Math 2001 Fall 25

MATH 2001: Introduction to Discrete Mathematics (Fall 2025)

Syllabus

Schedule

Numbers refer to sections in Hammack, Book of Proof.
  1. 08/22: Gauss formula for 1+2+...+n, Euclid's proof for infinitely many primes
  2. 08/25: sets and elements, equality by Axiom of Extensionality (1.1), subsets (1.3), empty set is a subset of any set
  3. 08/27: set builder notation, Axiom of Specification (1.1), Russell's paradox (1.10), Axiom of Replacement, cardinality (size) of sets (1.1)
  4. 08/29: unordered and ordered pairs (Axiom of Pairing), Cartesian products of 2 and more sets (1.2)
  5. 09/03: Axiom of Power Set, size of power set of a finite set (1.4)
  6. 09/05 union (Axiom of Unions), intersection, difference, (1.5) complements (1.6), Venn diagrams (1.7)
  7. 09/08: laws of set operations, proving inclusion/equality between sets, indexed unions and intersections (1.8)
  8. 09/10: review of Zermelo-Fraenkel set theory, axiom of choice
  9. 09/12: logical statements, and, or, not (2.1), truth tables
  10. 09/15: implication, different formulations and negation (2.3), logical equivalence (2.5)
  11. 09/17: if and only if (2.4), truth tables and Boolean functions
  12. 09/19: universal and existential quantifiers and their negations (2.7) [worksheet on quantifiers]
  13. 09/22: multiple quantifiers as game with spoiler and duplicator, comparing set theoretic and logical operations
  14. 09/24: counting lists with and without repetition of elements (3.1, 3.2)
  15. 09/26: review for midterm [pdf], [worksheet on negations], [practice exam] [solutions]
  16. 09/29: MIDTERM 1
  17. 10/01: introduction to LaTeX, OverLeaf, first documents [tex], [pdf]
  18. 10/03: subtraction principle (3.3) counting k-element subsets by binomial coefficients, Pascal's triangle, Binomial Theorem (3.5) [pdf] [video]
  19. 10/06: inclusion-exclusion (3.7)
  20. 10/08: discussion of midterm 1, writing project 1: balance puzzle
  21. 10/10: integer solutions of x1+x2+...+xn = k, counting k-element multisets (3.8)
  22. 10/13: combinatorics review, lists with/without repetition where order matters/does not matter
  23. 10/15: divisibility for integers (4.2), direct proof, greatest common divisor
  24. 10/17: Euclidean algorithm (4.2), Bezout's identity (Prop 7.1)
  25. 10/20: Die Hard, least common multiple, division algorithm, proof by contradiction
  26. 10/22: primes, Euclid's lemma, contrapositive proof, Poison
  27. 10/24: proof strategies (direct, contrapositive, contradiction, see handout `Proof strategies'), irrationality of the square root of 2 (6.1)
  28. 10/27: integers modulo n, Diffie-Hellman key exchange (Section 7 of handout `Integers')
  29. 10/29: induction proofs: sum 1+3+...+(2n-1), Binomial Theorem, Bernoulli's inequality (10.1)
  30. 10/31: REVIEW [pdf], [practice exam] [solutions]
  31. 11/03: MIDTERM 2

Homework (submit before class)

  1. due 09/05 [pdf] [tex] [solutions]
  2. due 09/12 [pdf] [tex] [solutions]
  3. due 09/19 [pdf] [tex] [solutions]
  4. due 09/26 [pdf] [tex] [solutions]
  5. due 10/03 [pdf] [tex] [solutions]
  6. due 10/10 [pdf] [tex] [solutions]
  7. due 10/17 [pdf] [tex] [solutions]
  8. due 10/24 [pdf] [tex] [solutions]
  9. due 10/31 [pdf] [tex] [solutions]
  10. due 11/07 [pdf] [tex]

Writing assignments (submit before class)

  1. due Wednesday 10/08, upload source code *.tex and compiled file *.pdf to Canvas [pdf], use the LaTeX template [tex]
  2. first draft due 10/15 [pdf] [tex], final draft due 10/22, see comments [pdf]
  3. first draft due 10/29 [pdf] [tex], see comments [pdf] final draft due 11/05

Handouts

  1. Axioms of Zermelo-Fraenkel set theory [pdf] [tex]
  2. How to show two sets are equal [pdf] [tex]
  3. Sets vs Logic [pdf] [tex]
  4. Combinatorics [pdf] [tex]
  5. Integers [pdf]
  6. Proof strategies [pdf]

Scientific writing

There is a variety of word-processing software for writing Mathematics. LaTeX is the most widespread. You can use it with many text editors or via some cloud-based service, like OverLeaf.