Mathematics 454 — Fall 2021

Prof. Weibel (640:454)

Tentative Course Syllabus   (go to homework table)

Week Lecture dates   Sections topics
19/2 (Thurs)---— Class cancelled due to flooding
19/8 (Wed)1, 2.1-2.3 Introduction, Permutations and Combinations
29/9 (Thurs)2.4–2.6, 3.1 r-permutations, r-combinations; probability; pigeonhole
39/13, 16 (MTh)Ch.5 Binomial cofficients; posets
49/20, 23 (MTh)Ch.6 Inclusion-exclusion principles
59/27, 30 (MTh)Ch.7 Generating functions, recurrence relations
610/4, 7 (MTh) 8.1-8.2 Catalan numbers, Difference sequences, Stirling numbers
710/11, 14 (MTh)Ch. 2, 5–8 Review, MIDTERM EXAM
8a10/18 (M)8.3–4 Partition numbers
910/21, 25 (ThM)Ch. 11 Paths and cycles in graphs, bipartite graphs, trees
1010/28, 11/1 (ThM)Ch. 12 graph colorings, chromatic polynomials,
planar graphs, clique numbers
1111/4, 11/8 (ThM)Ch. 10 Block designs, orthogonal block designs, Latin squares
1211/11, 15 (ThM)Ch. 13 Digraphs, Networks, Matching in bipartite graphs
1311/18, 11/22 (ThM)Chapters
8, 10–13
1412/2, 6 (ThM)Ch. 14 Permutations, Burnside's theorem and Polya counting
1512/9 (Thurs) 10.1 Finite fields
15 12/13 (Monday)all sections Review of entire semester
Sec.1: 12/20(M)
8:00--11 AM The final exam will be cumulative

go to homework table

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.
Course grade: 2 Midterms (20% each); Final Exam (40%); HW (15%); Quizzes (5%).
Self-Reporting Absence Website: Students are expected to attend all classes; if you expect to miss one or two classes, please use the University's absence reporting website to indicate the date and reason for your absence. An email is automatically sent to me.
Academic integrity policy: All students in the course are expected to be familiar with and abide by the academic integrity policy. Violations of the policy are taken very seriously.
Disabilities policy: Rutgers is fully committed to compliance with the Americans with Disabilities Act; see policies and procedures.

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Charles Weibel / Fall 2021

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