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Intro Abstract Algebra by Paul Garrett

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Intro Abstract Algebra written by Paul Garrett . This is an other great mathematics book cover the following topics.

  • (1) Basic Algebra of Polynomials
  • (2) Induction and the Well-ordering Principle
  • (3) Sets
  • (4) Some counting principles
  • (5) The Integers
  • (6) Unique factorization into primes
  • (7) (*) Prime Numbers
  • (8) Sun Ze's Theorem
  • (9) Good algorithm for exponentiation
  • (10) Fermat's Little Theorem
  • (11) Euler's Theorem, Primitive Roots, Exponents, Roots
  • (12) (*) Public-Key Ciphers
  • (13) (*) Pseudoprimes and Primality Tests
  • (14) Vectors and matrices
  • (15) Motions in two and three dimensions
  • (16) Permutations and Symmetric Groups
  • (17) Groups: Lagrange's Theorem, Euler's Theorem
  • (18) Rings and Fields: de nitions and rst examples
  • (19) Cyclotomic polynomials
  • (20) Primitive roots
  • (21) Group Homomorphisms
  • (22) Cyclic Groups
  • (23) (*) Carmichael numbers and witnesses
  • (24) More on groups
  • (25) Finite elds
  • (26) Linear Congruences
  • (27) Systems of Linear Congruences
  • (28) Abstract Sun Ze Theorem
  • (29) (*) The Hamiltonian Quaternions
  • (30) More about rings
  • (31) Tables

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