Bulletin description: Permutations and combinations, recurrence relations, inclusion and exclusion, Polya's theory of counting, graph theory, transport networks, matching theory. Prereq: MATH 2100 or MATH 2350.
Lectures: 
M, W, F  9:00am  9:50am 
Cudahy Hall 120  
Office Hours: 
Monday,  2:30pm  3:30pm 
Wednesday,  2:00pm  3:00pm  
Thursday,  10:30am  11:30am  
Cudahy Hall 307  and by appointment 
I recommend using Overleaf (free) to write your assignments in LaTeX.
I'm happy to help troubleshoot your LaTeX in office hours and over email!
Tues, Jan 16  Classes begin 
Wed, Jan 24  Last day to add/drop classes or request CR/NC option 
Mon, Mar 4 — Fri, Mar 8  Midterm exam period 
Mon, Mar 11 — Fri, Mar 15  Spring break, no classes 
Fri, Mar 29 and Mon, Apr 1  Easter break, no classes 
Fri, Apr 12  Last day to withdraw from classes 
Fri, May 3  Last day of classes 
Thursday, May 9 1:00pm  3:00pm 
Math 4670 / 5670 final exam 
#  Date  Topics  Suggested HW & Announcements 

Week 1  
1  Wed, Jan 17 
Syllabus Section 1.1: Principles of Combinatorics (started) 
Before Friday: read syllabus No suggested homework. 
2  Fri, Jan 19  Section 1.1: Principles of Combinatorics (continued) 
Read pages 14 Section 1.1: 2a, 3, 4, 7 
Week 2  
3  Mon, Jan 22  Section 1.1: Principles of Combinatorics (continued) 
Read pages 57 Section 1.1: 9ab 
4  Wed, Jan 24 
Homework 1 Assigned (link at top of page, due Friday, Feb 9) Section 1.1: Principles of Combinatorics (continued) 
Read pages 89 Section 1.1: 1bc, 2b, 9c, 18 
5  Fri, Jan 26 
Quiz 1 — covers all 1.1 suggested homework so far Section 1.1: Principles of Combinatorics (continued) 
Read pages 913 No new suggested homework, keep practicing and reading. 
Week 3  
6  Mon, Jan 29  Section 1.1: Principles of Combinatorics (finished) 
Read pages 1314. Section 1.1: 1a, 5, 11, 15, 17 
7  Wed, Jan 31  Section 1.2: Counting, overcounting, and the sum principle (started) 
Read pages 1516. Section 1.2: 1, 2, 4abc, 11 
8  Fri, Feb 2  Section 1.2: Counting, overcounting, and the sum principle (continued) 
Read pages 16 to middle of 18. Section 1.2: 4de, 6, 10, 16, 17 
Week 4  
9  Mon, Feb 5  Section 1.2: Counting, overcounting, and the sum principle (continued)  Read pages 1822. 
10  Wed, Feb 7 
Section 1.2: Counting, overcounting, and the sum principle (finished) Section 1.3: Functions and the Bijection Principle (started) 
Read pages 2425. Section 1.2: 3, 7, 9 Section 1.3: 1, 2 
11  Fri, Feb 9 
Homework 1 Due Homework 2 Assigned Quiz 2 Section 1.3: Functions and the Bijection Principle (continued) 
Read pages 2527. Section 1.3: 3, 4 
Week 5  
12  Mon, Feb 12  Section 1.3: Functions and the Bijection Principle (continued) 
Read pages 2730. Section 1.3: 9, 12 
13  Wed, Feb 14  Section 1.3: Functions and the Bijection Principle (finished) 
Read pages 2831 (skipping "Inverse" section). Section 1.3: Answer Question 34 on page 30. 
14  Fri, Feb 16  Exam 1  
Week 6  
15  Mon, Feb 19 
Section 1.4: Relations and the Equivalence Principle (we are covering just some of the material) 
Read from page 36 (starting at "The equivalence principle") up to 38 (stopping at "Are the equivalence relations?") and ignore parts about equivalence relations Section 1.4: 8, 9, 10 
16  Wed, Feb 21 
Homework 2 Due Homework 3 Assigned Section 2.1: Counting Functions (started) 
Read pages 4953 Section 2.1: 1ab, 2, 4abcd, 5, 6 
17  Fri, Feb 23 
Quiz 3 Section 2.1: Counting Functions (continued) 
Read pages 5356 Section 2.1: 9, 10 
Week 7  
18  Mon, Feb 26 
Section 2.1: Counting Functions (finished) Section 2.2: Counting Subsets and Multisets (started) 
Read pages 5560. Section 2.1: 1c, 14, 16 Section 2.2: 1, 2, 3 NOTE: Problems 2.1.14 and 2.1.16c are extra challenging, and will not be on the quiz, but they are still good practice. Questions 2.1.1c and 2.1.16ab are eligible quiz questions. 
19  Wed, Feb 28  Section 2.2: Counting Subsets and Multisets (continued) 
Read pages 5961. Section 2.2: 4a, 4b, 7abcd, 8 
20  Fri, Mar 1 
Quiz 4 Section 2.2: Counting Subsets and Multisets (continued) 
Read pages 6164. Section 2.2: 4ef 
Week 8  
21  Mon, Mar 4  Section 2.2: Counting Subsets and Multisets (finished) 
Section 2.2: 6 Plus the group work problems from lecture about the Binomial Theorem. 
22  Wed, Mar 6 
Homework 3 Due Homework 4 Assigned Section 2.3: Counting Set Partitions (started) 
Read pages 6769. Section 2.3: 1, 8, 9 
23  Fri, Mar 8  Exam 2  
Spring Break  
Mon, Mar 11  Spring Break — no class  
Wed, Mar 13  Spring Break — no class  
Fri, Mar 15  Spring Break — no class  
Week 9  
24  Mon, Mar 18  Section 2.3: Counting Set Partitions (continued) 
Read pages 6972. Section 2.3: 6, 11 
25  Wed, Mar 20 
Section 2.3: Counting Set Partitions (finished) Section 2.4: Counting Integer Partitions (started) 
Read pages 7376. Section 2.3: 2, 3, 4, 5 Section 2.4: 1 
26  Fri, Mar 22 
Quiz 5 Section 2.4: Counting Integer Partitions (continued) 
Read pages 7678. Section 2.4: 5, 6 
Week 10  
27  Mon, Mar 25  Section 2.4: Counting Integer Partitions (continued) 
Read pages 7880. Section 2.4: 2, 3 
28  Wed, Mar 27 
Homework 4 Due Section 2.4: Counting Integer Partitions (finishedish) 
Read pages 7981. Section 2.4: 8 
Fri, Mar 29  Easter Break — no class  
Week 11  
Mon, Apr 1  Easter Break — no class  
29  Wed, Apr 3 
Homework 5 Assigned Section 3.1: InclusionExclusion (started) 
Read pages 8388. Section 3.1: Questions 9094, and 96 on pages 8486 
30  Fri, Apr 5 
Quiz 6 Section 3.1: InclusionExclusion (nearly finished) 

