Garrett P. Intro Abstract Algebra

Garrett P. Intro Abstract Algebra — 1997-8 - 200 p.
Выходные данные неизвестны.Basic Algebra of Polynomials.
Induction and the Well-ordering Principle.
Sets.
Some counting principles.
The Integers.
Unique factorization into primes.
(*) Prime Numbers.
Sun Ze's Theorem.
Good algorithm for exponentiation.
Fermat's Little Theorem.
Euler's Theorem, Primitive Roots, Exponents, Roots.
(*) Public-Key Ciphers.
(*) Pseudoprimes and Primality Tests.
Vectors and matrices.
Motions in two and three dimensions.
Permutations and Symmetric Groups.
Groups: Lagrange's Theorem, Euler's Theorem.
Rings and Fields: denitions and rst examples.
Cyclotomic polynomials.
Primitive roots.
Group Homomorphisms.
Cyclic Groups.
(*) Carmichael numbers and witnesses.
More on groups.
Finite elds.
Linear Congruences.
Systems of Linear Congruences.
Abstract Sun Ze Theorem.
(*) The Hamiltonian Quaternions.
More about rings.
Tables.