MATH BC2006
Combinatorics
Spring 2016

http://www.math.columbia.edu/~bayer/S16/Combinatorics

Tuesdays and Thursdays, 10:10am - 11:25am
237 Milbank Hall (Barnard)

Dave Bayer
Office Hours
bayer@math.columbia.edu
426 Mathematics

Directory of Classes | Spring 2016 Mathematics | MATH BC2006

Content

This is an introductory course in combinatorics, with a focus on counting problems. As there are many methods that have been developed in calculus and analysis for measuring continuous quantities, there are also many methods that have been developed in combinatorics for counting finite sets. We will survey these methods, with a focus on problem solving.

Exams

Including our final, there will be a total of three exams:

• Exam 1 (30 pts), Tuesday, February 16
• Exam 2 (30 pts), Tuesday, March 29
• Final (48 pts), Tuesday, May 10, 9 AM - Noon

Please discuss other conflicts with me in advance of the exam in question. Missed exams will become grades of zero.

Barnard Final Examinations, Spring 2016
Master University Examination Schedule
University Academic Calendar
Columbia Disability Form
Religious Holidays

Preparation for Exams

The following pages are study guides for each exam.

• Preparation for Exam 1
• Preparation for Exam 2
• Preparation for Final

Blackboards

The following are a few blackboards that we decided to save between classes:

• Tuesday, February 9

Textbooks

Our textbooks are available freely online to Columbia University affiliates, through SpringerLink.

These books overlap in content, with varying styles and levels. As we study each topic, please work with the book(s) that you prefer.

The following books are good to read from the beginning, matching fairly well the material that we will cover in class. Go back and forth, or stick with the book that you prefer:

• 1983 Pólya, Tarjan, Woods - Notes on Elementary Combinatorics
• 2007 Aigner - A Course in Enumeration
• 2011 Camina, Lewis - An introduction to enumeration

The following is a great topics book. We are likely to study a few sections from this book, later in the course:

• 2010 Aigner, Ziegler - Proofs from The Book

The following are also of interest, but don’t match our syllabus as closely:

• 2010 Soifer - Geometric Etudes in Combinatorial Mathematics
• 2013 Soberón - Problem-Solving Methods in Combinatorics

For reference and the curious, here is the definitive graduate text on enumeration:

• 2011 Stanley - Enumerative Combinatorics Volume 1, second edition

I found this text after teaching this course; it looks like a good choice for future semesters:

• 2003 Lovasz, Pelikan, Vesztergombi - Discrete mathematics

Previous semesters

• Spring 2015 Combinatorics
• Spring 2014 Combinatorics
• Fall 2011 Combinatorics
• Fall 2000 Combinatorics

Calendar

This calendar gives our schedule of classes and exams:

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