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
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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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