**by John Scherk**

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This open book is an introduction to algebra for undergraduates who are interested in careers which require a strong background in mathematics. It will benefit students studying computer science and physical sciences, who plan to teach mathematics in schools, or to work in industry or finance. The book assumes that the reader has a solid background in linear algebra. For the first 12 chapters elementary operations, elementary matrices, linear independence and rank are important. In the second half of the book abstract vector spaces are used. Students will need to have experience proving results. Some acquaintance with Euclidean geometry is also desirable. In fact I have found that a course in Euclidean geometry fits together very well with the algebra in the first 12 chapters. But one can avoid the geometry in the book by simply omitting chapter 7 and the geometric parts of chapters 9 and 18. ### Table of Contents

### Book Details

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This open book is licensed under a Creative Commons License (CC BY-NC-SA). You can download Algebra ebook for free in PDF format (2.0 MB).

Chapter 1

Congruences

Chapter 2

Permutations

Chapter 3

Permutation Groups

Chapter 4

Linear Groups

Chapter 5

Groups

Chapter 6

Subgroups

Chapter 7

Symmetry Groups

Chapter 8

Group Actions

Chapter 9

Counting Formulas

Chapter 10

Cosets

Chapter 11

Sylow Subgroups

Chapter 12

Simple Groups

Chapter 13

Abelian Groups

Chapter 14

Polynomial Rings

Chapter 15

Symmetric Polynomials

Chapter 16

Roots of Equations

Chapter 17

Galois Groups

Chapter 18

Quartics

Chapter 19

The General Equation of the nth Degree

Chapter 20

Solution by Radicals

Chapter 21

Ruler-and-Compass Constructions

Title

Algebra

Subject

Science and Mathematics

Publisher

Self-publishing

Published

2009

Pages

419

Edition

1

Language

English

PDF Size

2.0 MB

License

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