| Week | Lecture dates | Sections | topics |
|---|---|---|---|
| 1 | 9/1 (Thurs) | 1, 2.1-2.3 | Introduction, Product and Sum Rules, Permutations |
| 2 | 9/6 (Tues only) | 2.5 –2.7 | r-permutations and r-combinations; Subsets |
| 3 | 9/13, 15 (TTh) | 2.8–2.11, 2.13, 2.14 | Probability, Distinguishable and indistinguishable sampling |
| 4 | 9/20, 22 (TTh) | 2.16–2.19 | Algorithms and combinations; Pigeonhole principles |
| 5 | 9/27, 29 (TTh) | 3.1, 3.2, 3.3 | Graphs, connectedness, BFS, colorings, planar graphs |
| 6 | 10/4, 6 (TTh) | 3.4, 3.5 | Chromatic polynomials, Trees and cycles |
| 7 | 10/11, 13 (TTh) | Chapters 2–3 | Review, Midterm |
| 8 | 10/18, 21 (TTh) | 5.1–5.4 | Generating functions and counting |
| 9 | 10/25, 27 (TTh) | 5.5–5.7, 2.15 | Generating functions, permutations, power indices |
| 10 | 11/1, 11/3 (TTh) | 6.1–6.3 | Recurrence relations |
| 11 | 11/8, 10 (TTh) | 9.1, 9.2, 9.3 | Latin squares, Block designs, orthogonal block designs |
| 12 | 11/15, 17 (TTh) | 9.5, review | Finite fields and projective planes, review |
| 13 | 11/22 (Tues) | Chapters 5-6, 9 | Midterm |
| 13 | 11/29, 12/1 (TTh) | 10.1–10.3 | Encoding, decoding and error-correcting codes |
| 14 | 12/6, 12/8 (TTh) | 9.4, 10.4, 10.5 | Linear codes, Hadamard matrices, Incomplete Block Designs |
| 15 | 12/13 (Tues) | all sections | Review of entire semester |
| FINAL | 12/16 (Fri) | FINAL EXAM 8:00--11 AM |
The exam will be cumulative, and will be in SERC 212 |
Syllabus in Catalogue: Existence and enumeration of designs and patterns such as codes, graphs, and block designs, and extremal problems related to such objects. Emphasis on applications to computer, biological, physical, and social problems.
Prerequisites: CALC2 and 01:640:250.
Charles Weibel / Fall 2011