Math 365, Spring 2018
Elements of combinatorics

 

Logistics

Professor: Zajj Daugherty
Office hours: Mo 12:45-1:45 in NAC 6/301.
Class: MoWe 2:00–3:40 in NAC 5/109
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
(1/29&31)
Read Sections 2.1 and 2.2, and the two handouts from the "Writing guide" section below.
Monday: handout, slides, notes.
Wednesday: handout, slides, notes.
Due Monday 2/5: Email zdaugherty@gmail.com from your preferred email account with subject line "Math 365: Homework 0" and the information below.
Due Wednesday 2/7: In-class Exercises 1–5; Book 2.1 #4, 10, 23, 30 (read and think about 31 first); 2.2 #1, 14, 50; and the Writing Exercise. (solutions)
Quiz Wednesday 2/7: covering sections 2.1 and 2.2. (solutions)
Week 2
(2/5&7)
Read Sections 2.3 and 2.4.
Monday: handout, slides, notes.
Wednesday: handout, slides, notes.
Due Wednesday 2/14: In-class Exercises 6–10; Book 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.; and the Writing Exercise. (solutions)
Practice quiz on sections 2.3 & 2.4: (quiz) (solutions)
Week 3
(2/14)
Read Section 2.5
No class Monday 2/12. Office hours on Tuesday.
Wednesday: slides, notes (no handout).
Due Wednesday 2/21: Section 2.5 # 2, 4, 10, 12, 16, 33; Copy by hand Examples 1 and 3 from Section 5.1.; and the Writing Exercise. (solutions)
Practice quiz on sections 2.5 & 5.1: (quiz) (solutions)
Week 4
(2/20&21)
Read Sections 5.1 and 6.1.
Class on Tuesday 2/20 and Wednesday 2/21. Office hours on Tuesday.
Tuesday: handout, slides, notes.
Wednesday: handout, slides, notes.
Due Wednesday 2/28: In-class Exercise 11—14; Section 5.1 #2, 49, 50, 51, 52. (Note: there are a lot more problems in section 6.1 for your own practice.) (solutions)
Week 5
(2/26&28)
Read Sections 6.2 and 6.3.
Monday/Wednesday: handout, slides, notes.
Due Wednesday 3/7: In-class Exercise 15—16. (solutions) (More practice for 6.1—3 from the book) (Solutions for odd problems from 6.1—6.3)
Practice quiz on sections 6.1—6.3: (quiz) (solutions)
Exam Monday 3/05: Sections 2.1, 2.2, 2.3, 2.4, 2.5, 5.1, 6.1, 6.2, 6.3. (solutions)
Week 6
(3/5&7)
Read Section 6.4. Class canceled due to snow.
Full notes on 6.4: slides, notes. Supplement: Example of the argument for the right hand side of Vandermonde's identity.
Week 7
(3/12&14)
Read Section 6.4, 6.5.
Monday: handout, slides, notes. Supplement: Example of the argument for the right hand side of Vandermonde's identity.
Wednesday: handout, slides, notes.
Quiz Monday 3/26 (RESCHEDULED) covering sections 6.1–6.5. (solutions)
Due Wednesday 3/21: In-class Exercises 17–21; Section 6.4 #10 (first try (x+1/x)^4, and other small examples), 12. Chapter 6 supplementary exercises (p440) #4, 7, 8, 14, 21, 39, 40. (solutions)
(answers to ch 6 supplementary exercises)
Week 8
(3/19&21)
Read Sections 8.1
Monday: handout, slides, notes.
Due Wednesday 3/28: In-class Exercises 22. (solutions)
Exam 1 rewrites due by 4pm 3/30: On any problem that you missed at least two points on, rewrite the entire problem (all parts). Your rewrite will be scored by taking your new grade on any rewritten problems, your old grade on any skipped problems for which you lost at most one point, and 0 for any skipped problems for which you lost more than one point.
Turn in your rewrite using this template, and attach your original exam. You total exam grade will be the higher of (1) your original score, and (2) the average of your original score and your rewrite.
(Example of scoring)
Week 9
(3/19&21)
Read Section 8.2
Monday: handout, slides, notes.
Wednesday: handout, slides, notes.
Due Thursday 4/12 (by 5pm): In-class Exercises 23—26; 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). Hand in by email, or put under my door by 5pm. (No class Wednesday) (solutions)
Spring break 3/30—4/8
Week
10 & 11
(4/9&18)
Read Section 8.4 (skip "Extended Binomial Theorem").
Review for partial fractions decomposition: Notes from math 202, corresponding slides with answers, Khan Academy tutorial
Monday: handout, slides, notes.
Wednesday: worksheet, solutions
Exam Monday 4/16 (RESCHEDULED): covering sections 6.1—6.5, 8.1, 8.2.
Due Wednesday 4/18: In-class Exercises 27 and 28; Section 8.4# 48 (a,b,c). (solutions)
Due Wednesday 4/25: In-class Exercises 29, 30, 31. (solutions)
Week 12
(4/23&25)
9.1 (skip "Combining Relations"), 9.5, 10.1, 10.2, 10.3 (skip adjacency and incidence matrices).
Monday: handout, slides, notes. Wednesday: handout, slides, notes.
Due Wednesday 5/2: In-class Exercises 32—37. (solutions)
Quiz Wednesday 5/2: covering sections 8.4, 10.1, 10.2 (except new graphs from old), 10.3 (skip adjacency and incidence matrices), and equivalence relations. (solutions)
Week 13
(4/30&5/2)
10.2 and 10.4 (pay special note to the remark on p679 - we will be using the other vocabulary)
Monday: handout, slides, notes. Wednesday: handout, slides, notes.
Due Wednesday 5/9: Exercises 38—40. (solutions)
Week 14
(5/7&9)
Read Sections 10.5 (skip Hamilton paths and cycles), 10.8, Chromatic polynomials
Monday: handout, slides, notes
Wednesday: handout, slides, notes
Due Wednesday 5/16: Exercises 41—44.
Week 15
(5/14&16)
Read Sections 11.1 (skip rooted trees), 11.4 (skip search and algorithms), Spanning trees, Cayley's formula, Prufer code
Monday: handout, slides, notes
Wednesday: handout, slides, notes
Due Wednesday 5/23: Exercises 45—47.

Writing guide

For the basic requirements of homework write-ups, see writing tips.
Also, 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: Email zdaugherty@gmail.com from your preferred email account with subject line "Math 365: Homework 0", including the following information:
(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) A photo or a physical description of yourself to help me learn your name faster. ("That guy who doesn't say anything" isn't sufficient.)