Intro to Abstract Algebra
by Paul Garrett
Number of pages: 200
The text covers basic algebra of polynomials, induction and the well-ordering principle, sets, counting principles, integers, unique factorization into primes, prime numbers, Sun Ze's theorem, hood algorithm for exponentiation, Fermat's little theorem, Euler's theorem, public-key ciphers, pseudoprimes and primality tests, vectors and matrices, motions in two and three dimensions, permutations and symmetric groups, rings and fields, etc.
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by Maya Mohsin Ahmed
The focus of this book is applications of Abstract Algebra to polynomial systems. It explores basic problems like polynomial division, solving systems of polynomials, formulas for roots of polynomials, counting integral roots of equations, etc.
by F. Oggier - Nanyang Technological University
Contents: Group Theory (Groups and subgroups, The isomorphism theorems); Ring Theory (Rings, ideals and homomorphisms); Field Theory (Field extension and minimal polynomial); Galois Theory (Galois group and fixed fields).
by Peter J. Cameron - Queen Mary, University of London
After a short introductory chapter consisting mainly of reminders about such topics as functions, equivalence relations, matrices, polynomials and permutations, the notes fall into two chapters, dealing with rings and groups respectively.
by Donu Arapura - Purdue University
This book covers basic abstract algebra. Rather than spending a lot of time on axiomatics and serious theorem proving, the author wanted to spend more time with examples, simple applications and with making scenic detours.