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.

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: Recap of the course: What did we learn in Math 28?

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

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