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

• ## 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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