MATH 360 Spring 2023Combinatorics and Graph Theory Archived Class
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# Schedule for weeks 1 through 16

 Wk Day Date Topic Resources Events 1 Tue Jan 10 Course Introduction Graphs Graph Terminology CGT 1-1.1.2 1.1.1: 3,4 1.1.2: 1,2,4,5,9, 12,15,16 Thu Jan 12 Special Types of Graphs CGT 1.1.3 1.1.3: 1,5,6,8,9,10 2 Tue Jan 17 Distance in Graphs CGT 1.2 1.2.1: 1,2,6,8,11 1.2.2: 1,2,4,6 1.2.3: 2,3 Thu Jan 19 Trees CGT 1.3-1.3.3 HW 1 due 1.3.1: 1,2,3 1.3.2: 1,3,5,8 1.3.3: 1,4,5,7 3 Tue Jan 24 Counting Trees CGT 1.3.4 1.3.4: 2,3,4,5,6 Thu Jan 26 Trails, Circuits, Paths, and Cycles CGT 1.4-1.4.2 HW 2 due 1.4.1: 2,3 1.4.2: 1,2,4,5,7,8 4 Tue Jan 31 Hamiltonian Paths and Cycles Three Open Problems CGT 1.4.3-1.4.4 HW 3 due 1.4.3: 1,4,6,7,9,12 1.4.4: 1,2,3,4 Thu Feb 02 Planarity Euler's Formula and Beyond CGT 1.5-1.5.2 1.5.1: 1,2,5,6,8 1.5.2: 1,2,4,7,9,10 Note: add "with triangular regions" to 10. (typo) 5 Tue Feb 07 Regular Polyhedra Kuratowski's Theorem CGT 1.5.3-1.5.4 HW 4 due 1.5.3: 1,2 1.5.4: 1,2,4 Thu Feb 09 Colorings CGT 1.6-1.6.2 1.6.1: 1,2,4,5 1.6.2: 2,5,6,7 6 Tue Feb 14 No Class Winter Recess Thu Feb 16 The Four Color Problem Chromatic Polynomials CGT 1.6.3-1.6.4 1.6.3: 1,3,5 1.6.4: 1,3,4 7 Tue Feb 21 Matchings Hall's Theorem and SDRs CGT 1.7-1.7.2 HW 5 due 1.7.1: 1,2 1.7.2: 1,2,3,4*,6 *4 has typo. Need n≥2 and |Si|=n-1 Thu Feb 23 Nothing Icepocalypse 2023: No class 8 Tue Feb 28 The König-Egerváry Theorem Perfect Matchings CGT 1.7.3-1.7.4 1.7.3: 1,2,3(hard?) 1.7.4: 1,2,4,5,6,7 Thu Mar 02 Midterm Exam 9 Tue Mar 07 Ramsey Theory CGT 1.8 1.8.1: 1,3,4 1.8.2: 1,2,4,5 1.8.3: 2,3,4 Thu Mar 09 Combinatorics: Some Essential Problems CGT 2-2.1 HW 6 due 2.1: 1,4,11,12,14 10 Tue Mar 14 Binomial Coefficients CGT 2.2 2.2: 1,2,4,6,7bd,8 Thu Mar 16 Multinomial Coefficients CGT 2.3 HW 7 due 2.3: 1,2,3,4,9ace,11 Typo in 4: sum indices are missing "=n" Spring Break Week 11 Tue Mar 28 The Pigeonhole Principle CGT 2.4 HW 8 due 2.4: 1,3,4,5,7,9,13 Thu Mar 30 The Principle of Inclusion and Exclusion CGT 2.5 2.5: 2,4,6,8,12 Error in 4: change 250 to 230 12 Tue Apr 04 Generating Functions CGT 2.6-2.6.2 HW 9 due 2.6: 1,2 2.6.1: 1,2,4 2.6.2: 1,3,5,8 Thu Apr 06 Changing Money Fibonacci Numbers CGT 2.6.3-2.6.4 2.6.3: 1,3,9,10 2.6.4: 1,2,5bd,10 13 Tue Apr 11 Recurrence Relations Catalan Numbers CGT 2.6.5-2.6.6 2.6.5:1,2ad,6,7 2.6.6: 2,3,4 Thu Apr 13 Counting ways to trianglalize n-gons 14 Tue Apr 18 Pólya's Theory of Counting Permutation Groups Burnside Lemma CGT 2.7-2.7.2 HW 10 due 2.7.1: 1,2,4,5,9 2.7.2: 1,2,4 Thu Apr 20 Partitions CGT 2.8-2.8.1 2.8.1: 1,2,3,5,10 15 Tue Apr 25 Stable Marriage CGT 2.9-2.9.1 HW 11 due 2.9: 1,4 2.9.1: 1,3,4,8,7 Thu Apr 27 Combinatorial Geometry CGT 2.10-2.10.1 HW 12 due 2.10.1: 1,2,6,9 Ex Fri May 05 Final Exam12:30-2:20pm