Discrete mathematics 1000-212bMD

* Mathematical induction and recursion
* Finite sums
* Binomial Coefficients
* Permutations and partitions
* Generating functions with application
* Counting methods:
- enumerators
- inclusion-exclusion principle
* Asymptotics:
- asymptotic notation
- Master theorem
* Elementary number theory:
- divisibility, primes, factorization
- gcd and Euclid's algorithm
* modular arithmetic:
- Fermat's little theorem and Euler's theorem
- Chinese remainder theorem
- solving modular equations
* Elements of the cryptography: Miller-Rabin primality and the RSA system
* Graphs:
- paths, trees and cycles
- Euler and Hamilton cycles
- bipartite graphs, transversals and Hall theorem
- planarity
- coloring