## Professor Andre Scedrov

Professor Scedrov's Office: DRL 4E6.
Professor Scedrov's Office Hours: Online by appointment.

Grader Marc's Office Hours: In person Tuesdays and Thursdays 9 am - 10 am and by appointment.

## Math 3400 / Lgic 2100 Fall 2022 Masking Policy

While you are not required to wear masks in other university buildings, I ask that everyone continue to wear masks in our classroom DRL 3C4 in class Math 3400 / Lgic 2100. I know that masks might feel awkward, but I also know that wearing masks plays a role in showing respect for each others' health and comfort.

## Prerequisites

Math 1140 (previously Math 114) or permission of the instructor.

## Textbook

Alan Tucker: "Applied Combinatorics", Wiley, Sixth Edition, 2012. ISBN-10: 0470458380. ISBN-13: 978-0470458389.

## Topics Covered

Textbook Chapters 1-2, some of Chapter 3, Chapter 5, Chapters 7-8, Chapter 10, and some selected topics:

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.

## Basic Course Information

Class participation and activity will be worth 5% of the grade.

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.

## Homework #1 due in pdf in Canvas by 12 noon on Tuesday, September 20, 2022

• 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.
Please put MATH 3400 HW1 and your initials in the name of the pdf file.

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

## Midterm #1 due in pdf in Canvas by 12 noon on Tuesday, October 4, 2022

• 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.
Please put MATH 3400 Midterm 1 and your initials in the name of the pdf file.

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

## 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 2.2.4bi 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.
Please put MATH 3400 HW 2 and your initials in the name of the pdf file.

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

## 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 2.4.14ad 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.
Please put MATH 3400 HW 3 and your initials in the name of the pdf file.

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

## Midterm #2 due in pdf in Canvas by 12 noon on Thursday, November 17, 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.
Please put MATH 3400 Midterm 2 and your initials in the name of the pdf file.

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

## Homework #4 due in pdf in Canvas by 12 noon on Thursday, December 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 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.
Please put MATH 3400 HW 4 and your initials in the name of the pdf file.

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.

## Final Exam is cumulative. It is due in pdf in Canvas by 5 p.m. on Friday, December 16, 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 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.
Please put MATH 3400 Final and your initials in the name of the pdf file.

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!