MATH 3400 / LGIC 2100 Fall 2024

Fall 2024

MATH 3400 / LGIC 2100, T Th 10:15 - 11:45 a.m., DRL 3C8

Discrete Mathematics I

Professor Andre Scedrov

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

Grader: Please see Canvas page
Grader's Email: Please see Canvas page
Grader's Office Hours: Please see Canvas page

Prerequisites

Math 1410 or permission of the instructor.

Textbook

Alan Tucker: "Applied Combinatorics", Wiley, Sixth Edition, 2012. Ebook: SKU:9781118324516R150 - 6TH 12 MBS 2760232.

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

There will be two take-home midterms, due in Canvas online in pdf Wednesday, October 2, 2024, and Thursday, November 21, 2024, respectively, and each worth 25% of the grade. Each midterm assignment will have at least ten days lead time, during which there will be no homework.

The final exam will also be take-home, due in Canvas online in pdf Monday, December 16, 2024 and will be worth 30% of the grade. The final exam will be cumulative and will be assigned with at least ten days lead time, during which there will be no homework.

Most other weeks during the semester there will be homework, assigned each time with at least one week lead time, and to be completed at home and turned in Canvas online in pdf. Total homework will be worth 20% of the grade. One lowest score homework can be dropped.

First homework will be assigned by Thursday, September 12, 2024 and it will be due in Canvas online in pdf on Thursday, September 19, 2024.

First midterm will be assigned on Thursday, September 19, 2024 and it will be due in Canvas online in pdf on Wednesday, October 2, 2024..

Homework #1 due in pdf in Canvas by 8 pm on Thursday, September 19, 2024

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 1.1.23ab(ii) only on pp. 12-13 of the textbook.
Exercise 1.2.6abcd only on p. 22 of the textbook.
Exercise 1.3.1abc on p. 29 of the textbook.
Exercise 1.4.3b only on p. 40 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 8 pm on Thursday, September 19, 2024.

Midterm #1 due in pdf in Canvas by 8 pm on Wednesday evening, October 2, 2024

Exercise 1.2.3b only on p. 18 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 2.1.3 on p. 54 of the textbook.
Exercise 2.2.8a only, on p. 67 of the textbook. Hint: Similar to Example 4 on pp. 61-62. Alternatively, you can prove this directly, as in Examples 2 or 3 on pp. 58-60. Your choice!

Please put MATH 3400 Mid1 and your full name in the name of the pdf file.

This is the complete set of problems for Midterm #1 due in pdf in Canvas by 8 pm on Wednesday, October 2, 2024.

Homework #2 due in pdf in Canvas by 8 pm on Thursday, October 17, 2024

Exercise 2.3.1i only, on p. 74 of the textbook.
Exercise 2.3.3a only, on p. 75 of the textbook.
Exercise 2.4.14d only, on p. 85 of the textbook.
Exercise 3.1.1c only on p. 100 of the textbook.

Please put MATH 3400 HW2 and your full name in the name of the pdf file.

This is the complete set of problems for Homework #2 due in pdf in Canvas by 8 pm on Thursday, October 17, 2024.

Homework #3 due in pdf in Canvas by 8 pm on Monday, October 28, 2024

Exercise 5.1.14, on p. 186 of the textbook.
Exercise 5.2.10, on p. 199 of the textbook.
Exercise 5.3.8ab, on p. 212 of the textbook.

Please put MATH 3400 HW3 and your full name in the name of the pdf file.

This is the complete set of problems for Homework #3 due in pdf in Canvas by 8 pm on Monday, October 28, 2024.

Homework #4 due in pdf in Canvas by 8 pm on Thursday evening, November 7, 2024

Exercise 5.3.18 on p. 212 of the textbook.
Exercise 5.4.6 on p. 221 of the textbook.
Exercise 5.4.42c only, on p. 224 of the textbook.
Exercise 5.5.1a only, on p. 233 of the textbook.

Please put MATH 3400 HW4 and your full name in the name of the pdf file.

This is the complete set of problems for Homework #4 due in pdf in Canvas by 8 pm on Thursday, November 7, 2024.

Please note this is the last homework. After this there will be only Midterm #2, due on Thursday evening, November 21, 2024 and the Final Exam, due Monday evening, December 16, 2024. Midterm # 2 will cover only the material since Midterm #1. The final exam will be cumulative, i.e., it will cover the entire semester.

Also, a reminder that on Tuesday, November 26, just before Thanksgiving, the class will be held but it will be a review only. No new material will be covered that day.

Midterm #2 due in pdf in Canvas by 8 pm on Thursday evening, November 21, 2024

Exercise 2.4.14e only, on p. 85 of the textbook.
Exercise 3.1.20b only on p. 102 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 Mid2 and your full name in the name of the pdf file.

This is the complete set of problems for Midterm #2 due in pdf in Canvas by 8 pm on Thursday evening, November 21, 2024.

After Midterm #2 the only assignment will be the take-home online Final Exam due at 8 pm Monday evening, December 16, 2024. The final exam will be cumulative, i.e., it will cover the entire semester.

In class we recently covered Appendix A.1. We are now covering Sections 8.1 and 8.2 only from Chapter 8. After that we will cover Sections 10.1 and 10.2 from Chapter 10.

A reminder that on Tuesday, November 26, just before Thanksgiving, the class will be held but it will be a review only. No new material will be covered that day.