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)

• The_specialization
• the_algorithms_and_data_sturcture_specializaion
• Discrete_mathematics_and_its_applications
• Your_second_mind_Google