Math 2001 Fall 15

MATH 2001: Introduction to Discrete Mathematics (Fall 2015)

Syllabus

New office hours:

Tuesday, 10 - 11 am Wednesday, 2 - 3 pm Thursday, 10 - 11 am

Schedule

  1. 08/24: arithmetic sum, infinitely many primes, Goldbach conjecture, continuum hypothesis
  2. 08/26: intro to sets (1.1) , Cartesian product (1.2)
  3. 08/28: subsets (1.3), power set (1.4), union, intersection, difference (1.5)
  4. 08/31: complement (1.6), laws of set operations, Venn diagrams (1.7)
  5. 09/02: proving identities for sets
  6. 09/04: infinite unions and intersections (1.8)
  7. 09/09: Russell's paradoxon (1.10), strategy for poison
  8. 09/11: statements (2.1), logical connectives (2.2)
  9. 09/14: if (2.3), truth tables (2.5), logical equivalence (2.6)
  10. 09/16: iff (2.4)
  11. 09/18: quantifiers (2.7)
  12. 09/21: negating quantifiers
  13. 09/23: counting, Towers of Hanoi
  14. 09/25: lists, permutations (3.1,, 3.2)
  15. 09/27: binomials (3.3)
  16. 09/30: first midterm
  17. 10/02: binomial theorem (3.4)
  18. 10/05: inclusion-exclusion (3.5)
  19. 10/07: combinations with repetitions
  20. 10/09: integers, divisibility, direct proofs (4.2, 4.3)
  21. 10/12: gcd, lcm, Euclidean algorithm
  22. 10/14: division algorithm, proof by contradiction
  23. 10/16: Bezout's identity, contrapositive proof
  24. 10/19: checking for primes, proof methods
  25. 10/21: proof by contradiction
  26. 10/23: congruences (5.2)
  27. 10/26: induction, sums (10)
  28. 10/28: Bernoulli's inequality
  29. 10/30: strong induction
  30. 11/02: fundamental theorem of arithmetic
  31. 11/04: second midterm
  32. 11/06: gcd, lcm
  33. 11/09: relations and their properties (11.1, 11.5)
  34. 11/11: partial orders, equivalences (11.2)
  35. 11/13: partitions (11.3)
  36. 11/16: integers mod n (11.4), Diffie-Hellman key exchange
  37. 11/18: functions (12)
  38. 11/20: injective, surjective, bijective
  39. 11/30: composition
  40. 12/02: inverse functions
  41. 12/04: inverse functions
  42. 12/07: cardinality of sets, countably infinite (13.1)
  43. 12/09: uncountable sets (13.2)
  44. 12/11: REVIEW
The numbering refers to sections in Hammack: Book of Proof.

Assignments

  1. due 09/02
  2. due 09/09
  3. due 09/16 and solutions
  4. due 09/23
  5. due 10/02
  6. due 10/09
  7. due 10/16
  8. due 10/23
  9. due 10/30
  10. due 11/06
  11. due 11/13
  12. due 11/20
  13. due 12/04
  14. due 12/09

Handouts

  1. sets/logic
  2. combinatorics
  3. integers
  4. review