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Sample Syllabus Combinatorics Mathematics 454 — Fall 2011

Combinatorics  Mathematics 454 — Fall 2011

(Sample Syllabus)

Prof. Weibel (640:454)

  • Lectures: TTh 5 (3:20 - 4:40 PM) in SERC 212 (Busch Campus);
  • Text: Roberts and Tesman, Applied Combinatorics (2nd edition) Prentice-Hall, ISBN # 0-13-079603-4
  • Weibel's  Office hours

Tentative Course Syllabus   (go to homework table)

WeekLecture datesSectionstopics
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

Homework Table

DueProblems
Sept. 13 2.5#3; 2.6#5; 2.7#12,15,22; 2.8#7,9; 2.9#3,5
Sept. 22 2.9#9; 2.10#3; 2.11#7,15; 2.13#2,11; 2.14#4,9
Sept. 27 2.16 #3,21,23; 2.18 #7,9c,9g; 2.19 #15,18,27
Oct. 6 2.19 #10; 3.1 #15,16; 3.2 #2,16; 3.3 #4,21 (explain)
Oct. 13 3.3 #24,26; 3.4 #5,12,24; 3.5 #2,7(f),12 (use BFS for 7)
Oct. 13 Midterm (Chapters 1,2,3)
Oct. 25 5.1#11 (explain); 5.2#4(a,b,c),14; 5.3#1(a,b,c),8,16; 5.4#2(b,d),7,13
Nov. 1 5.5 #1(a,e,f),6(a,b,c),11,13; 2.15 #3(a,d); 5.7 #1(a,b),5(for 1ab)
Nov. 8 6.1 #8,17,33; 6.2 #12(abc),18,26(a); 6.3 #3(abc),12,14
Nov. 15 9.1 #2(a-d),4; 9.2 #5(a-d),10,14; 9.3 #2(c,d),18(a)
Nov. 22 Midterm (Chapters 5,6,9)
Dec. 6 10.2 #1(b),3,5(b),9(a,b); 10.3 #1(b),3(b),4(b),8,23
Dec. 13 9.4 #1c,9c; 10.4 #4c,11,14,20; 10.5 #6,7,13 (transpose matrices if needed)

 

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 https://sims.rutgers.edu/ssra 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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