Intro Abstract Algera - P.Garret
(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 Numb ers
(8) Sun Ze's Theorem
(9) Go o d algorithm for exp onentiation
(10) Fermat's Little Theorem
(11) Euler's Theorem, Primitive Ro ots, Exp onents, Ro ots
(12) (*) Public-Key Ciphers
(13) (*) Pseudoprimes and PrimalityTests
(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 p olynomials
(20) Primitive ro ots
(21) Group Homomorphisms
(22) Cyclic Groups
(23) (*) Carmichael numb ers 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 ab out rings
(31) Table
