Math 3325 – Introduction to Discrete Mathematics

This course is intended to provide an introduction to the conceptual basis underlying high school mathematics. Emphasis will be placed on the in-depth understanding of fundamental mathematical ideas and the associated modes of reasoning and proof rather than on superficial coverage of many topics. The course will also help bridge the conceptual gap between the pre-calculus/calculus sequence and more advanced courses in mathematics by fostering the mathematical maturity necessary for success in those courses.

Semester II, 2017-18

Syllabus

Download printable PDF.

Tutor for CCOM 3020 and MATE 3325.
Lillian González
Mon, Wed, Fri: 2-2:50
Tue, Thur: 11-11:50
Fri: 9-10:50
Place: 3rd floor tutorial room.

Miscellaneous Notes

  1. Review of Precalculus
  2. On Definition (Definition according to Aristotle)
  3. On Truth
  4. On Sets
  5. On implication
  6. Logic-Set theory Correspondence
  7. Truth tables
  8. Connectives
  9. A list of tautologies
  10. On validity
  11. A list of valid argument forms
  12. Some Axioms for Set Theory
  13. The Symmetric Difference of two sets.
  14. Extension of Induction to Well-founded Sets
  15. Inverse Functions
  16. Introduction to digraphs
  17. Digraph taxonomy
  18. Equivalence Relations
  19. Lattices
  20. Edge unlabelled Multigraphs
  21. Elementary Combinatorial Formulae
  22. Multisets
  23. Balls in Boxes
  24. On the Number of Surjections
  25. Function Digraphs
  26. Drawings of Function Digraphs
  27. Max–min inequality
  28. Summary of Lecture on the GCD
  29. Whitney’s Theorem

Homeworks

  1. Set Theory
  2. Induction
  3. Relations and Digraphs
  4. Functions
  5. Elementary combinatorics -Exercises for MATH 3026
  6. The Pigeonhole Principle
  7. Balls in Boxes
  8. Binary Relations and Digraphs
  9. The Natural Numbers

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