CS313H - Logic, Sets, and Functions: Honors</a> - Fall 2012: Resources Page

Resources for Logic, Sets, and Functions: Honors (cs313H)

Week 0: Introduction (8/30)

  • The slides presented in class: Thursday;more from Thursday (the ones on RoboCup)
  • Patrick MacAlpine, Francisco Barrera, and Peter Stone. Positioning to Win: A Dynamic Role Assignment and FormationPositioning System. In Xiaoping Chen, Peter Stone, Luis Enrique Sucar, and Tijn Van der Zant, editors, RoboCup-2012: Robot Soccer World Cup XVI, Lecture Notes in Artificial Intelligence, Springer Verlag, Berlin, 2013.
    Accompanying video at http://www.cs.utexas.edu/~AustinVilla/sim/3dsimulation/AustinVilla3DSimulationFiles/2011/html/positioning.html
    Details     BibTeX     Download: [pdf] (255.9kB )  [ps] (722.6kB )  

    • Week 1: Satisfiability, Predicates, and Quantifiers (9/4,6)

  • The slides presented in class: Tuesday; Thursday.

    • Week 2: Basic Proof Techniques (9/11,13)

  • The slides presented in class: Tuesday; Thursday.

    • Week 3: Mathematical Induction (9/18,20)

  • The slides presented in class: Thursday.

    • Week 4: Sets and Functions (9/25,27)

  • The slides presented in class: Tuesday; Thursday.

    • Week 5: Infinite Sets (10/2,4)

  • The slides presented in class: Tuesday; Thursday.

    • Week 6: Graph Coloring (10/9,11)

  • The slides presented in class: Thursday.
  • An example of a graph with chromatic number greater than the maximum clique size: Grotsch graph.

    • Week 7: Special Types of Graphs (10/16,18)

  • The slides presented in class: Tuesday; Thursday.
  • Some applications of graph theory

    • Week 8: From Graph Theory to Counting (10/23,25)

  • The slides presented in class: Tuesday; Thursday.
  • Formal proofs of the Euler Circuit Theorem written by Jacob: here
  • Proof by induction on number of vertices
  • A different (from Jacob's) proof by strong induction on the number of edges

    • Week 9: Counting and Recurrences (10/30,11/1):

  • The slides presented in class: Tuesday; Thursday.

    • Week 10: Review and Test (11/6,8)

  • The slides presented in class: Tuesday;

    • Week 11: Big-O and Program Efficiency (11/13,15)

  • The slides presented in class: Tuesday; Thursday.
  • Those interested in the link between Big-O and limits can read more here
  • A more complicated/specific form of the Master Theorem can be read about here

    • Week 12: Analysis of Algorithms (11/20):

  • The slides presented in class: Tuesday.

    • Week 13: Proving Program Correctness (11/27,29):

  • The slides presented in class: Tuesday; Thursday.
  • Correctness proof of insertion sort. Another one.
  • Correctness proof of binary sesarch. Another one.
  • Stable Marriage Algorithm in practice to determine residency of medical students: here
  • The linear majority algorithm.

    • Week 14: Undecidability (12/4,6):

  • The slides presented in class: Tuesday; Thursday.
  • A poem on undecidability
  • Information on the Collatz conjecture.

    • Final Exam:

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