Math 28: Introduction to Combinatorics

Winter 2015


  • The latest homework will always appear on top.

  • In this class you will be writing lots of proofs, here is a pdf document with tips on writing proofs.

  • If you are interested in learning to typeset mathematics here is a list of resources compiled by Prof. 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.

    Graded assignments: These problems will graded in detail.

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


    Week 10
    Sunday, March 15:
    • Final Exam - 11:30 - 2:30 PM in KH 108
    Thursday, March 12:
    • Final Review - 11:30 - 1:00 PM
    Tuesday, March 10:
    • Work on last problems during x-hour
    Monday, March 9:

    Week 9
    Friday, March 6:
    • Read
      5.2
    • Topic:
      Principle of Inclusion and Exclusion
    • Problem Set --From Handout: Set # 1
    • Practice problems  (for next class period)
      186, 187
    • Graded assignment  (for Wednesday, March 11)
      188, 189, 190
    Wednesday, March 4:
    • Read
      5.1
    • Topic:
      Principle of inclusion and exclusion
    • Problem Set --From Handout: Set # 1
    • Practice problems  (for next class period)
      183, 184
    • Graded assignment  (for Wednesday, March 11)
      184, 185, 186
    Monday, March 2:
    • Read
      Section 5.1
    • Topic:
      Principle of Inclusion and Exclusion
    • Problem Set --From Handout: Set # 1
    • Practice problems  (for next class period)
      181, 182
    • Graded assignment  (for Wednesday, March 11)
      181, 182, 183

    Week 8
    Friday, February 27:
    • Read
      5.1
    • Topic:
      Principle of Inclusion and Exclusion
    • Problem Set --From Handout: Set # 1
    • Practice problems  (for next class period)
      176, 178
    • Graded assignment  (for Wednesday, March 4)
      177, 178, 179, 180
    Wednesday, February 25:
    • Read
      4.3
    • Topic:
      Application of generating functions to solve recurrences
    • Problem Set --From Handout: Set # 1
    • Practice problems  (for next class period)
      171, 173, 174
    • Graded assignment  (for Wednesday, March 4)
      171, 172, 173, 175
    Monday, February 23:
    • Read
      Section 4.3
    • Topic:
      Application of generating functions to solve recurrences
    • Problem Set --From Handout: Set # 1
    • Practice problems  (for next class period)
      166, 169, 170
    • Graded assignment  (for Wednesday, March 4)
      166, 167, 168, 170

    Week 7
    Friday, February 20:
    • Midterm Review
    Wednesday, February 18:
    • Read
      4.3
    • Topic:
      Application of generating functions to solve recurrences
    • Problem Set --From Handout: Set # 1
    • Practice problems  (for next class period)
      160, 162, 163
    • Graded assignment  (for Wednesday, February 25)
      160, 161, 162, 164, 165,
    Monday, February 16:
    • Read
      Section 4.2
    • Topic:
      Application of generating functions to integer partitions
    • Problem Set --From Handout: Set # 1
    • Practice problems  (for next class period)
      153, 154, 155, 157
    • Graded assignment  (for Wednesday, February 25)
      154, 155, 156, 158, 159

    Week 6
    Friday, February 13:
    • Read
      4.1.4, 4.1.5, 4.1.6
    • Topic:
      Generating Functions
    • Problem Set --From Handout: Set # 1
    • Practice problems  (for next class period)
      145, 148, 149, 152
    • Graded assignment  (for Wednesday, February 18)
      148, 150, 151, 152
    Wednesday, February 11:
    • Read
      4.1.1, 4.1.2, 4.1.3
    • Topic:
      Introduction to generating functions
    • Problem Set --From Handout: Set # 1
    • Practice problems  (for next class period)
      138, 139, 141, 144
    • Graded assignment  (for Wednesday, February 18)
      140, 142, 143, 146, 147
    Monday, February 9:
    • Read
      Section 3.3.3 and 3.3.4
    • Topic:
      Partitions and partitions into distinct parts
    • Problem Set --From Handout: Set # 1
    • Practice problems  (for next class period)
      133, 134, 135, 137
    • Graded assignment  (for Wednesday, February 18)
      131, 132, 134, 136, 139

