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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