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Math 301 Spring 2018
Combinatorics
Course Syllabus
Course: Math 301
Title: Combinatorics
Textbook: There is no required textbook for this course. I will work mostly from the book Applied Combinatorics by Keller and Trotter, available free on the web. Other reference materials will be provided as needed.
Subject Material:
This course will explore a variety of topics in combinatorics. Roughly, the course will look something like this:
- (4-5 lectures) Counting, binomial coefficients, the inclusion-exclusion theorem.
- (4-5 lectures) Generating functions and recurrence relations.
- The first exam happens.
- (6-7 lectures) Probabilistic methods, the Erdos-Ko-Rado theorem, concentration inequalities, the Lovasz Local Lemma.
- (2-3 lectures) Ramsey Theory.
- The second exam happens.
- (7 lectures) Some extremal combinatorics. Matchings, Turan's Theorem.
- The third exam happens.
- (6-7 lectures) Posets, Dilworth's Theorem.
- (remainder) Additional topics (we will discuss later)
- The fourth exam happens.
Lecture: Attending the lecture is a fundamental part of the course; you will be responsible for material presented in lecture regardless of whether it is discussed in the textbook.
Reading: Reading the assigned items corresponding to the class lectures and homework exercises is considered part of the homework assignment; you will be responsible for material in the assigned readings regardless of whether it is discussed in lecture. You are expected to read the assigned material in advance of the lecture.
Classroom Conduct: In the classroom, a certain level of respect and attentiveness is expected. Please do not use phones or computers, play games, or talk to friends during lecture. This can be distracting to other students and the instructor.
Calculators: A calculator is not required for this course. The use of any calculators or other electronic equipment will NOT be permitted on exams.
Homework: Homework problems will be assigned on the course homework page, and should be completed and turned in by the beginning of class on the indicated due date. You should make every effort to complete the homework assignments and seek help with problems you have been unable to solve. You may turn in one assignment late (no later than one class period) without permission.
Exams: There will be four exams given during the regular lecture hour. Please see the course calendar for the specific dates. More information will be provided within 1 week of the exam. These exams will not be cumulative. See exam policies below.
Final Exam: There will be no final exam.
Exam Policies: No calculators or other electronic devices will be allowed during the exams. Unless you have a very serious, well documented, and compelling reason to miss an exam, there will be no makeup exams, for any reason.
Grading: Your final course grade will be based on the following weighted average:
- 20% Homework
- 23% each of your best three exams
- 11% your lowest exam score
A curve may be applied to final scores or individual examinations at the instructor's discretion. Regardless of the curve, the following basic rubric will be in place:
- Scores above 90%: A
- Scores above 80%: At least B
- Scores above 70%: At least C
- Scores above 60%: At least D
Academic Honesty: Academic dishonesty is a serious offense, carrying serious administrative sanctions. Any instance of dishonesty will be pursued by the instructor. It is in your best interest to follow all policies laid out here and elsewhere on the website, and familiarize yourself with the university guidelines for academic honesty. Please help maintain both your own integrity and the integrity of Carnegie Mellon University.
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