Mathematics 454 — Fall 2011

Prof. Weibel (640:454)

Tentative Course Syllabus   (go to homework table)

Week Lecture dates Sections topics
19/1 (Thurs)1, 2.1-2.3 Introduction, Product and Sum Rules, Permutations
29/6 (Tues only)2.5 –2.7 r-permutations and r-combinations; Subsets
39/13, 15 (TTh)2.8–2.11,
2.13, 2.14
Probability, Distinguishable and indistinguishable sampling
49/20, 22 (TTh)2.16–2.19 Algorithms and combinations; Pigeonhole principles
59/27, 29 (TTh)3.1, 3.2, 3.3 Graphs, connectedness, BFS, colorings, planar graphs
610/4, 6 (TTh)3.4, 3.5 Chromatic polynomials, Trees and cycles
710/11, 13 (TTh)Chapters 2–3 Review, Midterm
810/18, 21 (TTh)5.1–5.4 Generating functions and counting
910/25, 27 (TTh)5.5–5.7, 2.15 Generating functions, permutations, power indices
1011/1, 11/3 (TTh)6.1–6.3 Recurrence relations
1111/8, 10 (TTh)9.1, 9.2, 9.3 Latin squares, Block designs, orthogonal block designs
1211/15, 17 (TTh)9.5, review Finite fields and projective planes, review
1311/22 (Tues)Chapters 5-6, 9 Midterm
1311/29, 12/1 (TTh)10.1–10.3 Encoding, decoding and error-correcting codes
1412/6, 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
8:00--11 AM
The exam will be cumulative, and will be in SERC 212

go to homework table

Self-Reporting Absence Website:
Students are expected to attend all classes; if you expect to miss one or two classes, please use the University absence reporting website to indicate the date and reason for your absence. An email is automatically sent to me.
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.

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Charles Weibel / Fall 2011