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.