# Math 28: Introduction to Combinatorics

Winter 2016

• The latest homework will always appear on top.

• If you are interested in learning to typeset mathematics here is a list of resources compiled by Rebecca Weber on LaTex

Homework assignments

• Late Homework will not be accepted. In order to qualify for a regrade you must have submitted your homework on the due date.
• Write the names of your the group members with whom you worked on the homework, please make sure that what you turned in for homework is your own understanding of how to do the problems.

Practice problems: These problems are very important. We will discuss these in class as a group. Please be sure that you understand these problems thoroughly as you will be asked to present/discuss these problems in class.

Homework due day: Homework will be assigned daily and will be collected once a week.

Week 10
 Sunday, March 13: Final Exam At 8:00 AM in Kemeny 105
 Monday, March 7: Topic: Review All The problems: Problem Set
Week 9
 Friday, March 4: Topic: Course Overview Slides for today: Review of Course Content All The problems: Problem Set
 Wednesday, March 2: Topic: Inclusion-Exclusion - Onto functions All The problems: Problem Set In class problems: # 186, 187, 188, 189, 190
 Monday, February 29: Topic: Inclusion-Exclusion All The problems: Problem Set
Week 8
 Friday, February 26: Topic: Inclusion-Exclusion All The problems: Problem Set In-class problems: # 174, 175, 177, 178, 182 Graded problems (Due Wednesday, March 2): # 176, 179, 180, 181, 183, 184, 185
 Wednesday, February 24: Topic: Solving recurrences with generating functions Slides for today: Euler's Pentagonal Number Theorem All The problems: Problem Set In-class problems: # 166, 169, 170 Graded problems (Due Wednesday, March 2): # 165, 167, 168, 171, 172, 173
 Monday, February 22: Topic: Generating Functions All The problems: Problem Set
Week 7
 Friday, February 19: Topic: Generating Functions for integer partitions Slides for today: Introduction to Generating Functions All The problems: Problem Set In-class problems: # 156, 157, 158, 160, 161 Graded problems (Due Wednesday, Feb. 24): # 154, 155, 159, 162, 163, 164
 Wednesday, February 17: Review: Here is the completed table Twenty-fold way Topic: Introduction to Generating Functions Slides for today: Introduction to Generating Functions All The problems: Problem Set In-class problems: # 141, 142, 144, 145, 147, 148, Graded problems (Due Wednesday, Feb. 24): # 143, 146, 149, 150, 151, 152, 153
 Monday, February 15: Topic: Partitions of integers All The problems: Problem Set
Week 6
 Friday, February 12: Topic: Review for midterm #2 All The problems: Problem Set In-class problems: # 131, 134, 135, 138, Graded problems (Due Wednesday, Feb. 17): # 132, 133, 136, 137, 139, 140
 Wednesday, February 10: Topic: Partitions of Numbers Bases for polynomials and partitions of numbers. All The problems: Problem Set In-class problems: # 125, 126, 127, 129, Graded problems (Due Wednesday, Feb. 17): # 123, 124, 128, 130
 Monday, February 8: Topic: Stirling Numbers Stirling numbers, onto functions, bases for polynomials. All The problems: Problem Set
Week 5
 Friday, February 5: Topic: Mathematical Objects Counted in Distributions Continue working on the twentyfold-way. Slides for today: Distributions and Related Math Objects II All The problems: Problem Set In-class problems: # 113, 115, 116, 117, 118, 121, Graded problems (Due Wednesday, Feb. 10): # 111, 112, 114, 119, 120, 122
 Wednesday, February 3: Topic: Mathematical Objects Counted in Distributions Continue working on the twentyfold-way. Slides for today: Distributions and Related Math Objects I All The problems: Problem Set In-class problems: # 100, 101, 104, 105, 106, 109, Graded problems (Due Wednesday, Feb. 10): # 99, 102, 103, 107, 108, 110
 Monday, February 1: Topic: Introduction to Distributions Discussion of in-class problems from last week. Slides for today: Distributions All The problems: Problem Set
Week 4
 Friday, January 29: Topic: Introduction to Distributions We will start talking about the twentyfold-way. Slides for today: Distributions All The problems: Problem Set In-class problems: # 93, 98 Graded problems (Due Wednesday, Feb. 3): # 94, 95, 96, 97
 Wednesday, January 27: Topic: Strong Induction and Graphs We will continue discussing applications of induction. Slides for today: Strong Induction and Graphs All The problems: Problem Set In-class problems: # 80, 82, 83, 84, 87, Graded problems (Due Wednesday, Feb. 3): # 81, 85, 86, 88, 89, 90, 91, 92
 Monday, January 25: Topic: Recursions and Induction Today we will discuss problems on finding recursions and inductive proofs. Slides for today: Math Induction All The problems: Problem Set
Week 3
 Friday, January 22: Topic: Principle of math Induction Today we will learn to use induction for proof and for recursive reasoning. Slides for today: Math Induction All The problems: Problem Set In-class problems: # 65, 66, 67, 69, 71, 72, 73, 74(a), 77 Graded problems (Due Wednesday, Jan. 27): # 63, 64, 68, 70, 74(b), 75, 76, 78, 79
 Wednesday, January 20: Topic: The pigeonhole principle Today we will work on problems related to Binomial Theorem and discuss the pigeonhole principle. Slides for today: Pigeonhole Principle All The problems: Problem Set In-class problems: # 50, 52, 53, 56, 57, 59 Graded problems (Due Wednesday, Jan. 27): # 51, 54, 55, 58, 60, 61, 62
 Tuesday, January 19: Topic: Lattice Paths We will count lattice paths and Catalan paths. All The problems: Problem Set
Week 2
 Friday, January 15: Topic: The quotient principle The product principle in a different light. Slides for today: Quotient Principle All The problems: Problem Set In-class problems: # 43, 44, 46, 48 Graded problems (Due Wednesday, Jan. 20): # 45, 47, 49
 Wednesday, January 13: Topic: The bijective principle Binomial coefficients and examples of bijective principle Slides for today: Bijective Principle and Binomial Coefficients All The problems: Problem Set In-class problems: # 37, 39 Graded problems (Due Wednesday, Jan. 20): # 36, 38, 40, 41, 42
 Monday, January 11: Topic: The Sum and Product Principles Complete the first set of problems. All the problems: Problem Set In-class problems: # 26, 27, 29, 31, 32 Graded problems (Due Wednesday, Jan. 20): # 28, 30, 33, 34, 35
Week 1
 Friday, January 8: Topic: The Sum and Product Principles Today we will continue working on functions and applications of sum and product principle. All the problems: Problem Set In-class problems: # 18, 19, 21, 22, 24, 25 Graded problems (Due Wednesday, Jan. 13): # 15, 16, 17, 20, 23
 Wednesday, January 6: Topic: The Sum and Product Principles Today we will begin working on problems that on the Sum and Product Principles. Slides for today: Sum Principle, Product principle and Functions All the problems: Problem Set In-class problems: # 1, 3, 5, 7, 8, 12, 13 Graded problems (Due Wednesday, Jan. 13): # 2, 4, 6, 9, 10, 11, 14
 Tuesday, January 5: Topic: Methods of Proof Slides for in-class presentation: Proofs Read Handout on proof writing click here for a copy. Today we will discuss different methods of proofs during the x-hour.
 Monday, January 4: Read 1.1 and 1.2 Topic: Basic Set Notation Slides for in-class presentation: Basic Set Notation Group Work: Working together helps everyone Problem Set: In-Class and Homework Problems

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