**Textbooks:**
We will use a combination of the following texts:

Discrete Mathematics: Elementary and Beyond, by L. Lovász, J. Pelikán, and K. Vesztergombi (Drexel Library online copy)
Introduction to Graph Theory, 2nd Edition, by Douglas B. West
Enumerative Combinatorics, vol.1, by R.P.Stanley
**Grading Scheme:**

30% Homework
30% Midterm
40% Final
**Grade Distribution:** Grades will curved so that approximately the top 50% of the class receive A's and the bottom 50% receive B's. Lower grades will be reserved for students generally not keeping up with the class, missing homeworks, quizzes, and not coming to class.

**Exam Policy:**
No books or electronic devices are allowed on the midterm or exam. No collaboration is permitted at the midterm or exam.
THERE WILL BE NO MAKE-UPS FOR EXAMS.

**The midterm will be in-class on October 25; it will be 80 minutes long. **

Students with special exam-taking requirements or time conflicts should contact me by October 11.

**Quiz Policy:**
Quizzes will be given in class most Wednesdays, and will be similar to some of the homework questions due that day. They will be about 15 minutes long. There will be about 8 quizzes total and the lowest quiz grade will be dropped to compute the quiz grade.
Same rules as the exams apply. THERE WILL BE NO MAKE-UPS FOR QUIZZES.

**Homework Policy:** You may consult each other and the textbook above.
List all people and sources who aided you and whom you aided, and write up the solutions independently, in your own language.
It is easy nowadays to find solutions to almost anything online.
DO NOT consult such solutions until after turning your homework.
Solutions to homeworks will be handed out in class and/or discussed in class.
Late homeworks will not be accepted.

**
Please visit this site frequently for new information.
Updates to the syllabus and reading assignments, homeworks, homework solutions, and practice exams will be posted here as the course progresses.
**
## Syllabus

Since we are using multiple textbooks, there will be some overlap with the reading assignments. The most important/relevant sources will be listed first.

Week 1: Sep 25, Sep 27

Set theory and functions: read the handout Joy of Sets, Section 1.2 and Theorem 1.3.1 of LPV (the textbook Discrete Mathematics: Elementary and Beyond).

Read the handout Mathematical Hygiene. We will discuss some of these concepts throughout the course as needed.

Homework 1 due Oct 04

Week 2: Oct 2, Oct 4

Pascal's triangle, counting, bijective proofs, inclusion-exclusion: Sections 1.7-1.8, 3.5-3.6, 2.3 of LPV

Wikipedia article on inclusion-exclusion

Homework 2 due Oct 11

Week 3: Oct 11

Inclusion-exclusion, Fibonacci numbers: Sections 6.9, 4.1-4.3 of LPV

Homework 3 due Oct 18

Week 4: Oct 16, Oct 18

Catalan numbers, generating functions: Section 3.1 of LPV

Homework 4 due Nov 01 (no homework due October 25 because of the midterm)

Week 5: Oct 23, Oct 25

Generating functions continued: Chapter 2 of generatingfunctionology

Week 6: Oct 30, Nov 1

Introduction to graph theory: vertex degrees, trees, paths, cycles: Sections 7.1-7.2, 8.1-8.2, 13.2 of LPV or Ch. 1-2 of West

Homework 5 due Nov 08

Week 7: Nov 6, Nov 8

Introduction to graph theory: vertex degrees, trees, paths, cycles: Sections 7.1-7.2, 8.1-8.2, 13.2 of LPV or Ch. 1-2 of West

Homework 6 due Nov 15

Week 8: Nov 13, Nov 15

Kruskal's algorithm, Hall's matching theorem (following parts of Ch. 2 and 3 of West)

Homework 7 due Nov 29

Week 9: Nov 20

Euler's formula, Platonic solids: Ch. 6.1 of West

Week 10: Nov 27, Nov 29

Graph coloring, coloring planar graphs: Ch. 5.1 and 6.3 of West

Homework 8 due Dec 06

Week 11: Dec 4, Dec 6

Fisher's inequality and other linear algebra applications (pages 46-56 of notes by Andras Gyarfas)