Math 2001 Fall 16

MATH 2001: Introduction to Discrete Mathematics (Fall 2016)

Syllabus

Final Exam:

Wednesday 12/14, 4:30-7 pm, in class
Exam problems might look something like this: review problems

Office hours:

Tuesday 3-4 pm Wednesday 11-12 am Friday 10-11 am

Schedule

Numbers refer to sections in Hammack, Book of Proof.
  1. 08/22: arithmetic sum, infinitely many primes, Goldbach conjecture, continuum hypothesis
  2. 08/24: sets (1.1)
  3. 08/26: cartesian products (1.2)
  4. 08/29: subsets (1.3), power set (1.4) union, intersection, difference (1.5)
  5. 08/31: complement (1.6), laws of set operations, Venn diagrams (1.7)
  6. 09/02: proving identities for sets
  7. 09/07: infinite unions and intersections (1.8), Russell's paradoxon (1.10)
  8. 09/09: poison, latex
  9. 09/12: logic, and, or, not (2.1) truthtables (2.5), logical equivalence (2.6)
  10. 09/14: if (2.3)
  11. 09/16: review for midterm
  12. 09/19: MIDTERM
  13. 09/21: iff (2.4), quantifiers (2.7)
  14. 09/23: permutations, factorial, binomial theorem
  15. 09/26: inclusion-exclusion
  16. 09/26: inclusion-exclusion
  17. 09/30: (un)ordered collections with/without repetiton
  18. 10/03: primes, divisibility
  19. 10/05: division algorithm
  20. 10/07: extended Euclidean algorithm
  21. 10/10: Bezout's identity
  22. 10/12: direct proof, contrapositive, contradiction
  23. 10/14: irrationality of root 2
  24. 10/17: modular arithmetic
  25. 10/19: Diffie-Hellmann key exchange
  26. 10/21: induction 10.1
  27. 10/24: REVIEW
  28. 10/26: MIDTERM
  29. 10/28: discussion of midterm, strong induction, minimal counterexample
  30. 10/31: Fundamental Theorem of Arithmetic (10.1)
  31. 11/02: gcd, lcm
  32. 11/04: relations, functions, reflexive, symmetric, anti-symmetric, transitive (11.1)
  33. 11/07: partial orders, equivalence relations (11.2)
  34. 11/09: partitions (11.3)
  35. 11/11: integers mod n (11.4)
  36. 11/14: functions (12)
  37. 11/16: injective, surjective, bijective
  38. 11/18: pigeon hole principle
  39. 11/28: composition, inverse functions
  40. 11/30: inverse functions
  41. 12/02: inverse functions
  42. 12/05: cardinality of sets, countably infinite (13.1)
  43. 12/07: uncountable sets (13.2)
  44. 12/09: REVIEW

Assignments

  1. due 08/24 [pdf] [tex]
  2. due 09/02 [pdf] [tex]
  3. due 09/09 [pdf] [tex]
  4. due 09/16 [pdf] [tex]
  5. due 09/23 [pdf] [tex]
  6. due 09/30 [pdf] [tex]
  7. due 10/07 [pdf] [tex]
  8. due 10/14 [pdf] [tex]
  9. due 10/21 [pdf] [tex]
  10. due 10/28 [pdf] [tex]
  11. due 11/04 [pdf] [tex]
  12. due 11/11 [pdf] [tex]
  13. due 11/18 [pdf] [tex]
  14. due 12/02 [pdf] [tex]
  15. due 12/07 [pdf] [tex]

Handouts

  1. Sets vs Logic [pdf] [pdf]
  2. Combinatorics [pdf] [tex]
  3. Integers [pdf] [tex]
  4. Review [pdf] [tex]

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 ShareLaTeX.
Here are the first files that we produced in class [pdf] [tex]
You can use files from the homework assignments as templates for your writing as well.