Math 2001 Spring 18

MATH 2001: Introduction to Discrete Mathematics (Spring 2018)

Syllabus

Final Exam:

Sunday 05/06, 7:30-10 pm, in class
Exam problems might look something like this: review problems

Office hours:

Monday 4-5 pm Tuesday 3-4 pm Wednesday 2-3 pm

Schedule

Numbers refer to sections in Hammack, Book of Proof.
  1. 01/17: Gauss formula for 1+2+...+n, Euclid's proof for infinitely many primes
  2. 01/19: set builder notation, cardinality (1.1)
  3. 01/22: Cartesian products (1.2)
  4. 01/24: subsets, power set (1.3, 1.4)
  5. 01/26: union, intersection, difference, (1.5) complements (1.6), Venn diagrams (1.7)
  6. 01/29: proving inclusion and identities between sets, distributive law, de Morgan
  7. 01/31: indexed unions and intersections (1.8), Russell's paradox (1.10)
  8. 02/02: logic, and, or, not (2.1), truthtables (2.5)
  9. 02/05: implication (2.3)
  10. 02/07: LaTeX
  11. 02/09: if and only if (2.4)
  12. 02/12: quantifiers and negations (2.7)
  13. 02/14: Poison
  14. 02/16: permutations, factorial (3.1, 3.2)
  15. 02/19: binomial coefficients (3.3), review for midterm [pdf]
  16. 02/21: MIDTERM
  17. 02/23: Pascal's triangle (3.4)
  18. 02/26: binomial theorem (3.4), inclusion-exclusion (3.5)
  19. 02/28: integer solutions of x1+x2+...+xn = k
  20. 03/02: direct proofs, primes, divisibility (4.2)
  21. 03/05: gcd, lcm, Euclidean algorithm
  22. 03/07: division algorithm
  23. 03/09: Bezout's identity
  24. 03/12: direct proof, contrapositive, proof by contradiction
  25. 03/14: irrationality of root of 2
  26. 03/16: modular arithmetic
  27. 03/19: Diffie-Hellman key exchange
  28. 03/21: induction (10)
  29. 03/23: Bernoulli's inequality, strong induction (10.1)
  30. 04/02: review for midterm [pdf]
  31. 04/04: MIDTERM
  32. 04/06: strong induction, proof by minimal counterexample, fundamental theorem of arithmetic (10.1)
  33. 04/09: gcd and lcm via prime factorization, relations (11.1)
  34. 04/11: functions, reflexive, symmetric, antisymmetric, transitive relations (11.1)
  35. 04/13: partial orders, equivalence relations (11.2)
  36. 04/16: integers modulo n, addition, multiplication well-defined (11.4)
  37. 04/18: functions, domain, codomain, range (12.1)
  38. 04/20: injective, surjective, bijective functions, pigeonhole principle (12.3)
  39. 04/23: composition (12.4)
  40. 04/25: inverse functions (12.5)
  41. 04/27: counting injective, surjective, bijective functions on finite sets
  42. 04/30: inverse functions (12.5)
  43. 05/02: review for final

Homework

  1. due 01/19 [pdf] [tex]
  2. due 01/26 [pdf] [tex]
  3. due 02/02 [pdf] [tex]
  4. due 02/09 [pdf] [tex]
  5. due 02/16 [pdf] [tex]
  6. due 02/23 [pdf] [tex]
  7. due 03/02 [pdf] [tex]
  8. due 03/09 [pdf] [tex]
  9. due 03/16 [pdf] [tex]
  10. due 03/23 [pdf] [tex]
  11. due 04/06 [pdf] [tex]
  12. due 04/13 [pdf] [tex]
  13. due 04/20 [pdf] [tex]
  14. due 04/27 [pdf] [tex]

Writing assignments

  1. due 02/14 [pdf]
  2. first draft due 02/21 [pdf] [tex], final draft due 02/28, see comments [pdf]
  3. first draft due 03/16 [pdf] [tex], final draft due 03/23
  4. first draft due 04/13 [pdf] [tex], final draft due 04/18
  5. first draft due 04/25 [pdf] [tex], final draft due 05/02

Texts

Richard Hammack. The Book of Proof. Creative Commons, 2nd edition, 2013. Available for free

Handouts

  1. How to show two sets are equal [pdf] [tex]
  2. Sets vs Logic [pdf] [tex]
  3. Combinatorics [pdf] [tex]
  4. Proof strategies [pdf] [tex]
  5. Integers [pdf]
  6. Relations [pdf] [tex]
  7. Functions [pdf] [tex]
  8. 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.