Week 12  
31  Mon, Apr 8 
No inperson lecture today. Video Lecture — GT1  Intro to Graph Theory 

32  Wed, Apr 10 
Section 3.1: InclusionExclusion (finish) GT2  Trees (started) 
Read pages 8892 of main textbook. Section 3.1: 1, 2, 4a, 5a, 8 Lecture GT 1 and GT2: Review definitions for Quiz 7. 
33  Fri, Apr 12 
Quiz 7 — One question from 3.1 and one definition from GT1 or GT2. GT2  Trees (continued) 
Read pages 6568 of Applied Combinatorics. Chapter 5, exercises 14, 7 in Applied Combinatorics. 
Week 13  
34  Mon, Apr 15  GT2  Trees (continued) 
Read pages 6870 of Applied Combinatorics. Suggested Homework 
35  Wed, Apr 17 
Homework 5 Due Homework 6 Assigned GT2  Trees (finished) GT3  Walks on Graphs (barely started) 
Same reading and suggested homework as 4/15. 
36  Fri, Apr 19  Exam 3  
Week 14  
37  Mon, Apr 22  GT3  Walks on Graphs (continued) 
Read pages 7071 of Applied Combinatorics. Chapter 5, exercises 8, 9 (ignore Hamiltonian), 10 in Applied Combinatorics. 
38  Wed, Apr 24  GT3  Walks on Graphs (continued) 
Read pages 7173 of Applied Combinatorics. For the graphs in exercises 8 and 9 of Chapter 5 in Applied Combinatorics, apply the algorithm we discussed in class today to compute an Eulerian circuit. 
39  Fri, Apr 26 
Lecture replaced by a prerecorded video lecture GT3  Walks on Graphs (finished) GT4  Graph Coloring (started) 
See Monday, April 29 
Week 15  
40  Mon, Apr 29 
Quiz 8 GT4  Graph Coloring (continued) 
Read pages 7376 of Applied Combinatorics. Chapter 5, exercises 9 (the Hamiltonian part), 12, 13, 14, 15, 25 in Applied Combinatorics. 
41  Wed, May 1 
Homework 6 Due GT4  Graph Coloring (continued) 
Read Section 5.4.1 in this other version of the book. Suggested Homework:

42  Fri, May 3 
GT4  Graph Coloring (finished) GT5  Planar Graphs (brief overview) 
Read end of page 85 (last paragraph) to middle of page 88 in Applied Combinatorics. Chapter 5, exercises 28, 29, 30, 31 in Applied Combinatorics. 
Thurs, May 9  Final Exam, 1:00pm  3:00pm 