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SMC: MATH 339 Discrete Mathematics

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SMC: MATH 339 Discrete Mathematics

Mathematics
Author
Rohatgi
Publisher
Saint Mary's College
Source
LibreTexts
License
CC BY-NC-SA
Language
EN
Category
Basic Sciences
Read online Download PDF (open licence)
Contents· 52 sections
  1. 0: Introduction and Preliminaries
  2. 0.1: What is Discrete Mathematics?
  3. 0.2: Mathematical Statements
  4. 0.3: Sets
  5. 0.4: Functions
  6. 0.E: Introduction and Preliminaries (Exercises)
  7. 1: Counting
  8. 1.1: Additive and Multiplicative Principles
  9. 1.2: Binomial Coefficients
  10. 1.3: Combinations and Permutations
  11. 1.4: Combinatorial Proofs
  12. 1.5: Stars and Bars
  13. 1.6: Advanced Counting Using PIE
  14. 1.7: Pigeonhole Principle
  15. 1.E: Counting (Exercises)
  16. 1.S: Counting (Summary)
  17. 2: Sequences
  18. 2.1: Definitions
  19. 2.2: Arithmetic and Geometric Sequences
  20. 2.3: Polynomial Fitting
  21. 2.4: Solving Recurrence Relations
  22. 2.5: Induction
  23. 2.E: Sequences (Exercises)
  24. 2.S: Chapter Summary
  25. 3: Symbolic Logic and Proofs
  26. 3.1: Prelude to Symbolic Logic and Proofs
  27. 3.2: Propositional Logic
  28. 3.3: Proofs
  29. 3.E: Symbolic Logic and Proofs (Exercises)
  30. 3.S: Symbolic Logic and Proofs (Summary)
  31. 4: Algorithms
  32. 4.1: Big-O Notation
  33. 4.2: Some Algorithms
  34. 4.E: Exercises
  35. 5: Graph Theory
  36. 5.1: Prelude to Graph Theory
  37. 5.2: Definitions
  38. 5.3: Planar Graphs
  39. 5.4: Coloring
  40. 5.5: Euler Paths and Circuits
  41. 5.6: Matching in Bipartite Graphs
  42. 5.7: Weighted Graphs and Dijkstra's Algorithm
  43. 5.8: Trees
  44. 5.9.1: Tree Traversal
  45. 5.9.2: Spanning Tree Algorithms
  46. 5.9.3: Transportation Networks and Flows
  47. 5.E: Graph Theory (Exercises)
  48. 5.S: Graph Theory (Summary)
  49. 6: Additional Topics
  50. 6.1: Generating Functions
  51. 6.2: Introduction to Number Theory
  52. 6.E: Additional Topics (Exercises)