Math 144

Set Theory

  • Instructor: Prof. Matthew Durham
  • Office: Surge/Skye 234
  • Email: mdurham [at] ucr [dot] edu
  • Class meets: 11:10a-12p MWF
  • Classroom: SPR 2355
  • Office hours:
    • M 12p-1p in Skye 277.
    • W 12p-1p in Skye 277.
    • F 2p-3p in Skye 347.
    • Also by appointment.



  • Discussion sections: T 10:10-11a in Skye 171, and T 12:10p-1p in Skye 170
  • Teaching assistant: Ben Russell
  • Contact info: bruss008 [at] ucr [dot] edu
  • Office hours: M 12p-2p in Bookstore Annex 128.


Syllabus

Resources:

The textbook for this course is:

  • Mathematical Reasoning: Writing and Proof, version 2.1, by Ted Sundstrom.

Available electronically at: https://www.tedsundstrom.com/mathreasoning

Secondary resource for the IBL part of the course:


This course was based in part on the Math 144 courses designed by Julie Bergner.

Assignments and classes:

  • Lecture 1 [Monday, 1/7]: Statements (Section 1.1)
      • For Wednesday 1/9:
        • Watch video 1.2.1
        • Do preview activities 1 and 2 from Section 2.1
      • Problems for HW1 from Section 1.1: 6e,f; 10a,c
      • Recommended exercises from Section 1.1: 1-4, 9
  • Discussion 1 [Tuesday, 1/8]: A Taste of Number Theory
  • Lecture 2 [Wednesday, 1/9]: Conditional statements, Closure properties, and proofs (Section 1.2)
      • For Friday 1/11:
      • Problems for HW1 from Section 1.2: 7, 11, 13
      • Recommended exercises for Section 1.2: 1, 3, 6 (starred parts)
  • Lecture 3 [Friday, 1/11]: Logical operators and truth tables (Section 2.1)
      • For Monday 1/14:
        • Watch 2.3.1, 2.3.3, and 2.3.4
        • Do preview activities for Sections 2.2 and 2.3
      • Problems for HW1 from Section 2.1: 6, 12
      • Recommended exercises from Section 2.1: 1, 2, 7, 11
  • IBL session 1 [Monday 1/14]: Logical equivalence (Sections 2.2 and 3.1)
      • Handout 1
      • For Wednesday 1/16:
        • Watch 2.4.2
        • Do preview activities for Section 2.4
      • Problems for HW1 from Section 2.2: 8, 9b, 13
      • Recommended exercises from Section 2.2: 1, 2, 7, 10
  • Lecture 5 [Wednesday 1/16]: Sets and quantifiers (Sections 2.3 and 2.4)
      • For Friday 1/18:
        • Do preview activities for Sections 3.1, 3.2, and 3.3
        • Watch 3.1.1 and 3.1.3
      • Problems for HW2 from Section 2.3: 4c, 5bd, 7
      • Problems for HW2 from Section 2.4: 9, 13, 14
      • Recommended exercises from Section 2.3: 1, 2, 3, 4ab, 5ace
      • Recommended exercises from Section 2.4: 1, 2ab, 3ac, 6, 10a
  • Lecture 6 [Friday 1/18]: Negating quantifiers and proof by contradiction (Sections 2.4 and 3.3)
      • For Tuesday 1/22:
        • Again, make sure to do the preview activities for Sections 3.1 and 3.2
        • Watch 3.2.2 and 3.2.4
      • Problems for HW2 from Section 3.1: 3c, 7, 19bc
      • Recommended exercises from Section 3.1: 1, 2ad, 4, 5, 8, 11ab, 12
  • Handout 2 [Discussion on Tuesday 1/22]
  • IBL session 2 [Wednesday 1/23]: Methods of proof (Sections 3.2 and 3.3)
      • For Friday 1/25:
        • Do preview activities for Section 3.4
        • Watch 3.4.1, and 3.4.2
      • Problems for HW3 from Section 3.2: 5, 11, 13, 19
      • Problems for HW3 from Section 3.3: 4, 13b, 20
      • Problems for HW3 from Section 3.4: 7
      • Recommended problems from Section 3.2: 5, 11, 19a
      • Recommended problems from Section 3.3: 4, 13b, 20
      • Recommended problems from Section 3.4: 1, 3, 4, 6a, 10a, 11a
  • Handout 2.5 [IBL Lecture on Wednesday 1/23]: Some more quantifier statements
  • Lecture 7 [Friday 1/25]: Modular congruence and the division algorithm
      • For Monday 1/28:
        • Read Handout 3 and Section 3.3
        • Problems for HW 4 from Section 3.5: 13, 18
        • Problems for HW 4 from Section 3.6: 3, 10
