Math 2390: Intro Logic, Sets, and Proofs (Spring 2022)

General Information

Instructor: Mikhail Lavrov
Location: Architecture 173
Lecture times: 3:30pm to 4:45pm on Monday and Wednesday
Textbook: Mathematical Proofs: A Transition to Advanced Mathematics by Chartrand et al., ISBN 0-13-474675-9
Office hours: Tuesday 2pm-3pm and Wednesday 1pm-2pm in my office (D245, in the Math building)
D2L page: https://kennesaw.view.usg.edu/d2l/home/2509913.

D2L will be used to submit assignments (these will be posted both here and on D2L, for convenience) and to view grades. The syllabus will also be posted there.

Homework and Exams

There will be eight homework assignments, two midterm exams, and one final exam; the dates are marked below. (I may change the midterm exam days by ±1 lecture if I have to adjust the pace of the class, but I'll announce this in advance if it must happen.)

I will post the homework assignments here and on D2L; they are always due on Friday at 11:59pm, via D2L, with the exception of the last assignment, which is due on Monday, instead.

Exams will be given in person during our ordinary 75-minute class period. (At least that's the current plan. I will update this schedule and send the class an email if the plan changes.)

Textbooks

Our official textbook for the course is Chartrand, Polimeni, and Zhang's Mathematical Proofs: A Transition to Advanced Mathematics. We will cover chapters 1-6 and 8-9 of this book, as seen in the detailed schedule below. I will refer to individual sections of this book by the abbreviation CPZ (for example, CPZ 3.1 refers to Chapter 3, Section 1 of the book).

Experimentally, I will also include references to An Infinite Descent into Pure Mathematics by Clive Newstead, available online at https://infinitedescent.xyz/. This presents the material in a different way; let me know if the alternate point of view is helpful!

I will refer to individual parts of this book by the abbreviation N. We may not always cover all of a section from N when we first see it.

Detailed Schedule

At the start of the semester, the schedule may look sparse; I'll fill in the details as we go, and I may adjust the pacing, since this is my first time teaching this class.

• Date
  Topic Covered
  Other details
• Mon 1/10
  Sets and set operations
  CPZ 1.1-1.3, N 2.1
• Wed 1/12
  Fancier set operations
  CPZ 1.4-1.6, N 2.2
• Mon 1/17
  No class
   
• Wed 1/19
  Statements
  CPZ 2.1-2.3, N 1.1
  HW 1 due Friday
• Mon 1/24
  Logical implications
  CPZ 2.4-2.6, N 1.1
• Wed 1/26
  Logical equivalence
  CPZ 2.7-2.9, N 1.3
• Mon 1/31
  Quantifiers
  CPZ 2.10-2.11, N 1.2
• Wed 2/2
  Intro to proofs
  CPZ 3.2
  HW 2 due Friday
• Mon 2/7
  Proving conditionals
  CPZ 3.1-3.2
• Wed 2/9
  Proof by contrapositive
  CPZ 3.3
• Mon 2/14
  Proof by cases
  CPZ 3.4
• Wed 2/16
  Review of proofs
  CPZ Chapter 3
  HW 3 due Friday
• Mon 2/21
  Proofs with sets
  CPZ 4.4-4.6, N 2.1-2.2
• Wed 2/23
  Exam 1
   
• Mon 2/28
  Modular arithmetic
  CPZ 4.1-4.2, N 6.1-6.3
• Wed 3/2
  Real numbers
  CPZ 4.3, N 8.1
  HW 4 due Friday
• Mon 3/7
  No class
   
• Wed 3/9
  No class
   
• Mon 3/14
  Counterexamples
  CPZ 5.1
• Wed 3/16
  Proof by contradiction
  CPZ 5.2
• Mon 3/21
  Existence statements
  CPZ 5.4-5.5
• Wed 3/23
  Peano's axioms
  N 4.1
  HW 5 due Friday
• Mon 3/28
  Weak induction
  CPZ 6.1-6.2, N 4.2
• Wed 3/30
  More weak induction
  CPZ 6.1-6.2, N 4.2
• Mon 4/4
  Strong induction
  CPZ 6.3, N 4.3
• Wed 4/6
  Minimum counterexample
  CPZ 6.4, N 4.3
  HW 6 due Friday
• Mon 4/11
  Practice with induction
   
• Wed 4/13
  Exam 2
   
• Mon 4/18
  Relations
  CPZ 9.1-9.2, N 5.1
• Wed 4/20
  Equivalence relations
  CPZ 9.3-9.4, N 5.2
  HW 7 due Friday
• Mon 4/25
  Functions
  CPZ 10.1, N 3.1
• Wed 4/27
  Injections and surjections
  CPZ 10.2, N 3.2
• Mon 5/2
  Bijections and inverses
  CPZ 10.3, N 3.2
  HW 8 due Monday
• Wed 5/4
  No class
  
   
• Mon 5/9
  Final exam (3:30pm - 5:30pm)