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Week

Date

Topic

Reading

Notes

1

08/26

Introduction Course Syllabus

Positive learning environment

  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
  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

Khan Academy: Mathematical induction

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)

Khan academy combinatorics

Permutations
11 11/04 Still counting: Permutations and Combinations

Rosen 6.3, 6.5

Khan academy permutations

Permutations and Martians, Sum, Inclusion-Exclusion
  11/06 Combinations

Rosen 6.3, 6.5

Khan academy combinations

Combinations
12 11/11 Binomial Coefficient and Combinatorial identities

Rosen 6.4

Khan academy Binomial theorem

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 Relations properties, composition
  11/27 Thanksgiving No class. Contemplating the recursive nature of consciousness  
15 12/02 Relations. Partial Order Sets Rosen 9.6 Partial Order Sets, Hasse diagrams, minimal and maximal elements
  12/04 Graphs Rosen 10.1, 10.2, 10.3,10.5 Graphs, terminology, Euler
  12/10 FINAL EXAM 3:30 - 5:30pm, room BSB 145
Topic attachments
I Attachment Action Size Date Who Comment
PowerPointppt 00The_First_Lecture-BergerWolf-Grid.ppt manage 2679.0 K 2012-08-28 - 20:34 UnknownUser  
PDFpdf 01logic.pdf manage 6496.7 K 2014-08-28 - 21:07 UnknownUser  
PDFpdf 02logic.pdf manage 684.8 K 2014-09-02 - 23:15 UnknownUser  
PDFpdf 03FOlogic.pdf manage 1456.7 K 2014-09-05 - 18:08 UnknownUser  
PDFpdf 04proof-1.pdf manage 570.2 K 2014-09-10 - 01:09 UnknownUser  
PDFpdf 04proof-2.pdf manage 838.4 K 2014-09-12 - 06:33 UnknownUser  
PDFpdf 04proof-3.pdf manage 345.9 K 2014-09-18 - 05:44 UnknownUser  
PDFpdf 04proof-4.pdf manage 790.3 K 2014-09-19 - 05:05 UnknownUser  
PDFpdf 05induction-1.pdf manage 884.1 K 2014-09-23 - 21:07 UnknownUser  
PDFpdf 05induction-2.pdf manage 328.5 K 2014-09-26 - 00:03 UnknownUser  
PDFpdf 05induction-3.pdf manage 290.4 K 2014-10-02 - 15:25 UnknownUser  
PDFpdf 05induction-4.pdf manage 91.7 K 2014-10-03 - 05:41 UnknownUser  
PDFpdf 05induction-5.pdf manage 5905.6 K 2014-10-08 - 17:44 UnknownUser  
PDFpdf 05induction-6.pdf manage 588.3 K 2014-10-13 - 19:34 UnknownUser  
PDFpdf 06settheory-1.pdf manage 591.1 K 2014-10-13 - 19:35 UnknownUser  
PDFpdf 06settheory-2.pdf manage 666.8 K 2014-10-18 - 23:41 UnknownUser  
PDFpdf 07functions-1.pdf manage 662.8 K 2014-10-22 - 03:42 UnknownUser  
PDFpdf 07functions-2.pdf manage 649.6 K 2014-10-23 - 21:20 UnknownUser  
PDFpdf 07functions-3notcountable.pdf manage 123.6 K 2014-11-03 - 20:02 UnknownUser  
PDFpdf 08counting-1.pdf manage 191.8 K 2014-11-03 - 20:02 UnknownUser  
PDFpdf 08counting-2.pdf manage 347.9 K 2014-11-03 - 20:11 UnknownUser  
PDFpdf 08counting-3.pdf manage 229.3 K 2014-11-05 - 04:49 UnknownUser  
PDFpdf 08counting-4.pdf manage 92.0 K 2014-11-07 - 03:55 UnknownUser  
PDFpdf 09counting-1.pdf manage 204.2 K 2014-11-13 - 05:02 UnknownUser  
PDFpdf 09counting-2.pdf manage 472.4 K 2014-11-19 - 01:01 UnknownUser  
PDFpdf 10probability-1.pdf manage 1327.4 K 2014-11-19 - 01:02 UnknownUser  
PDFpdf 10probability-2.pdf manage 148.8 K 2014-11-19 - 01:02 UnknownUser  
PDFpdf 11probability-1.pdf manage 60.5 K 2014-11-25 - 06:38 UnknownUser  
PDFpdf 12relations-1.pdf manage 71.3 K 2014-11-25 - 06:38 UnknownUser  
PDFpdf 12relations-2.pdf manage 156.8 K 2014-11-26 - 08:17 UnknownUser  
PDFpdf 12relations-3.pdf manage 182.0 K 2014-12-04 - 19:09 UnknownUser  
PDFpdf 13graphs-1.pdf manage 445.2 K 2014-12-10 - 05:56 UnknownUser  
Topic revision: r46 - 2014-12-10 - 05:59:45 - Main.tanyabw
 
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