• 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:

• Introduction to Proofs by Dana Ernst, et al

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

Homework [This pdf file will be updated regularly.]

Last quarter's midterm + solutions

Failed midterm

Successful midterm + solutions

Last quarter's final

Handouts:

• Handout 0
• Handout 1
• Handout 2
• Handout 3
• Handout 4
• Handout 5
• Handout 6
• Handout 7
• Handout 8

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:
    • Watch 2.1.1, 2.1.8, 2.2.2, and 2.2.3
  • 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:
    • Watch videos: 5.2.1, 5.2.3, 5.3.2, and 5.3.3
    • Do preview activities for Section 5.3
  • 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:
    • Watch videos 6.1.4, 6.1.5, 6.1.8
    • Do preview activities for Section 6.1
  • 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:
    • Watch videos 6.1.4, 6.1.5, 6.1.8, 6.2.1, and 6.2.2
    • Do preview activities for Section 6.1 and 6.2
  • 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