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Algebra

A Computational Introduction

by John Scherk

Algebra

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Book Description

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.

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).

Table of Contents

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

Book Details

Title
Algebra
Subject
Science and Mathematics
Publisher
Self-publishing
Published
2009
Pages
419
Edition
1
Language
English
PDF Size
2.0 MB
License
CC BY-NC-SA

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