Schedule of Topics - CS 313k - Fall 2011

This schedule is just a guide - the order and selection of topics may be changed during the semester. You are responsible for the material as it is presented in class.



Week
Topic
Reading and Events (all reading assignments are in Velleman unless otherwise noted)

Aug 24
  • class policies and introduction
  • Logic - why we need it
  • propositional logic intro
    • propositions
    • logical connectives

Notes:
Aug 29

  • more propositional logic
    • logical indentities
    • tautology, contradiction, contingency

Notes: More logic

Sep 5
  • propositional logic
    • logical implications: rules of inference
    • formal proofs
    • translating ideas into logic
    • translating logic into ideas

Notes: predicate logic
Sep 12
  • More propositional logic - proving arguments are valid
  • Intro to predicate logic
  • Read sections 2.1 and 2.2
  • Discussion section exercises - work before discussion
  • Discussion assignment solutions
Sep 19
  • More predicate logic
    • universal and existential quantifiers
    • negating quantified statements
    • translating English statements with quantifiers to logic, and vice versa
    • statements with multiple quantifiers
    • formal proofs
  • proof techniques

Notes:

  • Re-read sections 2.1 and 2.2
  • Midterm 1 review - work on these before discussion on Thursday.
  • In discussion this week, you will review for the exam.
  • Validity proofs - more practice
Sep 26
  • methods of proof and a little number theory
    • direct proof
    • indirect proof (proof of contrapositive)
    • proof by contradiction
Oct 3
  • More on proof methods
  • Finish reading chapter 3

Discussion assignment
Oct 10
  • Proof techniques
  • Sets
    • definitions and basic set operations
    • Venn diagrams
    • cardinality
    • set identities (associativity, distributivity, etc)
Notes:
sets
Oct 17
  • Sets
    • cartesian product
    • power set
    • proving theorems about sets

Notes:
Oct 24
  • Relations
    • definitions
    • properties: reflexive, symmetric, transitive, antisymmetric
    • binary relations

Notes:
Oct 31
  • Relations
    • equivalence relations and partitions
  • Functions
    • definition and properties (1-1, onto, etc)
    • inverses

Notes:
Nov 7
  • More on Relations
  • partitions
Discussion assignment : subset and existence proofs

Nov 14
  • order relations
  • Functions
    • definitions
    • properties
    • inverses
    • composition
    • proving theorems about functions
Notes:
Nov 21
  • partial orders
  • functions
  • mathematical induction

Notes:

Nov 28


Final Exam:





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