Description
Elementary Number Theory Divisibility Primes and factorization Congruences Solving congruences Theorems of Fermat and Euler RSA cryptosystem Groups De nition of a group Examples of groups Subgroups Cosets and Lagrange’s Theorem Rings Defiition of a ring Subrings and ideals Ring homomorphisms Integral domains Fields Definition and basic properties of a field Finite Fields Number of elements in a finite field How to construct finite fields Properties of finite fields Polynomials over finite fields Permutation polynomials Applications Orthogonal latin squares Die/Hellman key exchange Vector Spaces Definition and examples Basic properties of vector spaces Subspaces Polynomials Basics Unique factorization Polynomials over the real and complex numbers Root formulas Linear Codes Basics Hamming codes Encoding Decoding Further study Exercises Appendix Mathematical induction Well-ordering Principle Sets Functions Permutations Matrices Complex numbers Hints and Partial Solutions to Selected Exercises
