Learn Discrete Math Complete Guide Offline

Un guide de référence complet pour apprendre mathématiques discrètes

Discrete Mathematics is a branch of mathematics involving discrete elements that uses algebra and arithmetic. It is increasingly being applied in the practical fields of mathematics and computer science. It is a very good tool for improving reasoning and problem-solving capabilities. This tutorial explains the fundamental concepts of Sets, Relations and Functions, Mathematical Logic, Group theory, Counting Theory, Probability, Mathematical Induction and Recurrence Relations, Graph Theory, Trees and Boolean Algebra.

Some of the topics Covered in the app are:

1. Set Theory

2. Decimal number System

3. Binary Number System

4. Octal Number System

5. Hexadecimal Number System

6. Binary Arithmetic

7. Sets and Membership

8. Subsets

9. Introduction to Logical Operations

10. Logical Operations and Logical Connectivity

11. Logical Equivalence

12. Logical Implications

13. Normal Forms and Truth Table

14. Normal Form of a well formed formula

15. Principle Disjunctive Normal Form

16. Principal Conjunctive Normal form

17. Predicates and Quantifiers

18. Theory of inference for the Predicate Calculus

19. Mathematical Induction

20. Diagrammatic Representation of Sets

21. The Algebra of Sets

22. The Computer Representation of Sets

23. Relations

24. Representation of Relations

25. Introduction to Partial Order Relations

26. Diagrammatic Representation of Partial Order Relations and Posets

27. Maximal, Minimal Elements and Lattices

28. Recurrence Relation

29. Formulation of Recurrence Relation

30. Method of Solving Recurrence Relation

31. Method for solving linear homogeneous recurrence relations with constant coefficients:

32. Functions

33. Introduction to Graphs

34. Directed Graph

35. Graph Models

36. Graph Terminology

37. Some Special Simple Graphs

38. Bipartite Graphs

39. Bipartite Graphs and Matchings

40. Applications of Graphs

41. Original and Sub Graphs

42. Representing Graphs

43. Adjacency Matrices

44. Incidence Matrices

45. Isomorphism of Graphs

46. Paths in the Graphs

47. Connectedness in Undirected Graphs

48. Connectivity of Graphs

49. Paths and Isomorphism

50. Euler Paths and Circuits

51. Hamilton Paths and Circuits

52. Shortest-Path Problems

53. A Shortest-Path Algorithm (Dijkstra Algorithm.)

54. The Traveling Salesperson Problem

55. Introduction to Planer Graphs

56. Graph Coloring

57. Applications of Graph Colorings

58. Introduction to Trees

59. Rooted Trees

60. Trees as Models

61. Properties of Trees

62. Applications of Trees

63. Decision Trees

64. Prefix Codes

65. Huffman Coding

66. Game Trees

67. Tree Traversal

68. Boolean Algebra

69. Identities of Boolean Algebra

70. Duality

71. The Abstract Definition of a Boolean Algebra

72. Representing Boolean Functions

73. Logic Gates

74. Minimization of Circuits

75. Karnaugh Maps

76. Dont Care Conditions

77. The Quine MCCluskey Method

78. Introduction to Lattices

79. The Transitive Closure of a Relation

80. Cartesian Product of Lattices

81. Properties of Lattices

82. Lattices as Algebraic System

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