MATH 3400 / LGIC 2100 Fall 2023

Fall 2023

MATH 3400 / LGIC 2100, T Th 10:15 - 11:45, DRL 3C4

Discrete Mathematics I

Professor Andre Scedrov

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

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

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

"Bring Back Examinations" combine elements of homework and in-class timed assessment. Problems for the examination will be assigned as the course proceeds and each student will select from among them those problems to complete in class without the benefit of any text or notes.

There will be two "bring back" in-class midterms, Thursday evening, October 5, 2023 and Thursday evening, November 16, 2023, respectively, and each worth 25% of the grade. Please see Canvas page for exam time and room. Each midterm assignment will have at least a two-week lead time, during which there will be no homework.

The final exam will also be "bring back" in-class during the final exams period and will be worth 30% of the grade. The "bring back" in-class final exam will be cumulative and will be assigned with at least a two-week lead time, during which there will be no homework.

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

First homework will be assigned on Thursday, September 14 and it will be due in Canvas in pdf on Thursday, September 21 at 12 noon.

First midterm will be assigned on Thursday, September 21 and it will be held in person on Thursday evening, October 5 in the "bring back" format described above. Please see Canvas page for exam time and room.

Homework #1 due in pdf in Canvas by 3 pm on Thursday, September 21, 2023

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 on pp. 12-13 of the textbook.
Exercise 1.2.1 on p. 18 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 3 pm on Thursday, September 21, 2023.

Midterm #1 to be held in person on Thursday evening, October 5, 2023

Please choose 4 problems from the following list. Please show all your work and provide a detailed explanation of your reasoning. Please put MATH 3400 Midterm 1 and your full name on each page of the midterm.

Exercise 1.2.3a only on p. 18 of the textbook.
Exercise 1.3.3 on p. 29 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.2.1 on p. 421 of the textbook.
Exercise 2.1.3 on p. 54 of the textbook.

This is the complete set of problems for Midterm #1.

Homework #2 due in pdf in Canvas by 3 pm on Tuesday, October 24, 2023

Exercise 2.2.4a only, on p. 64 of the textbook. Prove this directly, as in Examples 2 or 3 on pp. 58-60.
Exercise 2.2.8a only, on p. 67 of the textbook. Hint: Similar to Example 4 on pp. 61-62.
Exercise 2.3.1i only, on p. 74 of the textbook.
Exercise 2.4.14d only, on p. 85 of the textbook.
Exercise 3.1.1b only on p. 100 of the textbook.

Please put MATH 3400 HW2 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 3 pm on Tuesday, October 24, 2023.

Homework #3 due in pdf in Canvas by 3 pm on Thursday, November 2, 2023

Exercise 5.2.24ab on p. 200 of the textbook.
Exercise 5.3.18 on p. 212 of the textbook.
Exercise 5.4.42c only, on p. 224 of the textbook.

Please put MATH 3400 HW3 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 3 pm on Thursday, November 2, 2023.

Midterm #2 to be held in person Thursday evening, November 16, 2023

Please choose 6 problems from the following list. Please show all your work and provide a detailed explanation of your reasoning.

Please put MATH 3400 Midterm 2 and your full name on each page of the midterm.

Exercise 2.2.9a only on p. 67 of the textbook, only for the complete bipartite graph with 4 vertices on the left side and 3 vertices on the right side, and edges between all pairs of left and right vertices. That is, show that this graph has no Hamilton circuit.
Exercise 2.3.3b only on p. 75 of the textbook.
Exercise 2.4.14e only, on p. 85 of the textbook.
Exercise 3.1.20b only on p. 102 of the textbook.
Exercise 5.2.14ab on p. 199 of the textbook.
Exercise 5.3.12 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 to be held in person Thursday evening, November 16, 2023.

Homework #4 due in pdf in Canvas by 3 pm on Thursday, November 30, 2023

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 3 pm on Thursday, November 30, 2023.

In Chapter 8 we cover 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 also cover Chapter 10.

The class on Tuesday, November 21, 2023 will be held but it will be a review only. No new textbook sections will be covered that day.

Final exam will be cumulative, and it will be held in person on Thursday, December 14, 2023, 12 noon - 2 pm.

Final Exam to be held in person on Thursday afternoon, December 14, 2023

Please choose 8 problems from the following list. Please show all your work and provide a detailed explanation of your reasoning.

Please write your full name on the front page of the exam.

Exercise 1.3.2a only, on p. 29 of the textbook.
Exercise 1.4.7a only, on p. 41 of the textbook.
Exercise 2.1.5b only, on p. 54 of the textbook. A bridge is an edge whose removal disconnects the graph.
Exercise 2.2.1b only, on p. 64 of the textbook.
Exercise 3.1.10 on p. 101 of the textbook.
Exercise 5.3.10a only, on p. 212 of the textbook.
Exercise 5.4.8 on p. 221 of the textbook.
Exercise 7.3.6 on p. 304 of the textbook.
Exercise A.1.12abcd on p. 419 of the textbook.
Exercise 8.1.8 on p. 326 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 to be held in person on Thursday afternoon, December 14, 2023. Good luck!