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introduction to abstract algebra 2e, jonathan smith [pdf]

Introduction to Abstract Algebra (2nd Edition) by Smith Jonathan D. H

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Introduction to Abstract Algebra (2nd Edition) written by Smith Jonathan D. H. , Iowa State University, Ames, Iowa, USA.

Introduction to Abstract Algebra (2nd Edition) written by Smith Jonathan D. H. cover the following topics.

• 1. NUMBERS
1.1 Ordering numbers
1.2 The Well-Ordering Principle
1.3 Divisibility
1.4 The Division Algorithm
1.5 Greatest common divisors
1.6 The Euclidean Algorithm
1.7 Primes and irreducibles
1.8 The Fundamental Theorem of Arithmetic
1.9 Exercises
1.10 Study projects
1.11 Notes

• 2. FUNCTIONS
2.1 Specifying functions
2.2 Composite functions
2.3 Linear functions
2.4 Semigroups of functions
2.5 Injectivity and surjectivity
2.6 Isomorphisms
2.7 Groups of permutations
2.8 Exercises
2.9 Study projects
2.10 Notes
2.11 Summary

• 3. EQUIVALENCE
3.1 Kernel and equivalence relations
3.2 Equivalence classes
3.3 Rational numbers
3.4 The First Isomorphism Theorem for Sets
3.5 Modular arithmetic
3.6 Exercises
3.7 Study projects
3.8 Notes

• 4. GROUPS AND MONOIDS
4.1 Semigroups
4.2 Monoids
4.3 Groups
4.4 Componentwise structure
4.5 Powers
4.6 Submonoids and subgroups
4.7 Cosets
4.8 Multiplication tables
4.9 Exercises
4.10 Study projects
4.11 Notes

• 5. HOMOMORPHISMS
5.1 Homomorphisms
5.2 Normal subgroups
5.3 Quotients
5.4 The First Isomorphism Theorem for Groups
5.5 The Law of Exponents
5.6 Cayley’s Theorem
5.7 Exercises
5.8 Study projects
5.9 Notes

• 6. RINGS
6.1 Rings
6.2 Distributivity
6.3 Subrings
6.4 Ring homomorphisms
6.5 Ideals
6.6 Quotient rings
6.7 Polynomial rings
6.8 Substitution
6.9 Exercises
6.10 Study projects
6.11 Notes

• 7. FIELDS
7.1 Integral domains
7.2 Degrees
7.3 Fields
7.4 Polynomials over fields
7.5 Principal ideal domains
7.6 Irreducible polynomials
7.7 Lagrange interpolation
7.8 Fields of fractions
7.9 Exercises
7.10 Study projects
7.11 Notes

• 8. FACTORIZATION
8.1 Factorization in integral domains
8.2 Noetherian domains
8.3 Unique factorization domains
8.4 Roots of polynomials
8.5 Splitting fields
8.6 Uniqueness of splitting fields
8.7 Structure of finite fields
8.8 Galois fields
8.9 Exercises
8.10 Study projects
8.11 Notes

• 9. MODULES
9.1 Endomorphisms
9.2 Representing a ring
9.3 Modules
9.4 Submodules
9.5 Direct sums
9.6 Free modules
9.7 Vector spaces
9.8 Abelian groups
9.9 Exercises
9.10 Study projects
9.11 Notes

• 10. GROUP ACTIONS
10.1 Actions
10.2 Orbits
10.3 Transitive actions
10.4 Fixed points
10.5 Faithful actions
10.6 Cores
10.7 Alternating groups
10.8 Sylow Theorems
10.9 Exercises
10.10 Study projects
10.11 Notes

• 11. QUASIGROUPS
11.1 Quasigroups
11.2 Latin squares
11.3 Division
11.4 Quasigroup homomorphisms
11.5 Quasigroup homotopies
11.6 Principal isotopy
11.7 Loops
11.8 Exercises
11.9 Study projects
11.10 Notes

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• A History of Abstract Algebra by Jeremy Gray
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