Math 28: Introduction to Combinatorics

Winter 2019


  • 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 some of these problems in class.

    Graded assignments: These problems will graded in detail.

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

    Week 9
    Saturday, March 09:
    • Final Exam in Kemeny Hall 006 from 3:00 - 6:00 PM
    Wednesday, March 06:
    • Topic: Review of Course Material
      Slides for in-class presentation: Review
    • All the problems: Problem Set
    Monday, March 04:
    • Topic: Problems using Inclusion-Exclusion
    • Problem Set: Problem Set
    • Go over in-class problems from Friday and work on practice Inclusion-Exclusion problems.
    Friday, March 01:

    Week 8
    Thursday, February 28:
    • Today we will go over in-class problems and continue to work on homework as needed.
    Wednesday, February 27:
    • Topic: Inclusion-Exclusion
    • We begin working on problems related to Inclusion-Exclusion
    • All the problems: Problem Set
    • In-class problems: # 169, 170
    • Graded problems (Due Friday, March 1): # 171, 172
    Monday, February 25:
    • Topic: Applications of generating Functions to solving recurrences
    • Problem Set: Problem Set
    • In-class problems: # 163, 165, 168
    • Graded problems (Due Friday, March 1): # 161, 162, 164, 167
    Friday, February 22:
    • Topic: Applications of generating functions to integer partitions
    • Problem Set: Problem Set
    • In-class problems: # 153, 154, 160
    • Graded problems (Due Friday, March 1): # 155, 156, 157, 158, 159
    Week 7
    Thursday, February 21:
    • Today we will go over in-class problems and continue to work on homework as needed.
    Wednesday, February 20:
    • Topic: Review for Midterm
    • We will go over review problems.
    • All the problems: Problem Set
    Monday, February 18:
    • Topic: Generating Functions and Counting
    • Problem Set: Problem Set
    • In-class problems: # 144, 145, 148, 151
    • Graded problems (Due Friday, Feb. 22): # 146, 147, 149, 150, 152
    Friday, February 15:
    • Topic: Introduction to Generating Functions
      Slides for in-class presentation: Generating Functions
    • Problem Set: Problem Set
    • In-class problems: # 135, 136, 139, 141, 142
    • Graded problems (Due Friday, Feb. 22): # 133, 134, 137, 138, 140, 143
    Week 6
    Thursday, February 14:
    • Topic: Review of Distributions problems
      Slides for in-class presentation: Distribution Summary 2
    • Today we will go over in-class problems and continue to work on homework as needed.
    Wednesday, February 13:
    • Topic: Partitions of Integers
    • All the problems: Problem Set
    • In-class problems: # 132
    • Graded problems (Due Friday, Feb. 15): # 130, 131
    Monday, February 11:
    • Topic: Multinomial coefficients and onto functions
    • Problem Set: Problem Set
    • In-class problems: # 124, 126, 129
    • Graded problems (Due Friday, Feb. 15): # 122, 123, 125, 127, 128
    Friday, February 8:
    • Topic: Stirling numbers and onto functions
      Slides for in-class presentation: Distributions Summary 1
    • Problem Set: Problem Set
    • In-class problems: # 115, 116, 117, 119, 120, 121
    • Graded problems (Due Friday, Feb. 15): # 111, 112, 113, 114, 118
    Week 5
    Thursday, February 7:
    • Today we will go over in-class problems and continue to work on homework as needed.
    Wednesday, February 6:
    • Topic: Stirling Numbers
    • All the problems: Problem Set
    • In-class problems: # 107, 108, 109, 111,
    • Graded problems (Due Friday, Feb. 8): # 110
    Monday, February 4:
    • Topic: Distributions
      Slides for in-class presentation: Intro to Distributions
    • Problem Set: Problem Set
    • In-class problems: # 97, 98, 99, 104
    • Graded problems (Due Friday, Feb. 8): # 100, 101, 102, 103, 105, 106
    Friday, February 1:
    • Topic: Applications of induction in graph theory
    • Problem Set: Problem Set
    • In-class problems: # 87, 88, 90, 93
    • Graded problems (Due Friday, Feb. 8): # 89, 91, 92, 94, 95, 96
    Week 4
    Thursday, January 31:
    • Today we will go over in-class problems and continue to work on homework as needed.
    Wednesday, January 30:
    Monday, January 28:
    • Topic: Recurrences
      Slides for in-class presentation: Recurrences
    • Problem Set: Problem Set
    • In-class problems: # 77, 78, 81, 84, 85
    • Graded problems (Due Friday, Feb. 1): # 79, 80, 82, 83, 86
    Friday, January 25:
    • Topic: Principle of Math Induction
      Slides for in-class presentation: Principle of Math Induction
    • Problem Set: Problem Set
    • In-class problems: # 67, 69, 70, 73, 75
    • Graded problems (Due Friday, Feb. 1): # 68, 71, 72, 74, 76
    Week 3
    Thursday, January 24:
    • Today we will go over in-class problems and continue to work on homework as needed.
    Wednesday, January 23:
    • Topic: Binomial Theorem and Pigeonhole principle continued
    • All the problems: Problem Set
    • In-class problems: # 64
    • Graded problems (Due Friday, Jan. 25): # 65, 66
    Monday, January 21:
    • MLK - Day of Observance - Class moved to x-hour.
    Friday, January 18:
    • Topic: Binomial Theorem and Pigeonhole Principle
      Slides for in-class presentation: Pigeonhole Principle
    • Problem Set: Problem Set
    • In-class problems: # 56, 58, 61, 62,
    • Graded problems (Due Friday, Jan. 25): # 57, 59, 60, 63
    Week 2
    Thursday, January 17:
    • Topic: Lattice paths and Catalan paths
    • Slides for today: Lattice and Catalan Paths
    • Today we will go over in-class problems and continue to work on homework as needed.
    • All the problems: Problem Set
    • In-class problems: # 48, 49, 51, 53
    • Graded problems (Due Friday, Jan. 25): # 46, 47, 50, 52, 54, 55
    Wednesday, January 16:
    • Topic: Quotient Principle and binomial coefficients
    • All the problems: Problem Set
    • In-class problems: # 43, 45
    • Graded problems (Due Friday, Jan. 18): # 42, 44
    Monday, January 14:
    • Topic: Quotient Principle
    • We work on problems that use the bijection principle and quotient principle
    • Slides for today: The Quotient Principle
    • All the problems: Problem Set
    • In-class problems: # 33, 34, 37, 38
    • Graded problems (Due Friday, Jan. 18): # 35, 36, 39, 40, 41
    Friday, January 11:
    • Topic: Difference and Bijection Principles and the Binomial Coefficients
      Slides for in-class presentation: Difference and Bijection Principles
    • Problem Set: Problem Set
    • In-class problems: # 21, 23, 25, 26, 28, 29, 30
    • Graded problems (Due Friday, Jan. 18): # 22, 24, 27, 31, 32
    Week 1
    Thursday, January 10:
    • Topic: Sum and Product Principle
    • Today we will go over in-class problems and continue to work on homework as needed.
    Wednesday, January 9:
    • 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: # 12, 13, 15, 17
    • Graded problems (Due Friday, Jan. 11): # 16, 18, 19, 20
    Monday, January 7:
    • 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, 4, 5, 7, 8, 10,
    • Graded problems (Due Friday, Jan. 11): # 2, 6, 9, 11, 14
    Friday, January 4:


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