• Instructor: Prof. Matthew Durham
• Office: Surge/Skye 234
• Email: mdurham [at] ucr [dot] edu
• Class meets: 10:10-11a MWF
• Office hours: M 11:30-12:30p, W 5-6p, F 4-5p

(or by appointment)

• Classroom: SPR 2340

• Discussion section 1: T 8:10-9a in SPR 2351
• Teaching assistant for section 1: Ben Russell
• Contact info: bruss008 [at] ucr [dot] edu
• Office hours: MW 1-2p in Webber 1303A

• Discussion section 2: T 10:10-11a in SPR 2365
• Teaching assistant for section 2: Alex Rowell
• Contact info: arowe004 [at] ucr [dot] edu
• Office hours:
  • Tuesday 3:30-4p in Webber 1301 (glassroom)
  • Tuesday 4-5p in Webber 1301 (entrance room)

Syllabus

Textbook

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

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

Homework [This pdf file will be updated regularly.]

Assignments and classes:

• Lecture 1 [Friday, 9/28]: Statements and Conditional Statements (Section 1.1)
  • For Monday 10/1:
    • 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
• Lecture 2 [Monday, 10/1]: Truth tables, number systems, and our first (direct) proof
  • For Wednesday 10/3:
    • Watch videos 2.1.1 and 2.1.8
    • Do preview activities in Sections 2.2 and 2.3
  • Problems for HW1 from Section 1.2: 2b, 4c, 7b
  • Problems for HW1 from Section 2.1: 6, 12
  • Recommended exercises from Section 1.2: 1, 3, 6 (starred parts)
• Lecture 3 [Wednesday, 10/3]: Compound Statements and Logical equivalence (Sections 2.1 and 2.2)
  • For Friday 10/5:
    • Watch videos 2.2.2, 2.2.3, and 2.3.1
    • Do preview activities in Sections 2.2 and 2.3
  • Problems for HW2 from Section 2.1: 6, 12
  • Recommended exercises from Section 2.1: 1, 2, 7, 11
• Lecture 4 [Friday, 10/5]: More logical equivalence; Sets (Sections 2.2-2.3)
  • For Monday 10/8:
    • Watch videos 2.3.3, 2.3.4, and 2.4.2.
    • Do preview activities from Section 2.4 and 3.1
  • Problems for HW2 from Section 2.2: 5, 9b, 11a
  • Problems for HW2 from Section 2.3: 4c, 5b
  • Recommended exercises from Section 2.2: 1, 2, 7, 10
  • Recommended exercises from Section 2.3: 1, 2, 3, 4ab, 5ace
• Lecture 5 [Monday, 10/8]: Sets (Section 2.3)
  • For Wednesday 10/10:
    • Watch videos 2.4.2, and then 3.1.1 and 3.1.3
    • Do preview activities for Sections 2.4 and 3.1
  • No new problems for HW2
  • No new recommended exercises
• Lecture 6 [Wednesday, 10/10]: Quantifiers and quantified statements (Section 2.4)
  • For Friday 10/12:
    • Watch videos 3.1.1 and 3.1.3
    • Do preview activities for Sections 3.1 and 3.2
  • Problems for HW3 from Section 2.4: 2e, 11, 14a-d
  • Recommended exercises for Section 2.4: 1, 2ab, 3ac, 6, 10a
• Lecture 7 [Friday, 10/12]: Negating multiple quantifiers, proof by contrapositive (Sections 2.4, 3.1, and 3.2)
  • For Monday 10/15:
    • Watch videos 3.2.2 and 3.2.4
    • Do preview activities for Section 3.3
  • Problems for HW3 from Section 3.1: 3c, 7, 19b
  • Recommended exercises for Section 3.1: 1, 2ad, 4, 5, 8, 11ab, 12
  • Recommended exercises for Section 3.2: 1, 3, 4, 6, 9, 15
• Lecture 8 [Monday 10/15]: Proving biconditional statements, proof by contradiction (Sections 3.2 and 3.3)
  • For Wednesday 10/17:
    • Watch videos 3.3.2, 3.3.3, 3.4.1, and 3.4.2
