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 1-4 Section 1.1: 2a, 3, 4, 7 |
| Week 2 | |||
| 3 | Mon, Jan 22 | Section 1.1: Principles of Combinatorics (continued) |
Read pages 5-7 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 8-9 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 9-13 No new suggested homework, keep practicing and reading. |
| Week 3 | |||
| 6 | Mon, Jan 29 | Section 1.1: Principles of Combinatorics (finished) |
Read pages 13-14. Section 1.1: 1a, 5, 11, 15, 17 |
| 7 | Wed, Jan 31 | Section 1.2: Counting, overcounting, and the sum principle (started) |
Read pages 15-16. 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 18-22. |
| 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 24-25. 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 25-27. Section 1.3: 3, 4 |
| Week 5 | |||
| 12 | Mon, Feb 12 | Section 1.3: Functions and the Bijection Principle (continued) |
Read pages 27-30. Section 1.3: 9, 12 |
| 13 | Wed, Feb 14 | Section 1.3: Functions and the Bijection Principle (finished) |
Read pages 28-31 (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 49-53 Section 2.1: 1ab, 2, 4abcd, 5, 6 |
| 17 | Fri, Feb 23 |
Quiz 3 Section 2.1: Counting Functions (continued) |
Read pages 53-56 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 55-60. 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 59-61. Section 2.2: 4a, 4b, 7abcd, 8 |
| 20 | Fri, Mar 1 |
Quiz 4 Section 2.2: Counting Subsets and Multisets (continued) |
Read pages 61-64. 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 67-69. 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 69-72. 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 73-76. 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 76-78. Section 2.4: 5, 6 |
| Week 10 | |||
| 27 | Mon, Mar 25 | Section 2.4: Counting Integer Partitions (continued) |
Read pages 78-80. Section 2.4: 2, 3 |
| 28 | Wed, Mar 27 |
Homework 4 Due Section 2.4: Counting Integer Partitions (finished-ish) |
Read pages 79-81. 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: Inclusion-Exclusion (started) |
Read pages 83-88. Section 3.1: Questions 90-94, and 96 on pages 84-86 |
| 30 | Fri, Apr 5 |
Quiz 6 Section 3.1: Inclusion-Exclusion (nearly finished) |
|
| Week 12 | |||
| 31 | Mon, Apr 8 |
No in-person lecture today. Video Lecture — GT1 - Intro to Graph Theory |
|
| 32 | Wed, Apr 10 |
Section 3.1: Inclusion-Exclusion (finish) GT2 - Trees (started) |
Read pages 88-92 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 65-68 of Applied Combinatorics. Chapter 5, exercises 1-4, 7 in Applied Combinatorics. |
| Week 13 | |||
| 34 | Mon, Apr 15 | GT2 - Trees (continued) |
Read pages 68-70 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 70-71 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 71-73 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 pre-recorded 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 73-76 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 |