Math 447/557, Combinatorial Mathematics, Spring 2019

Topics, Exams and Homework Assignments

Week Dates Topics Sections Covered Homework Due
1—2 Jan 9—Jan 18 Graph Theory Basics, Isomorphism 1.1, 1.2, 1.3 1.1: 1, 6, 9, 14, 16, 20, 23, 1.2: 4, 5bck, 6cdef, 7, 1.3 : 1, 6, 10 Jan 30
3 Jan 21—Jan 25 Planar Graphs, Euler Cycles 1.4, 2.1 1.4: 3bh, 7befgh, 8, 11, 15, 16, 20, 25, 2.1: 2, 4, 9, 10 Feb 6
4 Jan 28—Feb 1 Planar Graphs, Euler Cycles and Trails 1.4, 2.1
5 Feb 4—Feb 8 Hamilton Circuits, Graph Coloring 2.2, 2.3, 2.4 2.2: 3, 4bjko, 7b, 9, 16, 2.3: 1abcgl, 14, 15 Feb 20
6 Feb 11—Feb 15 Graph Coloring, Trees and Searching 2.4, 3.1, 3.2 2.4 : 7a, 3.1: 1a, 4, 6, 11, 13, 19, 25, 29, 3.2: 1ab, 4 Feb 21
7 Feb 18—Feb 22 Graph Coloring, Trees and Searching, Traveling Salesperson Problem 2.4, 3.1, 3.2, 3.3 3.2: 5, 16b, 25, 3.3: 1, 5 Feb 25
8 Feb 25 Review for Midterm 1
8 Feb 27 Midterm 1
8 Mar 1 Basic Permutations and Combinations 5.1, 5.2 5.1: 6, 7, 9, 12, 13, 16abc, 20, 22, 25, 26, 33, 36, 5.2: 4, 5, 8, 10, 16bcd, 25, 42, 53, 69a Mar 21
Mar 2—Mar 10 Spring Recess
9 Mar 11—Mar 15 Counting Problems with Repetition 5.3, 5.4 5.1: 24, 29, 30, 5.2: 32, 38, 55, 5.3: 2, 4, 5, 7, 9, 12, 21, 5.4: 11, 19, 21, 28, 47, 48, 6.1: 2b, 4bc, 6, 7, 10 Mar 20
10 Mar 18—Mar 22 Counting Problems with Repetition, Generating Function Models 5.3, 5.4, 6.1
11 Mar 25—Mar 29 Generating Function Models, Evaluating Generating Function Coefficients 6.1, 6.2 5.2: 26, 46, 56, 5.3: 15, 19, 22, 5.4: 2ab, 3ab, 7, 10, 27, 6.1: 3ac, 8, 13, 16 Apr 10
12 Apr 1 Review for Midterm 2
12 Apr 3 Midterm 2
12 Apr 1 Evaluating Generating Function Coefficients, Recurrence Relations 6.2, 7.1 6.2: 1, 2, 5, 13, 15b, 17ab, 20, 22 Apr 17
13 Apr 8—Apr 12 Recurrence Relations 7.1, 7.3 7.1: 2, 4, 6ab, 7, 11, 12, 15, 19, 20, 28, 30, 7.3: 1, 2, 3a Apr 24
14 Apr 15—Apr 19 Inclusion-Exclusion Principle 8.1, 8.2 8.1: 9, 10, 11, 12, 15, 16, 24, 26, 29, 36, 8.2: 2, 5, 8, 11, 13, 15, 19, 23b Apr 28
15 Apr 22—Apr 26 Chromatic Polynomials, Rook Polynomials, Review and/or Optional Topics 8.3 8.2: 31, 32, 8.3: 2b, 4, 6 Apr 30
16 Apr 28—May 1 Review and/or Optional Topics
Finals Week May 3 Final Exam, 1:00 pm - 3:00 pm (regular room)