Math 187
Fall 2009
Diary
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- August 24, 2009:
- Course description
- Discuss core, outline of course
- August 25, 2009:
- Connectives and truth tables
- Proof that if x and y are even integers, then x+y is an even integer
- August 26, 2009:
- Proof that for integers a, b and c: If a|b and b|c then a|c is true.
- August 28, 2009:
- Proof that if x > 1 is an integer then x3+1 is composite.
- 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.
- September 1, 2009:
- Modus ponens, tautologies and contrdictions.
- September 2, 2009:
- Problems from the text worked in class.
- 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.
- September 8, 2009:
- Returned Assignment 1.
- Counting: Multiplication principle
- September 9, 2009:
- Counting: Multiplication principle, factorials, examples
- September 11, 2009:
- Collected Assignment 2.
- Sets and subsets
- September 14, 2009:
- Returned graded Assignment 2.
- Quantifiers
- September 15, 2009:
- September 16, 2009:
- Collected Assignment 3.
- Set operations: Powerset, union, intersection, symmetric difference, difference
- Cardinality of the power set.
- Principle of inclusion and exclusion.
- September 18, 2009:
- Combinatorial proofs: Inclusion and Exclusion.
- September 21, 2009:
- Combinatorial Proofs: n2 = n(n-1) + n.
- September 22, 2009:
- Combinatorial Proofs: n3 = n(n-1)(n-2) + 3 n(n-1) + n.
- n4 = ?.
- September 23, 2009:
- September 25, 2009:
- September 28, 2009:
- Returned Test 1.
- Discussed some of the problems from Test 1.
- September 29, 2009:
- Combinatorial Proofs: 3n-1 = ?
- September 30, 2009:
- Combinatorial Proofs: 3n-1 = ?
- October 2, 2009:
- October 5, 2009:
- October 6, 2009:
- Antisymmetry, irreflexivity
- October 7, 2009:
- October 9, 2009:
- Collected Assignment 4
- Equivalence Relations
- October 12, 2009:
- Returned Assignment 4
- Equivalence classes
- October 13, 2009:
- The number of equivalence classes
- October 14, 2009:
- Counting using equivalence relations: 15.3
- October 16, 2009:
- Collected Assignment 5
- Counting using equivalence relations: 15.10, 15.14.
- October 19, 2009:
- Returned Assignment 5
- Proof techniques again: Proof by reductio ad absurdum
- October 20, 2009:
- Proof techniques again: Well ordering principle
- October 21, 2009:
- Binomial coefficients: guest lecture
- October 23, 2009:
- Proof techniques again: Induction: guest lecture
- Collect Assignment 6
- October 26, 2009:
- Multisets.
- Inclusion and Exclusion.
- October 27, 2009:
- Inclusion and Exclusion and two examples
- October 30, 2009:
- Recurrences: guest lecture
- October 30, 2009:
- Recurrences: guest lecture
- Collect Assignment 7
- November 2, 2009:
- Returned Assignments 6, 7
- Inclusion and Exclusion: derangements
- November 3, 2009:
- November 4, 2009:
- November 6, 2009:
- November 9, 2009:
- Returned Test 2
- Number Theory
- November 10, 2009:
- November 11, 2009:
- November 13, 2009:
- Collected Assignment 8
- Euclidean Algorithm
- November 16, 2009:
- Euclidean Algorithm
- Modular Arithmetic
- November 17, 2009:
- Solving equations of the form a*x mod b = c
- November 18, 2009:
- Solving equations of the form a*x mod b = c
- November 20, 2009:
- Returned Assignment 7
- Collected Assignment 9
- Number Theory: Chinese Remainder Theorem
- November 30, 2009:
- Returned Assignments 8, 9
- Group Theory: Group Axioms
- December 1, 2009:
- December 2, 2009:
- Group Theory
- A non-commutative group
- December 4, 2009:
- Collected Assignment 10
- Group Theory: Gauss' Theorem, Lagrange's Theorem
- December 7, 2009:
- Returned Assignment 10
- Group Theory