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## Notes

1

08/26

Introduction Course Syllabus
08/28 Logic

History's Worst Software Bugs

Rosen 1.1, 1.2

Logic, propositions, basic functions, truth tables
2 09/02 Propositional Logic, Implications and inference Rosen 1.3 Implications, equivalence
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

Structural induction

Sets

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

xkcd Lorenz (and possibilities tree)

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
Probability definition
13 11/18 Probability. Birthday problem,
conditional probability
Birthday problem, conditional probability
11/20 Probability.
Relations

14 11/25 Thanksgiving No class. Conteplating the recursive nature of consciousness
11/27 Relations
15 12/02 Graphs
12/04 Graphs
12/10 FINAL EXAM 3:30 - 5:30pm
Topic attachments
I Attachment Action Size Date Who Comment
pdf 05induction-4.pdf manage 91.7 K 2014-10-03 - 05:41 UnknownUser
pdf 08counting-4.pdf manage 92.0 K 2014-11-07 - 03:55 UnknownUser
pdf 07functions-3notcountable.pdf manage 123.6 K 2014-11-03 - 20:02 UnknownUser
pdf 10probability-2.pdf manage 148.8 K 2014-11-19 - 01:02 UnknownUser
pdf 08counting-1.pdf manage 191.8 K 2014-11-03 - 20:02 UnknownUser
pdf 09counting-1.pdf manage 204.2 K 2014-11-13 - 05:02 UnknownUser
pdf 08counting-3.pdf manage 229.3 K 2014-11-05 - 04:49 UnknownUser
pdf 05induction-3.pdf manage 290.4 K 2014-10-02 - 15:25 UnknownUser
pdf 05induction-2.pdf manage 328.5 K 2014-09-26 - 00:03 UnknownUser
pdf 04proof-3.pdf manage 345.9 K 2014-09-18 - 05:44 UnknownUser
pdf 08counting-2.pdf manage 347.9 K 2014-11-03 - 20:11 UnknownUser
pdf 09counting-2.pdf manage 472.4 K 2014-11-19 - 01:01 UnknownUser
pdf 04proof-1.pdf manage 570.2 K 2014-09-10 - 01:09 UnknownUser
pdf 05induction-6.pdf manage 588.3 K 2014-10-13 - 19:34 UnknownUser
pdf 06settheory-1.pdf manage 591.1 K 2014-10-13 - 19:35 UnknownUser
pdf 07functions-2.pdf manage 649.6 K 2014-10-23 - 21:20 UnknownUser
pdf 07functions-1.pdf manage 662.8 K 2014-10-22 - 03:42 UnknownUser
pdf 06settheory-2.pdf manage 666.8 K 2014-10-18 - 23:41 UnknownUser
pdf 02logic.pdf manage 684.8 K 2014-09-02 - 23:15 UnknownUser
pdf 04proof-4.pdf manage 790.3 K 2014-09-19 - 05:05 UnknownUser
pdf 04proof-2.pdf manage 838.4 K 2014-09-12 - 06:33 UnknownUser
pdf 05induction-1.pdf manage 884.1 K 2014-09-23 - 21:07 UnknownUser
pdf 10probability-1.pdf manage 1327.4 K 2014-11-19 - 01:02 UnknownUser
pdf 03FOlogic.pdf manage 1456.7 K 2014-09-05 - 18:08 UnknownUser
ppt 00The_First_Lecture-BergerWolf-Grid.ppt manage 2679.0 K 2012-08-28 - 20:34 UnknownUser
pdf 05induction-5.pdf manage 5905.6 K 2014-10-08 - 17:44 UnknownUser
pdf 01logic.pdf manage 6496.7 K 2014-08-28 - 21:07 UnknownUser
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Topic revision: r42 - 2014-11-19 - 01:16:39 - Main.tanyabw

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