Grader: Marc Muhleisen

Chapter 1. Elements of Graph Theory: Graph Models, Isomorphism, Edge Counting, Planar Graphs.

Appendix A.2. Mathematical Induction.

Chapter 2. Covering Circuits and Graph Coloring: Euler Cycles, Hamilton Circuts, Graph Coloring, Coloring Theorems.

Chapter 3. Trees: Properties of Trees.

Chapter 5. General Counting Methods for Arrangements and Selections: Two Basic Counting Principles, Simple Arrangements and Selections, Arrangements and Selections with Repetitions, Distributions, Binomial Identities.

Chapter 7. Recurrence Relations: Recurrence Relations Models, Divide-and-Counter Relations, Solution of Linear Recurrence Relations, Solution of Inhomogeneous Recurrence Relations.

Appendix A.1. Basic Set Theory.

Chapter 8. Inclusion-Exclusion: Counting with Venn Diagrams, Inclusion-Exclusion Formula.

Chapter 10. Games with Graphs: Progressively Finite Games, Nim-Type Games.

There will be two take-home midterms,the first one due in class on **Tuesday,
October 4, 2021** and the second one due in class on **Thursday, November
17, 2021**. First midterm will be
worth 20% of the grade. Second midterm will be worth 25% of the grade. Each
midterm will have at least a two-week lead time, during which there will be
no homework.

The take-home final exam will be due during the final exams period and will be worth 30% of the grade. The take-home final exam will be cumulative and will have at least a two-week lead time, during which there will be no homework.

Most other weeks during the semester there will be homework, each time with at least one week lead time. Total homework will be worth 20% of the grade. One lowest score homework can be dropped.

First homework will be assigned on Tuesday, September 13 and it will be due in class on Tuesday, September 20.

First midterm will be assigned on Tuesday, September 20 and it will be due in class on Tuesday, October 4.

Please show all your work and provide a detailed explanation of your reasoning.

- Exercise 1.1.23ab on pp. 12-13 of the textbook.
- Exercise 1.2.1 on p. 18 of the textbook.
- Exercise 1.2.2 on p. 18 of the textbook.
- Exercise 1.2.6abcdefgh on p. 22 of the textbook.
- Exercise 1.3.1abc on p. 29 of the textbook.

This is the complete set of problems for Homework #1 due in pdf in Canvas by 12 noon on Tuesday, September 20, 2022.

Please show all your work and provide a detailed explanation of your reasoning.

- Exercise 1.1.19 on p. 12 of the textbook, only regarding minimal block surveillance.
- Exercise 1.3.16 on p. 30 of the textbook.
- Exercise 1.4.2 on p. 40 of the textbook.
- Exercise 1.4.8 on p. 41 of the textbook.
- Exercise A.2.2 on p. 421 of the textbook.
- Exercise A.2.5 on p. 421 of the textbook.
- Exercise 2.1.2abc on p. 54 of the textbook.

This is the complete set of problems for Midterm #1 due in pdf in Canvas by 12 noon on Tuesday, October 4, 2022.

Please bear in mind that everyone is expected to submit written solutions individually. That is, even if in some cases your work may be a result of group discussions, each person is responsible to write up the solutions in their own words by themselves. Please take the time to show all your work and provide a detailed explanation of your reasoning in your own words.

- Exercise 2.2.4bi only, on pp. 64-65 of the textbook.
- Exercise 2.2.8a only, on p. 67 of the textbook. Hint: Similar to Example 4 on pp. 61-62.
- Exercise 2.3.1im only, on p. 74 of the textbook.

This is the complete set of problems for Homework #2 due in pdf in Canvas by 12 noon on Thursday, October 20, 2022.

Please bear in mind that everyone is expected to submit written solutions individually. That is, even if in some cases your work may be a result of group discussions, each person is responsible to write up the solutions in their own words by themselves. Please take the time to show all your work and provide a detailed explanation of your reasoning in your own words.

- Exercise 2.4.14ad only, on p. 85 of the textbook.
- Exercise 3.1.1c only, on p. 100 of the textbook.
- Exercise 5.2.28 on p. 201 of the textbook.
- Exercise 5.3.18 on p. 212 of the textbook.

This is the complete set of problems for Homework #3 due in pdf in Canvas by 12 noon on Tuesday, November 1, 2022.

Please bear in mind that everyone is expected to submit written solutions individually. That is, even if in some cases your work may be a result of group discussions, each person is responsible to write up the solutions in their own words by themselves. Please take the time to show all your work and provide a detailed explanation of your reasoning in your own words.

- Exercise 2.2.8b only on p. 67 of the textbook.
- Exercise 2.3.1n only on p. 75 of the textbook.
- Exercise 2.4.14e only, on p. 85 of the textbook.
- Exercise 3.1.10 on p. 101 of the textbook.
- Exercise 5.2.24ab on p. 200 of the textbook.
- Exercise 5.3.16 on p. 212 of the textbook.
- Exercise 5.4.40 on p. 224 of the textbook.
- Exercise 5.5.4c only on p. 233 of the textbook.
- Exercise 7.2.2 on p. 299 of the textbook.
- Exercise 7.3.2 on p. 303 of the textbook.

This is the complete set of problems for Midterm #2 due in pdf in Canvas by 12 noon on Thursday, November 17, 2022.

- Exercise 7.4.6 on p. 307 of the textbook.
- Exercise A.1.10 on p. 419 of the textbook, for any three sets A, B, and C.
- Exercise 8.1.6 on p. 326 of the textbook.
- Exercise 8.2.14 on p. 337 of the textbook.
- Exercise 10.1.6a only on p. 392 of the textbook.

This is the complete set of problems for Homework #4 due in pdf in Canvas by 12 noon on Thursday, December 1, 2022.

In Chapter 8 we covered section 8.1 and a part of section 8.2 up to and including Example 5. We do not cover the rest of section 8.2 nor section 8.3. We started discussing Chapter 10.

The class on Tuesday, November 22 will be held and it will be a review only. No new textbook sections will be covered that day.

Final exam will be cumulative, and it will be due on Friday, December 16, 2022.

- Exercise 1.3.15c only, on p. 30 of the textbook.
- Exercise 1.4.4 on p. 40 of the textbook.
- Exercise 2.1.4 on p. 54 of the textbook.
- Exercise 2.4.14c only, on p. 85 of the textbook.
- Exercise 3.1.20b only, on p. 102 of the textbook.
- Exercise 5.3.12 on p. 212 of the textbook.
- Exercise 5.4.42c only, on p. 224 of the textbook.
- Exercise 5.5.4d only, on p. 233 of the textbook.
- Exercise 7.3.6 on p. 304 of the textbook.
- Exercise A.1.12abcd on p. 419 of the textbook.
- Exercise 8.2.12 on p. 337 of the textbook.
- Exercise 10.2.2c only, on p. 398 of the textbook.

This is the complete set of problems for the Final Exam due in pdf in Canvas by 5 p.m. on Friday, December 16, 2022. Good luck!