    Week 5
    Friday, February 6:
    • Winter Carnival!
    Wednesday, February 4:
    • Read
      3.3
    • Topic:
      Partitions of numbers
    • Problem Set --From Handout: Set # 1
    • Practice problems  (for next class period)
      124, 125, 127, 128
    • Graded assignment  (for Wednesday, February 11)
      121, 122, 126, 129, 130
    Tuesday, February 3:
    • We meet during x-period today to make-up Friday's class (Winter carnival)
    Monday, February 2:
    • Read
      Section 3.2
    • Topic:
      Multinomial coefficients, bases for space of polynomials
    • Problem Set --From Handout: Set # 1
    • Practice problems  (for next class period)
      110, 113, 114, 115, 119, 120, 123
    • Graded assignment  (for Wednesday, February 11)
      109, 111, 112, 116, 117, 118, 120

    Week 4
    Friday, January 30:
    • Read
      2.3
    • Topic:
      Multisets, Compositions, Stirling Numbers of the Second kind
    • Problem Set --From Handout: Set # 1
    • Practice problems  (for next class period)
      99, 101, 102, 103, 104, 109
    • Graded assignment  (for Wednesday, February 4)
      97, 100, 103, 105, 106, 107, 108
    Thursday, January 29:
    • Midterm 1
    Wednesday, January 28:
    • Read
      2.3.3, 2.3.4, 2.3.6
    • Topic:
      Labelled and spanning trees and Distributions
    • Problem Set --From Handout: Set # 1
    • Practice problems  (for next class period)
      86, 89, 90, 91, 93, 94, 98
    • Graded assignment  (for Wednesday, February 4)
      86, 87, 88, 90, 92, 95, 96
    Monday, January 26:
    • Review for Midterm 1

    Week 3
    Friday, January 23:
    • Read
      2.3
    • Topic:
      Graphs and trees
    • Problem Set --From Handout: Set # 1
    • Practice problems  (for next class period)
      72, 75, 78, 80, 81, 85
    • Graded assignment  (for Wednesday, January 28)
      74, 76, 77, 79, 82, 83, 84
    Wednesday, January 21:
    • Read
      2.1.1, 2.1.2, 2.1.3, 2.2 (If you have never seen induction before see Appendix B)
    • Topic:
      Induction and Recurrences
    • Problem Set --From Handout: Set # 1
    • Practice problems  (for next class period)
      62, 64, 66, 69, 70, 71,
    • Graded assignment  (for Wednesday, January 28)
      63, 65, 67, 68, 69, 73

    Week 2
    Friday, January 16:
    • Read
      1.3.2 and 1.3.3
    • Topic:
      Binomial Theorem and Pigeonhole principle
    • Problem Set --From Handout: Set # 1
    • Practice problems  (for next class period)
      51, 54, 55, 56, 60, 61
    • Graded assignment  (for Wednesday, January 21)
      52, 53, 57, 58, 59
    Wednesday, January 14:
    • Read
      1.3.1
    • Topic:
      Lattice paths and Catalan numbers
    • Problem Set --From Handout: Set # 1
    • Practice problems  (for next class period)
      43, 44, 46, 47, 48, 49
    • Graded assignment  (for Wednesday, January 21)
      45, 47, 48, 50
    Monday, January 12:
    • Read
      1.2.6
    • Topic:
      Quotient principle
    • Problem Set --From Handout: Set # 1
    • Practice problems  (for next class period)
      31, 32, 35, 37, 39, 41
    • Graded assignment  (for Wednesday, January 21)
      33, 34, 36, 38, 40, 42

    Week 1
    Friday, January 9:
    • Read
      1.2.2, 1.2.3, 1.2.4 and 1.2.5
    • Topic:
      Functions and Digraphs and Bijection principle
    • Problem Set --From Handout: Set # 1
    • Practice problems  (for next class period)
      21, 22, 24, 25, 26, 29
    • Graded assignment  (for Wednesday, January 14)
      23, 27, 28, 30
    Wednesday, January 7:
    • Read
      1.1 and 1.2
    • Topic
      Sum and product principles
    • Problem Set --From Handout: Set # 1
    • Practice problems  (for next class period)
      13, 16, 18, 20
    • Graded assignment  (for Wednesday, January 14)
      14, 15, 17, 19
    Tuesday, January 6:
    • Read
      Handout on proof writing click here for a copy.
    • Today we will discuss different methods of proofs during the x-hour.
    • If time permits we will continue solving problems.
    Monday, January 5:
    • Read
      1.1 and 1.2
    • Topic
      Introduction to counting
    • Problem Set --From Handout: Set # 1
    • Practice problems  (for next class period)
      1, 3, 5, 7, 8, 9, 12.
    • Graded assignment  (for Wednesday, January 14)
      2, 4, 8, 10, 11


  • Page created and maintained by R. Orellana