Contact information and Office hours
- Office: Boyd 401
- Email: Please use the WebCT mail tool
- Office hours: Tuesday and Thursday, 1-2 p.m.
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
- Midterms: 20% + 20%
- Homework: 30%
- Final: 30%