Math/CS 103: Topics in Discrete Mathematics
Course Information:
- Professor: Padraic Bartlett.
- Class Time/Location: MWF 11-12:20pm, Bldg. 494, Rm. 160B.
- Office Hours: MTThF, 1-2pm, South Hall 6516.
- Email: padraic at math dot ucsb dot edu.
- Syllabus: linked here.
Lecture Notes:
- Lecture 1: Algorithms.
- Lecture 2: Sorting algorithms.
- Lecture 3: Sim.
- Lecture 4: Ramsey theory.
- Lecture 5: NP problems.
- Lecture 6: NP-completeness.
- Lecture 7: Latin squares, triangulations, and 3SAT.
- Lecture 8: Voting systems.
- Lecture 9: A (false) proof of the four-color theorem.
- Lecture 10: Period three implies chaos.
- Lecture 11: The unit distance graph problem and equivalence relations.
Presentations:
- Presentation 1: (Nick) Matchings in graphs.
- Presentation 2: (Alex) Tetration.
- Presentation 3: (Zhixing/Alice) The Cantor set.
- Presentation 4: (Landon) Bertrand's paradox.
- Presentation 5: (Eric B.) Combinatorial games.
- Presentation 6: (Stephen) The Rubik's Cube and groups.
- Presentation 7: (Kayla) Fermat's little theorem and Lagrange's theorem.
- Presentation 8: (Zihan) Quadratic residues.
- Presentation 9: (Yukang) The birthday paradox.
- Presentation 10: (Mao) Magic squares.
- Presentation 11: (Taom) Gödel's incompleteness theorems.
- Presentation 12: (Eric R.) Euler characteristic.
- Presentation 13: (Tianruo) Random walks.
- Presentation 14: (Ryan) Topology.
- Presentation 15: (Landon) Minimal critical sets in Latin squares.
- Presentation 16: (Nick) Curvature.
- Presentation 17: (Zhixing/Alice) Parrondo's paradox.
- Presentation 18: (Tianruo) The surreal numbers.
- Presentation 19: (Jay) Knot theory.
- Presentation 20: (Kayla) Cellular automata.
- Presentation 21: (Declan/Zehui) Fair division algorithms.
- Presentation 22: (Ziming) Chinese reminder theorem.
Handouts:
- Homework 1: Algorithms.
- Homework 2: Sorting algorithms.
- Homework 3: Problems from presentations 1-3.
- Homework 4: NP problems; Tetration.
- Homework 5: NP-completeness.
- Homework 6: Latin squares, triangulations, and 3SAT.
- Homework 7: More problems on triangulations.
- Homework 8: Voting systems.
- Homework 9: Presentations (Alice and Landon.)
- Homework 10: Presentations (Eric B. and Stephen.)
- Homework 11: A (false) proof of the four-color theorem.
- Homework 12: Presentations (Zihan, Kayla and Declan.)
- Homework 13: Presentations (Yukang, Mao and Taom.)
- Homework 14: Presentations (Eric R., Tianruo and Ryan.)
- Homework 15: Period three implies chaos; the unit distance graph problem.
- Homework 16: More unit distance graph problems.
- Homework 17: Presentations (Nick and Landon.)
- Homework 18: Presentations (Alice, Jay and Tianruo.)
Bonus:
- Homework 19: Presentations (Kayla, Declan and Ziming).
- Quiz 9: Presentations (many!).
LaTeX information:
- To download the .tex for any file here: simply click on the .pdf link and replace the .pdf with .tex.
- To compile the .tex, you may find this preamble file useful.