Math 365, Spring 2017
Elements of combinatorics

 

Logistics

Professor: Zajj Daugherty
Office hours: Mo 3:50–5:00 in NAC 6/301.
Class: MoWe 2:00–3:40 in NAC 5/102
Textbook: Discrete Mathematics and Its Applications (7th edition), by Kenneth Rosen. [pdf]
Grades: (Click for grading rubric and details on course expectations.)

Schedule

Week 1 Read Sections 2.1 and 2.2.
Handouts: [Monday] [Wednesday]
Slides: [Monday] [Wednesday]
Due Monday 2/6: Email zdaugherty@gmail.com from your preferred email account with subject line "Math 365: Homework 0" and the information below.
Due Wednesday 2/8: In-class Exercises 1–5, 2.1 #4, 10, 23, 28, 30 (read and think about 31 first), 2.2 #1, 14, 28, 32, 34, 36 (argue formally), 39, 50. (Careful with big Venn diagrams!! With 4 sets, you can no longer just use circles! See wikipedia. ) [solutions]
Quiz Wednesday 2/8: covering sections 2.1 and 2.2. [solutions]
Week 2 Read Sections 2.3 and 2.4.
Handouts: [Monday] [Wednesday]
Slides: [Monday] [Wednesday]
Due Wednesday 2/15: In-class Exercises 6–10, 2.3 #2, 6 (a,b,d), 16, 32, 42; 2.4 # 4, 8, 10(b,c), 12 (b,c), 14 (c,d,e), 43(a,b,c), 44. [solutions]
Week 3 Read Sections 2.5 and 5.1.
No class Monday 2/13. Office hours on Wednesdays 2/15.
Handouts: (no handout for 2/15)
Slides: [Wednesday]
Due Wednesday 2/22: Section 2.5 # 2, 4, 10, 12, 16, 33; Copy by hand Examples 1 and 3 from Section 5.1. [solutions]
Week 4 Read Section 5.1.
No class Monday 2/20. Office hours on Wednesday 2/22.
Handouts: [Wednesday]
Slides: [Wednesday]
Quiz Monday 2/27: covering sections 2.3, 2.4, 2.5, 5.1. [solutions]
Due Wednesday 3/01: In-class Exercise 11; Section 5.1 #2, 49, 50, 51, 52. [solutions]
Week 5 Read Sections 6.1 and 6.3.
Handouts: [Monday] [Wednesday]
Slides: [Monday] [Wednesday]
Due Wednesday 3/08: In-class Exercises 12–15. (Note: there are a lot more practice problems in sections 6.1 and 6.3.) [solutions]
Exam Wednesday 3/08: covering sections 2.1, 2.2, 2.3, 2.4, 2.5, 5.1, 6.1, 6.3. [solutions]
Week 6 Read Section 6.2. Study for exam.
Handouts: [Monday]
Slides: [Monday]
Due Wednesday 3/15: In-class Exercises 16. (Note: there are a lot more practice problems in section 6.2.) [solutions]
Week 7 Read Section 6.4, 6.5.
Monday: [handout] [slides] [notes packet]
Monday supplement: [Example of the argument for the right hand side of Vandermonde's identity]
Wednesday: [handout] [slides] [notes packet]
Due Wednesday 3/22: In-class Exercises 17–20. Section 6.4 #10 (first try (x+1/x)^4, and other small examples), 12, 33. [solutions]
Week 8 Read Sections 6.5, 8.1.
Monday: [Exercise 21] [Ch 6 review problems]
Wednesday: [handout] [slides] [notes packet]
Quiz Monday 3/27: covering sections 6.1–6.5. [solutions]
Due Wednesday 3/29: In-class Exercises 21–22. Chapter 6 supplementary exercises (p440) #4, 7, 8, 14, 21, 39, 40, 42. [solutions] [Answers to Ch 6 review problems]
Week 9 Read Sections 8.2, 8.4.
Monday: [handout] [slides] [notes packet]
Wednesday: [handout] [slides] [notes packet]
[Exampe of solving a non-homogeneous recursion relation]
Due Wednesday 4/05: In-class Exercises 23–28. Outline the proof of Theorem 1 of Section 8.2, and prove Theorem 2 (the proof will be almost exactly the same -- mimic the book's language). [solutions]
Exam Wednesday 4/05: covering sections 6.1—6.5, 8.1, 8.2, some of 8.4. [solutions]
Week 10 Read Section 8.4 (skip "Extended Binomial Theorem").
Monday: [handout] [slides] [notes packet]
Review for partial fractions decomposition: Notes from math 202, corresponding slides with answers, Khan Academy tutorial
Spring break
Due 4/20: In-class Exercises 29, 30, 31; Section 8.4# 48 (a,b,c). [solutions]
Week 11
(4/17-21)
Read Sections 8.4 (skip "Extended Binomial Theorem"), 8.5, 9.1 (skip "Combining Relations"), 9.5.
Wednesday: [worksheet] [solutions]
Thursday: [handout] [slides] [notes packet]
Due 4/26: In-class Exercises 33-37 (we skipped a number) [solutions]
Week 12
(4/24-28)
Read Sections 10.1, 10.2, 10.3 (skip adjacency and incidence matrices), 10.4 (pay special note to the remark on p679 - we will be using the other vocabulary)
Monday: [handout] [slides] [notes packet]
Wednesday: [handout] [slides] [notes packet]
Quiz Wednesday 4/26: covering sections 8.4, 8.5, and equivalence relations. [solutions]
Due 5/3: In-class Exercises 38-42, Section 10.2 #42 (For 42, notice your graphs have to be simple. Also, keep in mind Theorem 2.); Section 10.4#5. [solutions]
Week 13 Read Sections 10.4, 10.5, 10.7
Monday: [handout] [slides] [notes packet]
Wednesday: [handout] [slides] [notes packet]
Due 5/10: In-class Exercises 43-48 Section 10.4#31--32, 50. Section 10.5 # 57, (read 58), 59. [solutions]
Quiz Wednesday 5/10: covering sections 10.1,2,3,4,5,7.
Week 14 Read Sections 10.8, 11.1, Chromatic polynomials
Monday: [handout] [slides] [notes packet]
Wednesday: [handout] [slides] [notes packet]
Due 5/17: In-class Exercises 49-52. [solutions]
Week 15 Read Sections 11.1 (skip rooted trees), 11.4 (skip search and algorithms), Spanning trees, Cayley's formula, Prufer code
Monday: [handout] [slides] [notes packet]
Wednesday: [handout] [slides] [notes packet]

Due 5/24: In-class Exercises 53--55.

Writing guide

For the basic requirements of homework write-ups, see writing tips.
Alternatively, see Francis Su's Guidelines for Good Mathematical Writing.

If you are interested in learning to type up your homework using LaTeX, there are lots of great resources out there. To see my code, the LaTeX files for notes and handouts can be found by replacing .pdf with .tex for most of the files above. You'll also need preamble.tex (occasionally updated). You can find another sample on my teaching page, and lots of sample code at TeXample.net. The Not So Short guide to LaTeX is linked from my resources page. You can obtain LaTeX via LaTeXproject.org.

Extra details for special homework assignments

Homework 0 info:
(a) What name you like to go by, and how is it pronounced.
(b) What you're majoring in, and why.
(c) What your general long-term goals are.
(d) Something that you're really good at.
(e) Optional: a photo or a description of yourself to help me learn your name faster.