The calendar below provides information on the course's lecture (L) and quiz (E) sessions.
| SES # | TOPICS | KEY DATES |
|---|---|---|
| L1 | Introduction to course, walks on graphs, rational generating functions and Fibonacci numbers | |
| L2 | Walks on graphs II: walks on complete graphs and cubes | |
| L3 | Walks on graphs III: the Radon transform | |
| L4 | Random walks, the Perron-Frobenius theorem | Homework 1 due |
| L5 | Introduction to partially ordered sets and the Boolean poset | |
| L6 | Partially ordered sets II: Dilworth's and Sperner's theorem | |
| L7 | Partially ordered sets III: the Mobius function | Homework 2 due |
| L8 | Group actions on Boolean algebras | |
| L9 | Group actions on Boolean algebras II: proof of the Sperner property | |
| L10 | Introduction to partitions and two proofs of Euler's theorem | Homework 3 due |
| L11 | Partitions II: Euler Pentagonal theorem and other identities | |
| L12 | Partitions in a box, q-binomial coefficients, and introduction to Young tableaux | |
| L13 | Standard Young tableaux and the Hook length formula | Homework 4 due |
| L14 | The Hook length formula II, and introduction to the RSK algorithm | |
| L15 | Proof of Schensted's theorem | |
| L16 | Catalan numbers | Homework 5 due |
| E1 | In-class quiz 1 | |
| L17 | Counting Hasse walks in Young's lattice | |
| L18 | An introduction to symmetric functions | |
| L19 | Symmetric functions II | Homework 6 due |
| L20 | Polya theory I | |
| L21 | Polya theory II | Homework 7 due |
| L22 | Polya theory III, intro to exponential generating functions | |
| L23 | Exponential generating functions and tree enumeration | |
| L24 | Tree enumeration II | Homework 8 due |
| L25 | Matrix tree theorem | |
| L26 | Matrix tree theorem II and Eulerian tours | |
| L27 | Eulerian tours II | Homework 9 due |
| E2 | In-class quiz 2 | |
| L28 | Binary de Brujin sequences | |
| L29 | Chip firing games I | |
| L30 | Chip firing games II: the critical group | |
| L31 | Chip firing games III: proof of uniqueness | |
| L32 | Perfect matchings and Domino tilings | Homework 10 due |
| L33 | Perfect matchings and Domino tilings II | |
| L34 | Pfaffians and matching enumeration | |
| L35 | Aztec diamonds | |
| L36 | Aztec diamonds II; Lattice path enumeration | |
| L37 | Lattice path enumeration II |