Discrete Mathematics

Discrete Mathematics is a free Computer Science and Engineering handbook covering important course topics, detailed notes, diagrams, equations, formulas and study materials. Download this digital book and reference guide for Diploma, BE, BTech, BCA, BSc, MCA and other degree courses.

Explore 100 topics across 5 chapters on set theory, mathematical logic, relations, functions, recurrence relations, graph theory, trees, Boolean algebra and lattices. Useful for university exams, GATE preparation, viva, technical interviews, assignments and quick revision.

RELATED ENGINEERING BRANCHES
Computer Science Engineering (CSE), Information Technology (IT), Computer Engineering, Software Engineering, Artificial Intelligence, Data Science, Electronics Engineering and Mathematics.

82 LISTED TOPICS FROM 100

SET THEORY, NUMBER SYSTEMS & LOGIC
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 Connectives
11. Logical Equivalence
12. Logical Implications
13. Normal Forms and Truth Tables
14. Normal Form of a Well-Formed Formula
15. Principal Disjunctive Normal Form (PDNF)
16. Principal Conjunctive Normal Form (PCNF)
17. Predicates and Quantifiers
18. Inference Theory for Predicate Calculus
19. Mathematical Induction
20. Diagrammatic Representation of Sets
21. Algebra of Sets
22. Computer Representation of Sets

RELATIONS, FUNCTIONS & RECURRENCES
23. Relations
24. Representation of Relations
25. Introduction to Partial Order Relations
26. Diagrams of Partial Orders and Posets
27. Maximal and Minimal Elements and Lattices
28. Recurrence Relations
29. Formulation of Recurrence Relations
30. Methods for Solving Recurrence Relations
31. Linear Homogeneous Recurrences with Constant Coefficients
32. Functions

GRAPH THEORY & ALGORITHMS
33. Introduction to Graphs
34. Directed Graphs
35. Graph Models
36. Graph Terminology
37. Special Simple Graphs
38. Bipartite Graphs
39. Bipartite Graphs and Matchings
40. Applications of Graphs
41. Original Graphs and Subgraphs
42. Graph Representation
43. Adjacency Matrices
44. Incidence Matrices
45. Graph Isomorphism
46. Paths in Graphs
47. Connectedness in Undirected Graphs
48. Graph Connectivity
49. Paths and Isomorphism
50. Euler Paths and Circuits
51. Hamilton Paths and Circuits
52. Shortest-Path Problems
53. Dijkstra's Shortest-Path Algorithm
54. Traveling Salesperson Problem
55. Introduction to Planar Graphs
56. Graph Coloring
57. Applications of Graph Coloring

TREES & CODING
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

BOOLEAN ALGEBRA & CIRCUIT DESIGN
68. Boolean Algebra
69. Boolean Algebra Identities
70. Duality
71. Abstract Definition of Boolean Algebra
72. Representation of Boolean Functions
73. Logic Gates
74. Circuit Minimization
75. Karnaugh Maps
76. Don't-Care Conditions
77. Quine-McCluskey Method

LATTICES & ORDER THEORY
78. Introduction to Lattices
79. Transitive Closure of a Relation
80. Cartesian Product of Lattices
81. Properties of Lattices
82. Lattices as Algebraic Systems

Study with this free Discrete Mathematics ebook for engineering coursework, exam revision and practical problem-solving.

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