Contact information and Office hours

Course philosophy and outline

Combinatorics is the art of counting. In how many parts can you cut a pizza with n cuts? How many ways are there to make change for a dollar? What is the sum of cubes of integers from 1 to 100? In this course we will get very good at solving all kinds of counting problems.

Book

Concrete Mathematics by Ronald L. L. Graham, Donald E. Knuth, Oren Patashnik, ISBN: 0201558025.

This is an exceptional book. I highly recommend just reading it for fun, entertaiment, and inspiration, including the chapters we do not have time for in class.

Plan of the course (subject to change)

Dates (no. of lectures) Chapters Material covered
January (7) Ch. 1 Recurrent problems
Ch. 2 Sums
Part of Ch. 3 Integer functions
February 1 First midterm Chapters 1,2 and part of 3
February (7) Ch. 5 Binomial coefficients
March (6) Ch. 6 Special numbers
March 29 Second midterm Chapters 5 and 6
April (8) Ch. 7 Generating functions
Ch. 8 Discrete probability

Homeworks

Homeworks will be assigned weekly on Thursdays and collected on the next Thursday. Some of them will be from the book, and you will notice that the book comes with solutions. For these problems your solution will be graded on neatness and completeness, with an extra credit given for unusual and original solutions. Try doing the problem yourself before looking at the end of the book.

You are encouraged to work in groups, the same credit will be given. However, you must write the solutions yourself and joint work must be acknowledged on the first page.

Occasionally, I will assign some "research" problems. Making any progress on them will earn you major bonus points.

Difference between 4690 and 6690

The students in 6690 will be given more and harder homework and exam problems.

Course grade