Schedule of Topics - CS 301k - Spring 2013

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)

Jan 14
  • class policies and introduction
  • Logic - why we need it
  • propositional logic intro
    • propositions
    • logical connectives

Notes:
Jan 21

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

Notes: More logic

Jan 28
  • propositional logic
    • logical implications: rules of inference
    • formal proofs
    • translating ideas into logic
    • translating logic into ideas

Notes: predicate logic

Feb 4
  • 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
Feb 11
  • 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
Feb 18
  • methods of proof and a little number theory
    • direct proof
    • indirect proof (proof of contrapositive)
    • proof by contradiction
Feb 25
  • More on proof methods
  • Finish reading chapter 3
  • Midterm 1 on Wednesday

Discussion assignment
Mar 4
  • Proof techniques
  • Sets
    • definitions and basic set operations
    • Venn diagrams
    • cardinality
    • set identities (associativity, distributivity, etc)
Notes:
sets
Mar 11
spring break

Mar 18
  • Sets
    • cartesian product
    • power set
    • proving theorems about sets

Notes:
Mar 25
  • Relations
    • definitions
    • properties: reflexive, symmetric, transitive, antisymmetric
    • binary relations

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

Notes:

Apr 8
  • More on Relations
  • partitions
Discussion assignment : subset and existence proofs

Apr 15
  • order relations
  • Functions
    • definitions
    • properties
    • inverses
    • composition
    • proving theorems about functions
Notes:
Apr 22
  • partial orders
  • functions

Notes:

Apr 29
  • functions
  • induction
Discussion assignment: practice with properties of relations
Exam review


Final Exam Period:
May 8-11, 13-14
Our final exam: TBD





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