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abstract algebra john beachy, william blair [pdf]

### Abstract Algebra by John A. Beachy and William D. Blair

MathSchoolinternational.com contain houndreds of Free Math e-Books. Which cover almost all topics of mathematics. To see an extisive list of Abstract Algebra eBooks . We hope mathematician or person who’s interested in mathematics like these books. Abstract Algebra written by John A. Beachy and William D. Blair . This is an other great mathematics book cover the following topics.

• Introduction
Some history, Biographies (from the MacTutor History of Mathematics archives), Some help with logic and proofs, Links to some algebra sites

• Chapter 1: INTEGERS
Divisors, Primes, Congruences, Integers Modulo n, Review

• Chapter 2: FUNCTIONS
Functions, Equivalence relations, Permutations, Review

• Chapter 3: GROUPS
Definition of a Group, Subgroups, Constructing Examples, Isomorphisms, Cyclic Groups, Permutation Groups, Homomorphisms, Cosets, Normal Subgroups, and Factor Groups

• Chapter 4: POLYNOMIALS
Fields; Roots of Polynomials, Factors, Polynomials with Integer Coefficients, Existence of Roots

• Chapter 5: COMMUTATIVE RINGS
Commutative rings; Integral Domains, Ring Homomorphisms, Ideals and Factor Rings, Quotient Fields

• Chapter 6: FIELDS
Algebraic Elements, Finite and Algebraic Extensions, Geometric Constructions, Splitting fields, Finite Fields, Irreducible Polynomials over Finite Fields, Quadratic Reciprocity

• Chapter 7: STRUCTURE OF GROUPS
Isomorphism Theorems, Automorphisms, Conjugacy, Groups Acting on Sets, The Sylow Theorems, Finite Abelian Groups, Solvable Groups, Simple Groups

• Chapter 8: GALOIS THEORY
The Galois Group of a Polynomial, Multiplicity of Roots, The Fundamental Theorem of Galois Theory, Solvability by Radicals, Cyclotomic Polynomials, Computing Galois Groups

• Chapter 9: UNIQUE FACTORIZATION
Principal Ideal Domains, Unique Factorization Domains, Some Diophantine Equations, INDEX

• Index of Definitions
• Index of Theorems
##### SHORTCUT TRICKS (Division)
• Divisible by 2 Shortcut trick
• Divisible by 3 Shortcut trick
• Divisible by 4 Shortcut trick
• Divisible by 5 Shortcut trick
• Divisible by 6 Shortcut trick • Divisible by 7 Shortcut trick • Divisible by 8 Shortcut trick • Divisible by 9 Shortcut trick
• Divisible by 10 Shortcut trick

##### Worksheets (Solved)

###### Integration     