Notes from the 2014 Canada/USA Mathcamp:
Mathcamp Crash Course
- Lecture 1: The art and language of proof.
- Lecture 2: Proof techniques.
- Lecture 3: Equivalence relations.
- Lecture 4: Injection, surjection, and cardinality.
- Homework sets: 1, 2, 3, 4.
Electrical Networks and Graphs
- Homework+Lecture 1: Random walks and electrical networks.
- Homework+Lecture 2: Simplifying circuits via effective resistance.
- Homework+Lecture 3: Correspondences between current and random walks.
- Homework+Lecture 4: Pólya's random walk problem in dimensions 1 and 2.
- Homework+Lecture 5: Pólya's random walk problem in dimensions 3 and higher.
The Intermediate Value Theorem and Chaos
- Lecture 1: The itinerary lemma.
- Lecture 2: Period three implies chaos.
- Lecture 3: The alternating points lemma.
- Lecture 4: Sharkovsky's theorem.
- Homework sets: 1, 2, 3, 4.
NP-Completeness and Partial Latin Squares
- Lecture 1: P and NP.
- Lecture 2: NP-completeness.
- Lecture 3: Triangulations and NP-completeness.
- Lecture 4: Latin squares and NP-completeness.
- Homework sets: 1, 2, 3, 4.
The Unit Distance Graph Problem and the Axiom of Choice
- Lecture 1: The unit distance graph problem and the axiom of choice.
- Homework sets: 1.
Algebraic Graph Theory
- Lecture 1: Background material; Cayley graphs.
- Lecture 2: Schreier graphs; subgroups of free groups.
- Homework sets: 1.