Math 187

Fall 2009

Diary

[home] [assignments] [diary][office hours][Test dates]

1. August 24, 2009:
   • Course description
   • Discuss core, outline of course
2. August 25, 2009:
   • Connectives and truth tables
   • Proof that if x and y are even integers, then x+y is an even integer
3. August 26, 2009:
   • Proof that for integers a, b and c: If a|b and b|c then a|c is true.
4. August 28, 2009:
   • Proof that if x > 1 is an integer then x³+1 is composite.
5. August 31, 2009:
   • The notion of a counter example.
   • Counter example to "If n is a positive integer then n²+n+41 is prime.".
   • Fermat numbers and Fermat primes.
   • Even perfect numbers and Mersenne primes.
6. September 1, 2009:
   • Modus ponens, tautologies and contrdictions.
7. September 2, 2009:
   • Problems from the text worked in class.
8. September 4, 2009:
   • Collected Assignment 1.
   • Counter example to "If n is a positive integer then n²+n+41 is prime.".
   • Fermat numbers and Fermat primes.
   • Even perfect numbers and Mersenne primes.
9. September 8, 2009:
   • Returned Assignment 1.
   • Counting: Multiplication principle
10. September 9, 2009:
    • Counting: Multiplication principle, factorials, examples
11. September 11, 2009:
    • Collected Assignment 2.
    • Sets and subsets
12. September 14, 2009:
    • Returned graded Assignment 2.
    • Quantifiers
13. September 15, 2009:
    • Set equality and subsets
14. September 16, 2009:
    • Collected Assignment 3.
    • Set operations: Powerset, union, intersection, symmetric difference, difference
    • Cardinality of the power set.
    • Principle of inclusion and exclusion.
15. September 18, 2009:
    • Combinatorial proofs: Inclusion and Exclusion.
16. September 21, 2009:
    • Combinatorial Proofs: n² = n(n-1) + n.
17. September 22, 2009:
    • Combinatorial Proofs: n³ = n(n-1)(n-2) + 3 n(n-1) + n.
    • n⁴ = ?.
18. September 23, 2009:
    • Review for Test 1.
19. September 25, 2009:
    • Administered Test 1.
20. September 28, 2009:
    • Returned Test 1.
    • Discussed some of the problems from Test 1.
21. September 29, 2009:
    • Combinatorial Proofs: 3ⁿ-1 = ?
22. September 30, 2009:
    • Combinatorial Proofs: 3ⁿ-1 = ?
23. October 2, 2009:
    • Relations
24. October 5, 2009:
    • Symmetry, Reflexivity
25. October 6, 2009:
    • Antisymmetry, irreflexivity
26. October 7, 2009:
    • Transitivity
27. October 9, 2009:
    • Collected Assignment 4
    • Equivalence Relations
28. October 12, 2009:
    • Returned Assignment 4
    • Equivalence classes
29. October 13, 2009:
    • The number of equivalence classes
30. October 14, 2009:
    • Counting using equivalence relations: 15.3
31. October 16, 2009:
    • Collected Assignment 5
    • Counting using equivalence relations: 15.10, 15.14.
32. October 19, 2009:
    • Returned Assignment 5
    • Proof techniques again: Proof by reductio ad absurdum
33. October 20, 2009:
    • Proof techniques again: Well ordering principle
34. October 21, 2009:
    • Binomial coefficients: guest lecture
35. October 23, 2009:
    • Proof techniques again: Induction: guest lecture
    • Collect Assignment 6
36. October 26, 2009:
    • Multisets.
    • Inclusion and Exclusion.
37. October 27, 2009:
    • Inclusion and Exclusion and two examples
38. October 30, 2009:
    • Recurrences: guest lecture
39. October 30, 2009:
    • Recurrences: guest lecture
    • Collect Assignment 7
40. November 2, 2009:
    • Returned Assignments 6, 7
    • Inclusion and Exclusion: derangements
41. November 3, 2009:
    • Induction revisited
42. November 4, 2009:
    • Review for Test 2
43. November 6, 2009:
    • Administered Test 2
44. November 9, 2009:
    • Returned Test 2
    • Number Theory
45. November 10, 2009:
    • Number Theory
46. November 11, 2009:
    • Greatest Common Divisor
47. November 13, 2009:
    • Collected Assignment 8
    • Euclidean Algorithm
48. November 16, 2009:
    • Euclidean Algorithm
    • Modular Arithmetic
49. November 17, 2009:
    • Solving equations of the form a*x mod b = c
50. November 18, 2009:
    • Solving equations of the form a*x mod b = c
51. November 20, 2009:
    • Returned Assignment 7
    • Collected Assignment 9
    • Number Theory: Chinese Remainder Theorem
52. November 30, 2009:
    • Returned Assignments 8, 9
    • Group Theory: Group Axioms
53. December 1, 2009:
    • Group Theory: Generators
54. December 2, 2009:
    • Group Theory
    • A non-commutative group
55. December 4, 2009:
    • Collected Assignment 10
    • Group Theory: Gauss' Theorem, Lagrange's Theorem
56. December 7, 2009:
    • Returned Assignment 10
    • Group Theory