# Math 28: Introduction to Combinatorics

Winter 2018

• 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
 Friday, March 9: Final Exam 8:00 - 11:00 AM in Kemeny 007 Last regrades are due.
 Wednesday, March 7: Topic: Final Review 12:00 - 2:00 Work on the review problems distributed in class.
Week 9
 Monday, March 5: Topic: Review Problems Slides for today: Final Review All The problems: Problem Set
 Friday, March 2: Topic: Review Review of course material All The problems: Problem Set
 Wednesday, February 28: Topic: Inclusion-Exclusion Examples Applying I-E principle for solving problems All The problems: Problem Set In-class problems: # 184, 185, 186
Week 8
 Monday, February 26: Topic: Derangements, onto functions, Stirling numbers All The problems: Problem Set In-class problems: # 179, 184, 185, 186 Graded problems (Due Friday, March 2): # 180, 181, 182, 183,
 Friday, February 23: Topic: Principle of Inclusion-Exclusion Introduction of the idea of inclusion/exclusion. All The problems: Problem Set In-class problems: # 171, 172, 173, 174, 175, Graded problems (Due Friday, March 2): # 176, 177, 178
 Wednesday, February 21: Topic: Solving recurrences with generating functions We will use generating functions for solving recurrences All The problems: Problem Set In-class problems: # 163, 166, 167, Graded problems (Due Friday, March 2): # 164, 165, 168, 169(b), 170
Week 7
 Monday, February 19: Topic: Generating functions for integer partitions All The problems: Problem Set In-class problems: Practice Problems Graded problems (Due Friday, Feb. 23): # 159, 160, 161, 162
 Friday, February 16: Topic: Generating functions for counting Finding generating functions All The problems: Problem Set In-class problems: # 151, 154, 156, 157 Graded problems (Due Friday, Feb. 23): # 152, 153, 155, 158
 Wednesday, February 14: Topic: Introduction to generating functions We will learn to use series for counting Slides for today: Intro to Generating Functions All The problems: Problem Set In-class problems: # 142, 144, 145, 147, 148 Graded problems (Due Friday, Feb. 23): # 143, 146, 149, 150
Week 6
 Monday, February 12: Topic: Finish with Distribution problems Slides for today: Math Objects Counted - Part II All The problems: Problem Set In-class problems: # 135, 138, 139, Graded problems (Due Friday, Feb. 16): # 136, 137, 140, 141
 Friday, February 9: Topic: Partitions of numbers Distributions of identical objects to identical recipients All The problems: Problem Set In-class problems: # 128, 131, 134 Graded problems (Due Friday, Feb. 16): # 129, 130, 132, 133,
 Wednesday, February 7: Topic: Bases for polynomials and partitions of numbers. We will learn how the numbers that we have been talking about come up in linear algebra Slides for today: Math Objects Counted - Part I All The problems: Problem Set In-class problems: # 121, 125, 126 Graded problems (Due Friday, Feb. 16): # 122, 123, 124, 127
Week 5
 Monday, February 5: Topic: Multinomial Coefficients Connections to functions and the Multinomial Theorem All The problems: Problem Set In-class problems: # 115, 116, 117, 118, 120 Graded problems (Due Friday, Feb. 9): # 112, 113, 114, 119
 Friday, February 2: Topic: Stirling Numbers Counting set partitions All The problems: Problem Set In-class problems: # 105, 106, 107, 110 Graded problems (Due Friday, Feb. 9): # 104, 108, 109, 111
 Wednesday, January 31: Topic: Introduction to Distributions The twenty-fold way Slides for today: Distributions All The problems: Problem Set In-class problems: # 95, 96, 97, 102 Graded problems (Due Friday, Feb. 9): # 98, 99, 100, 101, 103
Week 4
 Monday, January 29: Topic: Graphs and Induction Today we will continue working on problems related to graphs. All The problems: Problem Set In-class problems: Review Problems Graded problems (Due Friday, Feb. 2): # 91, 92, 93, 94
 Friday, January 26: Topic: Graphs and Induction We continue working on induction and problems on graph theory All The problems: Problem Set In-class problems: # 83, 84, 86, 89 Graded problems (Due Friday, Feb. 2): # 85, 87, 88, 90
 Wednesday, January 24: Topic: Graphs and Induction Basic introduction to graph theory and applications of induction to graphs. Slides for today: Graphs All The problems: Problem Set In-class problems: # 74, 77, 80, 81 Graded problems (Due Friday, Feb. 2): # 75, 76, 78, 79, 82
Week 3
 Monday, January 22: Topic: Recursions Basic Introduction to recursions. Slides for today: Recursions All The problems: Problem Set In-class problems: # 66, 69, 71, 73 Graded problems (Due Friday, Jan. 26): # 67, 68, 70, 72
 Friday, January 19: Topic: The Induction Principle Today we will work on some problems related to the pigeonhole principle and Induction Principle. Slides for today: Induction Principle All The problems: Problem Set In-class problems: # 57, 59 63, 65 Graded problems (Due Friday, Jan. 26): # 60, 61, 62, 64
 Wednesday, January 17: Topic: Pigeonhole Principle Today we do problems related to the binomial theorem and the Pigeonhole Principle. Slides for today: Pigeonhole Principle All The problems: Problem Set In-class problems: # 50, 52, 53, 56 Graded problems (Due Friday, Jan. 26): # 51, 54, 55, 58
Week 2
 Tuesday, January 16: Topic: Lattice Paths All The problems: Problem Set In-class problems: # 45, 47 Graded problems (Due Friday, Jan. 19): # 48, 49
 Friday, January 12: Topic: The quotient principle The product principle in a different light. Slides for today: Quotient Principle and Lattice Paths All The problems: Problem Set In-class problems: # 37, 39, 42, 43 Graded problems (Due Friday, Jan. 19): # 38, 40, 41, 44, 46
 Wednesday, January 10: Topic: Bijective Principle Slides for today: Bijective Principle and Binomial Coefficients All the problems: Problem Set In-class problems: # 26, 29, 30, 31, 32 Graded problems (Due Friday, Jan. 19): # 27, 28, 33, 34, 35, 36
Week 1
 Tuesday, January 9: 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 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 Friday, Jan. 12): # 15, 16, 17, 20, 23
 Friday, January 5: 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 Friday, Jan. 12): # 2, 4, 6, 9, 10, 11, 14
 Wednesday, January 3: Read/Study: Slides on Set Notation and handouts on group work and proof writing all available in Canvas. Topic: Basic Set Notation Slides for in-class presentation: Basic Set Notation Group Work: Working together helps everyone Proof Writing: Proof Writing Problem Set: Problem Set

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