## Introduction to Combinatorics

 General Information Syllabus Homework Assignments Exam Related

## Syllabus

The following is a tentative partial syllabus for the course, and will be updated regularly.  X-hours will occasionally be used in place of or in addition to scheduled lectures.

Lectures Sections in Text Brief Description
Day 1:  1/5 1.1, 1.2 Introduction, basic counting principles
Day 2:  1/7 1.2.1 Sum and product principles
Day 3:  1/10 1.2.2-1.2.4 Functions, directed graphs, bijections, subsets
Day 4:  1/12 1.2.5-1.2.6 Pascal's triangle, quotient principle
Day 5:  1/14 1.2.6-1.3.1 Quotient principle, lattice paths, Catalan numbers
1/17 Martin Luther King Day - Class moved to x-period
Day 6:  1/18 1.3.1-1.3.2. Catalan numbers, Binomial Theorem
Day 7:  1/19 1.3.2-1.3.3 Binomial Theorem, Pigeonhole Prinicple
Day 8:  1/21 TNN handout Total nonnegativity
Day 9:  1/24 2.1-2.1.3, 2.2-2.2.1 Induction, recurrence relations
Day 10:  1/26 2.2.3-2.3.2 Linear recurrences, graphss
Day 11:  1/28 2.3.3 Trees
Day 12:  1/31 2.3.4, 2.4 Spanning trees, review
Day 13:  2/2 3.1-3.1.2 Functions, ordered functions
Day 14:  2/4 3.1.3, 3.1.4 Multisets, integer compositions
Day 16:  2/7 First Midterm exam
Day 17:  2/8 3.2.1 Set partitions and Stirling numbers
Day 18:  2/9 3.2.2-3.2.3 Surjective functions and Stirling numbers
2/11 Winter Carnival - Class moved to x-period
Day 19:  2/14 3.3-3.3.3 Integer partitions
Day 20:  2/16 3.3.3 Integer partitions
Day 21:  2/18 3.3.4-3.3.5 Integer partitions with distinct parts
Day 22:  2/21 Second midterm exam
Day 23:  2/23 4.1-4.1.2 Picture functions
2/23   Last day to drop
Day 24:  2/25 4.1.3-4.1.5 Generating functions
Day 25:  2/28 4.1.5-4.1.6 Generating function product principle
Day 26:  3/2 4.2 Integer partition generating functions
Day 27:  3/4 4.2-4.3.1 Generating functions and recurrence relations
Day 28:  3/8 4.3.2-4.3.4 Fibonacci numbers
Day 29:  3/9 4.3.5-4.4 Catalan numbers and review