  • Handout 3 [IBL Lecture on Monday 1/28]: Contradiction (Section 3.4)
  • Lecture 8 [Wednesday 1/30]: There are infinitely many primes
      • For Friday 2/1:
        • Do preview activities for Section 4.1
        • Watch 4.1.3 and 4.1.5
  • Lecture 9 [Friday 2/1]: The Principle of Mathematical Induction (Section 4.1)
      • For Monday:
        • Read Handout 4
        • Do preview activities for Section 4.1
      • Problems for HW 4 from Section 4.1: 3bc, 8b
  • Handout 4 [IBL Lecture on Monday 2/4]: Induction (Section 4.1)
      • For Wednesday:
        • Do preview activities for Section 4.2
        • Watch 4.2.1
      • Problems for HW 5 from Section 4.1: 11, 18ac
      • Recommended problems from Section 4.2: 2, 5, 8, 12, 16
  • Lecture 10 [Wednesday 2/6]: Extended PMI (Section 4.2)
      • For Friday (and Monday): study!
      • Problems for HW 5 from Section 4.2: 1b, 7, 9, 17
  • Lecture 11 [Wednesday 2/13]: Strong PMI (Section 4.2)
      • For Friday:
        • If you haven't already, do preview activities for Sections 4.1 and 4.2
        • Do preview activities for Section 4.3
  • Handout 5 [IBL Lecture on Friday 2/15]: Extended and Strong Induction
      • For Wednesday:
        • If you haven't already, do preview activities for Section 4.3
  • Lecture 12 [Wednesday 2/20]: Recursion (Section 4.3)
      • For Friday:
        • Do preview activities for Section 5.1 on basic set operations
        • Watch 5.1.1, 5.1.2, and 5.1.3
      • Recommended problems from Section 4.3: 1, 2af, 6, 8, 18a
  • Lecture 13 [Friday 2/22]: Basic set operations (Section 5.1)
      • For Monday 2/25:
        • Watch videos 5.1.2 and 5.1.3
        • Do preview activities for Section 5.2
      • Problems for HW 6 from Section 5.1: 11b, 12c
      • Recommended problems for Section 5.1: 1, 2, 3, 4, 5, 6a, 7, 17
  • Handout 6 [IBL Lecture on Monday 2/25]: Basic operations on sets
  • Lecture 14 [Wednesday 2/27]: Proving set relations (Section 5.2)
      • Friday 3/1:
      • Problems for HW 7 from Section 5.2: 2, 8, 13ae
      • Recommended problems for Section 5.2: 1, 3, 5a, 7abe, 12a, 15ab
  • Lecture 15 [Friday 3/1]: Algebra of set operations (Section 5.3)
      • For Monday 3/4:
        • Watch videos: 5.4.1
        • Do preview activities for Section 5.4
      • Problems for HW 7 from Section 5.3: 10, 12
      • Recommended problems for Section 5.3: 1ac, 6a, 9a
  • Handout 7 [IBL Lecture on Monday 3/4]: Proving set relations
  • Lecture 16 [Wednesday 3/6]: Products and their subsets (Section 5.4)
      • For Friday 3/8:
      • Problems for HW 7 from Section 5.4: 6, 7, 9
      • Recommended problems from Section 5.4: 1, 3, 4
  • Lecture 17 [Friday 3/8]: Functions (Section 6.1)
      • For Monday 3/11:
      • Problems for HW 8 from Sections 6.1: 5ac, 7deg, 8
      • Problems for HW 8 from Sections 6.2: 2, 5bd
      • Recommended problems from Section 6.1: 1, 3, 4, 5bd, 6, 7abc
      • Recommended problems from Section 6.2: 1, 3, 4ad, 5ac, 6, 7, 8ac
  • Handout 8 [Monday 3/11]: Functions: injections, surjections, and bijections (Sections 6.1-6.3)
      • For Wednesday 3/11:
        • Watch videos 6.3.2 and 6.3.4
        • Do preview activities for Section 6.3
      • Problems for HW 8 from Sections 6.1: 5ac, 7deg, 8
      • Problems for HW 8 from Sections 6.2: 2, 5bd
      • Recommended problems from Section 6.1: 1, 3, 4, 5bd, 6, 7abc
      • Recommended problems from Section 6.2: 1, 3, 4ad, 5ac, 6, 7, 8ac
  • Lecture 18 [Wednesday 3/13]: Products and graphs of functions
      • For Friday 3/13:
        • Watch 6.4.1
        • Do preview activities for Section 6.4
      • Problems for HW 8 from Section 6.3: 2b, 3cd, 8, 13
      • Recommended problems from Section 6.3: 2a, 3abh, 4ab, 7, 9
  • Lecture 19 [Friday 3/13]: Composition of functions