Phu Xuan University Library
|
PXU E-LIB
Sign in
A Spiral Workbook for Discrete Mathematics

External

A Spiral Workbook for Discrete Mathematics

In contrast to real numbers that have the property of varying "smoothly", the objects studied in discrete mathematics – such as integers, graphs, and statements in logic – do not vary smoothly in this way, but have distinct, separated values.

Combinatorics and Discrete MathematicsMathematics
Author
Harris Kwong
Publisher
State University of New York at Fredonia
Source
LibreTexts
License
CC BY-NC-SA
Language
EN
Category
Basic Sciences
Read online Download PDF (open licence)
Contents· 54 sections
  1. 01: Introduction to Discrete Mathematics
  2. 1.01: An Overview of Discrete Mathematics
  3. 1.02: Suggestions to Students
  4. 1.03: How to Read and Write Mathematics
  5. 1.04: Proving Identities
  6. 02: Logic
  7. 2.01: Propositions
  8. 2.02: Conjunctions and Disjunctions
  9. 2.03: Implications
  10. 2.04: Biconditional Statements
  11. 2.05: Logical Equivalences
  12. 2.06: Logical Quantiers
  13. 03: Proof Techniques
  14. 3.01: An Introduction to Proof Techniques
  15. 3.02: Direct Proofs
  16. 3.03: Indirect Proofs
  17. 3.04: Mathematical Induction - An Introduction
  18. 3.05: More on Mathematical Induction
  19. 3.06: Mathematical Induction - The Strong Form
  20. 04: Sets
  21. 4.01: An Introduction to Sets
  22. 4.02: Subsets and Power Sets
  23. 4.03: Unions and Intersections
  24. 4.04: Cartesian Products
  25. 4.05: Index Sets
  26. 05: Basic Number Theory
  27. 5.01: The Principle of Well-Ordering
  28. 5.02: Division Algorithm
  29. 5.03: Divisibility
  30. 5.04: Greatest Common Divisors
  31. 5.05: More on GCD
  32. 5.06: Fundamental Theorem of Arithmetic
  33. 5.07: Modular Arithmetic
  34. 06: Functions
  35. 6.01: An Introduction to Functions
  36. 6.02: Denition of Functions
  37. 6.03: One-to-One Functions
  38. 6.04: Onto Functions
  39. 6.05: Properties of Functions
  40. 6.06: Inverse Functions
  41. 6.07: Composite Functions
  42. 07: Relations
  43. 7.01: Denition of Relations
  44. 7.02: Properties of Relations
  45. 7.03: Equivalence Relations
  46. 7.04: Partial and Total Ordering
  47. 08: Combinatorics
  48. 8.01: What is Combinatorics
  49. 8.02: Addition and Multiplication Principles
  50. 8.03: Permutations
  51. 8.04: Combinations
  52. 8.05: The Binomial Theorem
  53. 09: Appendices
  54. 9.01: Answers