CS311H - Discrete Math for Computer Science: Honors - Fall 2013: Resources Page

Resources for Discrete Math for Computer Science: Honors (cs311H)

Week 0: Introduction

  • 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

  • The slides presented in class: Tuesday; Thursday.

    • Week 2: Basic Proof Techniques

  • The slides presented in class: Tuesday; Thursday.

    • Week 3: Mathematical Induction

  • The slides presented in class: Tuesday. Thursday.

    • Week 4: Sets and Functions

  • The slides presented in class: Tuesday; Thursday.

    • Week 5: Infinite Sets

  • The slides presented in class: Tuesday; Thursday.

    • Week 6: Graph Coloring

  • 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

  • The slides presented in class: Tuesday; Thursday.
  • Some applications of graph theory
  • An application of Hamiltonian and Eulerian paths to genome sequence assembly.

    • Week 8: From Graph Theory to Counting

  • The slides presented in class: Tuesday; Thursday.
  • Formal proofs of the Euler Circuit Theorem written by Jacob Schrum: 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

  • The slides presented in class: Tuesday; Thursday.
  • Some more patterns in Pascal's triangle

    • Week 10: Review and Test

  • The slides presented in class: Tuesday;

    • Week 11: Big-O and Program Efficiency

  • 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, Proving Program Correctness:

  • The slides presented in class: Tuesday; Thursday.
  • Another explanation of fast multiplication.
  • Many more multiplication algorithms, including what's known about runtimes.
  • Correctness proof of insertion sort. Another one.
  • Correctness proof of binary sesarch. Another one.

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

  • The slides presented in class: Tuesday.
  • Stable Marriage Algorithm in practice to determine residency of medical students: here
  • An average runtime analysis of the Stable Marriage Algorithm.
  • The linear majority algorithm.

    • Week 14: Undecidability:

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

    • Final Exam:

    Saturday, December 14th, 7pm-10pm in JGB 2.216.
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