Week |
Date |
Topic |
Reading |
Notes |
1 |
08/26 |
Introduction | Course Syllabus | |
08/28 | Logic | Rosen 1.1, 1.2 |
Logic, propositions, basic functions, truth tables | |
2 | 09/02 | Propositional Logic, Implications and inference | Rosen 1.3 | Implications, equivalence |
09/04 | Tautologies, contraditions, proofs | IFF, tautologies, contradictions, equivalence proofs | ||
3 | 09/09 | Predicates and quantifiers | Rosen 1.4, 1.5 | Predicates, universal and existential quantifiers |
09/11 | Proofs | Rosen 1.6, 1.7 | Predicate negation, universal inference rules | |
4 | 09/16 | Proofs | Rosen 1.8 | Direct proof |
09/18 | Proofs: Induction | Rosen 5.1 | Proof by contradiction, cases, induction | |
5 | 09/23 | Proofs: Induction | Rosen 5.2 | Induction: equalities, properties, horses |
09/25 | Still induction and strong induction | Rosen 5.2 |
Structural induction, strong induction | |
6 | 09/30 | Inductive/recursive definitions | Rosen 5.3, 5.4 | Structural induction, recursive definitions |
10/02 | Recursive definitions and algorithms | Rosen 5.3, 5.4 | Recursive/inductive definitions | |
7 | 10/07 | Recursive definitions and inductive proofs | Rosen 5.3, 5.4 | Recursive/inductive definitions and proofs |
10/09 | Recursive definitions, structural induction Sets review |
Rosen 5.3
Rosen 2.1, 2.2 |
||
8 | 10/14 | Midterm | In class | |
10/16 | Sets review | Rosen 2.2 | Power sets | |
9 | 10/21 | Functions review, Pigeonhole Principle | Rosen 2.3, 6.2 | Functions: injective, surjective, bijective. Pigeonhole principle |
10/23 | Generalized Pigeonhole Principle, Countable sets | Rosen 6.2, 2.5 | Generalized Pigeonhole principle, Subset sum, Countable sets | |
10 | 10/28 | Uncountable sets Counting |
Rosen 2.5 Rosen 6.1, 6.3 |
Uncountable sets Product rule, simple counting |
10/30 | Counting, Permutations | Rosen 6.3, 6.5 |
Permutations | |
11 | 11/04 | Still counting: Permutations and Combinations | Rosen 6.3, 6.5 |
Permutations and Martians, Sum, Inclusion-Exclusion |
11/06 | Combinations | Rosen 6.3, 6.5 |
Combinations | |
12 | 11/11 | Binomial Coefficient and Combinatorial identities | Rosen 6.4 |
Binomial theorem |
11/13 | Pascal's triangle Probability |
Rosen 6.4 Rosen 7.1 |
Pascal's triangle Probability definition |
|
13 | 11/18 | Probability. Birthday problem, conditional probability |
Rosen 7.2 | Birthday problem, conditional probability |
11/20 | Probability. Relations |
Rosen 7.2 Rosen 9.1 |
Bernoulli trials Relations and basic properties |
|
14 | 11/25 | Relation properties, equivalence, closure | Rosen 9.1, 9.3, 9.4, 9.5 | |
11/27 | Thanksgiving | No class. Contemplating the recursive nature of consciousness | ||
15 | 12/02 | Graphs | ||
12/04 | Graphs | |||
12/10 | FINAL EXAM | 3:30 - 5:30pm |
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