21-228: Discrete Mathematics (Spring 2015)

Po-Shen Loh

Last updated 14 May 2015.

Location

Grading

The course grade will be calculated as follows: All exams will be open notes / open book.

Homework

The only way to learn mathematics is to do mathematics. (Paul Halmos)

In order to encourage students to experiment with the concepts taught in class, homework assignments will be given on alternate weeks. They will be due in class on Fridays, at the beginning of lecture.

Since homework is a learning activity, students are welcome to discuss ideas with each other, although collaboration in the writing stage is not permitted. In other words, please do not look at the actual document that another student is handing in.

Exams

There will be 3 in-class exams, on Wed Feb 4, Wed Mar 18, and Mon Apr 27. There will also be a comprehensive final exam on Mon May 11, from 1-4pm.

Make-up exams will be given only in the case of a documented medical excuse, a university-sanctioned absence (e.g., participation in a varsity sporting event), or a family emergency. However, this must be requested before the official start time of each exam.

Detailed syllabus

The course follows the order of topics in the well-written book Discrete Mathematics, by L. Lovász, J. Pelikán, and K. Vesztergombi. To adjust for the level of students at CMU, a substantial amount of extra material (not in the textbook) is covered in class. Students are encouraged to read the book, as it provides a clear presentation of an alternate perspective on the content discussed in class. The semester's tentative schedule is detailed below.

Week Topic Alternate reference Work due
Week 1
(Mon Jan 12)    		Basic counting; induction Chapter 1; Fwd-backward induction Homework 1
Week 2
(Mon Jan 19) 		Inclusion-exclusion,
pigeonhole principle
(No class Mon Jan 19 - MLK Day)
Chapter 2;
Dirichlet's approximation theorem
(on AoPS)
Week 3
(Mon Jan 26) 		Homework 2
Week 4
(Mon Feb 2) 		Binomial coefficients Chapter 3; Lucas' Theorem Exam 1 on Wed
Week 5
(Mon Feb 9) 		Linear algebra and recurrences Chapter 4; Wikipedia, Croot's notes Homework 3
Week 6
(Mon Feb 16) 		Generating functions Generatingfunctionology (free book),
by H. Wilf. Sections 1.1-1.3, 2.1-2.3;
notes from MIT's OpenCourseWare
Week 7
(Mon Feb 23) 		More generating functions Homework 4
Week 8
(Mon Mar 2) 		Introduction to graphs
(No class Fri Mar 6) 		Chapter 7
Spring break
(Mon Mar 9) 		Relax
Week 9
(Mon Mar 16) 		Trees Chapter 8 Exam 2 on Wed
Homework 5
Week 10
(Mon Mar 23) 		Traveling salesman problem Chapter 9
Week 11
(Mon Mar 30) 		Matchings Chapter 10 Homework 6
Week 12
(Mon Apr 6) 		Combinatorial geometry Chapter 11
Week 13
(Mon Apr 13) 		Ramsey theory
(No class Fri Apr 17) 		Alt refs #1 and #2 from B. Sudakov's
Princeton Combinatorics course. 		Homework 7
Week 14
(Mon Apr 20) 		Planar graphs Chapter 12
Week 15
(Mon Apr 27) 		Coloring Chapter 13 Exam 3 on Mon
Homework 8
Final exam
(Mon May 11) 		In HH B103, from 1:00 - 4:00pm.

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