but the material has been organized in such a way that the most technical details can be skipped by readers who are interested primarily in a broad survey of the theory. This book will appeal to both undergraduate and graduate students in mathematics and the history of science, and also to teachers and mathematicians who wish to obtain a historical perspective of the field. The text has been designed to be self-contained, but some familiarity with basic mathematical structures and with some elementary notions of linear algebra is desirable for a good understanding of the technical discussions in the later chapters.