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

General Information

Instructor: Mikhail Lavrov
Location: Mathematics 250
Lecture times: 2:00pm to 3:15pm on Tuesday and Thursday
Textbook: Book of Proof by Richard Hammack, available online from the author's website: http://www.people.vcu.edu/~rhammack/BookOfProof/.
Office hours: TBD
D2L page: TBD

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 on D2L.

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.

Exams will be given in person during our ordinary 75-minute class period.

Textbooks

Our official textbook for the course is Richard Hammack's Book of Proof. We will cover chapters 1-2 and 4-12 of the textbook, as seen in the detailed schedule below. I will refer to individual sections of this book by the abbreviation RH (for example, RH 1.4 refers to Chapter 1, Section 4: Power Sets).

Some other sections of this course use Chartrand, Polimeni, and Zhang's Mathematical Proofs: A Transition to Advanced Mathematics. This textbook is also a good resource, and I especially recommend its examples and its exercises. To make your life easier, I will also include references to sections of this textbook in the schedule. I will refer to individual sections of this book by the abbreviation CPZ (for example, CPZ 3.2 refers to Chapter 3, Section 2: Direct Proofs).

Detailed Schedule

  • Date
    Topic Covered
    Other details
  • Tue 8/16
    Sets and set operations
    RH 1.1,1.3,1.5-1.7, CPZ 1.1-1.3
  • Thu 8/18
    Fancier set operations
    RH 1.2,1.4,1.8, CPZ 1.4-1.6
  • Tue 8/23
    Statements
    RH 2.1-2.2, CPZ 2.1-2.3
  • Thu 8/25
    Logical implications
    RH 2.3-2.4, CPZ 2.4-2.6
    HW1 due Friday
  • Tue 8/30
    Truth tables
    RH 2.5-2.6, 2.10, CPZ 2.7-2.9
  • Thu 9/1
    Quantifiers
    RH 2.7-2.9, CPZ 2.10-2.11
  • Tue 9/6
    Intro to proofs
    RH 4.1-4.3, CPZ 3.2
  • Thu 9/8
    Direct proof
    RH 4.3, CPZ 3.1-3.2
    HW2 due Friday
  • Tue 9/13
    Proof by cases
    RH 4.4-4.5, CPZ 3.4
  • Thu 9/15
    Proof by contrapositive
    RH 5.1, CPZ 3.3
  • Tue 9/20
    Congruence of integers
    RH 5.2, CPZ 4.2
  • Thu 9/22
    Review of proofs
    HW3 due Friday
  • Tue 9/27
    Exam 1
     
  • Thu 9/29
    Proofs with sets
    RH 8.1-8.3, CPZ 4.4-4.6
  • Tue 10/4
    Proofs with functions
    RH 12.1, CPZ 10.1
  • Thu 10/6
    Proof by contradiction
    RH 6.1, CPZ 5.2
    HW4 due Friday
  • Tue 10/11
    Contradiction and conditionals
    RH 6.2-6.3, CPZ 5.3
  • Thu 10/13
    If-and-only-if proof
    RH 7.1-7.2
  • Tue 10/18
    Existence statements
    RH 7.3-7.4, CPZ 5.4
  • Thu 10/20
    Disproof
    RH 9.1-9.3, CPZ 5.1, 5.5
    HW5 due Friday
  • Tue 10/25
    Weak induction
    RH 10.1, CPZ 6.1-6.2
  • Thu 10/27
    More weak induction
    RH 10.1, CPZ 6.1-6.2
  • Tue 11/1
    Strong induction
    RH 10.2, CPZ 6.3
  • Thu 11/3
    Minimum counterexample
    RH 10.3, CPZ 10.4
    HW6 due Friday
  • Tue 11/8
    Review of induction
     
  • Thu 11/10
    Exam 2
     
  • Tue 11/15
    Relations
    RH 11.1-11.2, CPZ 9.1-9.2
  • Thu 11/17
    Equivalence relations
    RH 11.3-11.4, CPZ 9.3-9.4
    HW7 due Friday
  • Tue 11/22
    No class
     
  • Thu 11/24
    No class
     
  • Tue 11/29
    Injections and surjections
    RH 12.1-12.2, CPZ 10.1-10.2
  • Thu 12/1
    Inverse functions
    RH 12.5, CPZ 10.5
    HW8 due Friday
  • Tue 12/6
    Final exam (1:00pm - 3:00pm)
     
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