this specialization about my studying and training discrete math specialization on coursera. It is divide into 4 courses with good final project about the deliverly problem.
- Making Convincing Arguments
- How to find an example : brute force, backtraking, optimal solution, simple puzzles
- Recursion and Induction : tower of hanio, binarysearch, proof by induction , contradiction
- Logic : Examples, counterExamples, Logic, antimagic square, pigeonhole Principle, proof by contradiction
- Invariant : Double Counting, invariants, termination, even and odd numbers
- project_15_puzzle : permutations, cycle notation, 15-puzzle, A* serach
- Basic Counting : rule of sum, rule of product, tuples, comination, permutation, Basic counting principle
- Binomial Coefficients : combinatorics, tuples, permutation, pascal's triangle, counting
- ِِِAdvanced Counting : combinatorics with repetition, permutation with indistinguishable objects.
- Probability : bean-machine, probability calculation, tree diagram, conditional probability, Monty Hall paradox
- Random Variable and expected value : random variable, expected value of an expriment, linearity of expectation, Markouv inequality
- Dice_game_Project : dice game, probability is tricky and sometimes counter-intuitive
- What is a Graph? : directed graphs, undirected graphs, connected components, Guarini puzzle, cyclic graph, apps, bipartite graphs
- CYCLES : Handshake lemma, connected components, eulerian cycle, Hamiltonain cycle, overlap graph, Debruijn graph
- Graph Classes : Tree, Bipartite Graphs, Planar Graphs, MST, kruskal's algorithm, prime's algorithm
- Graph Parameters : Graph coloring, Cliques and independent sets, vertex cover, ramzy numbers
- Flows and Matchings : networks, flow, cuts, stable matching, Gale-shabley algorithm
- Modular Arithmetic : Divisability, remainder, binary system, modular division
- Euclid's Algorithm : Euclid's algorithm, extended Euclidean algorithm, modular division, multiplicative inverse of module, Diophantine equations
- Building Blocks for Cryptography : prime factorization, chinese remainder theorem, Modular exponentiation, Fermat's Little Theorem, Euler's Theorem, Euler't Totient
- Cryptography : One Time Pad, RSA cryptoSystem, RSA attacks
- BruteForce and Approximation : travel sales man problem, permutations search, nearset neighbor algorithm
- Exact Algorithms : Branch and Bound algorithm, dynamic programming algorithm, linear programming
- Approximation Algorithms : local search, 2-approximation(MST_based)