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Discrete_Math_Specialization

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.

Language : python

Mathematical thinking in computer science

  • 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

Combinatorics and Probability

  • 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

Introduction To Graph Theory :

  • 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

Number theory and Cryptography

  • 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

The Delivery Problem

  • 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)

Resouces