    • Do preview activities for Section 3.4 and 3.5
  • Problems for HW3 from Section 3.2: 5, 11, 19a
  • Problems for HW4 from Section 3.3: 4, 13b, 20
• Lecture 9 [Wednesday 10/17]: Proof by cases, the division algorithm and congruence (Section 3.4 and 3.5)
  • For Friday 10/19:
    • Watch video 3.5.2 (optional: 3.5.4 has some nice relations to cryptography)
    • Read Section 3.6 (this will not be covered during lecture)
    • Do preview activities for Section 4.1
  • Problems for HW 4 from Section 3.4: 7, 14
  • Problems for HW 4 from Section 3.5: 13, 22b
  • Problems for HW 4 from Section 3.6: 10
  • Recommended problems from Section 3.4: 1, 3, 4, 6a, 10a, 11a
• Lecture 10 [Friday 10/19]: Properties of congruence
  • For Monday 10/21:
    • Watch videos 4.1.3 and 4.1.5
    • Do preview activities for Section 4.2
  • No new HW problems from Section 3.5
  • Recommended problems from Section 3.5: 2, 3, 4, 5, 6
• Lecture 11 [Monday 10/22]: The Principle of Mathematical Induction
  • For Wednesday 10/24:
    • Watch video 4.2.1
    • Do preview activities for Section 4.2 if you haven't already
  • Problems for HW 4 for Section 4.1: 8b
  • Problems for HW 5 for Section 4.1: 11, 18ac
  • Recommended problems from Section 4.1: 1, 2, 3a, 6, 7
• Lecture 12 [Wednesday 10/24]: Extended PMI
  • For Friday 10/26:
    • Do preview activities for Section 4.3
  • Problems for HW 5 from Section 4.2: 1b, 9, 17a
  • Recommended problems from Section 4.2: 2, 5, 8, 12, 16
• Lecture 13 [Friday 10/26]: 2nd PMI
  • For Monday 10/29:
    • Prepare questions for review session from 5-7p in Skye 284
• Lecture 14 [Monday 10/29]: Recursion
  • For Wednesday 10/31:
    • Study!
  • Problems for HW 6 from Section 4.3: 10, 21
  • Recommended problems from Section 4.3: 1, 2af, 6, 8, 18a
• Midterm [Wednesday 10/31]
  • Solutions (coming soon)
  • For Friday 11/2:
    • Watch video 5.1.1
    • Do preview activities for Section 5.1
• Lecture 15 [Friday 11/2]: Basic operations on sets
  • For Monday 11/5:
    • 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, 15
  • Recommended problems for Section 5.1: 1, 2, 3, 4, 5, 6a, 7, 17
• Lecture 16 [Monday 11/5]: Proving set relations
  • For Wednesday 11/7:
    • 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 17 [Wednesday 11/7]: Algebra of sets
  • For Friday 11/9:
    • 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
• Lecture 18 [Friday 11/9]: Cartesian Products
  • For Wednesday 11/14:
    • Do preview activities for Section 5.5
  • Problems for HW 7 from Section 5.4: 6, 7, 9
  • Recommended problems from Section 5.4: 1, 3, 4
• Lecture 19 [Wednesday 11/14]: Indexed sets
  • For Friday 11/16:
    • 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 Section 5.5: 5b, 7a, 8b, 11
  • Recommended problems from Section 5.5: 1ad, 2cdf, 3ab, 8a, 12a
• Lecture 20 [Friday 11/16]: Functions
  • For Monday 11/19:
    • 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 21 [Monday 11/19]: Injections, surjections, and bijections
  • For Wednesday 11/21:
    • Watch videos: 6.4.1
    • Do preview activities for Section 6.4
  • Problems for HW 9 from Section 6.3: 2b, 3cd, 8, 12, 13
  • Recommended problems from Section 6.3: 2a, 3abh, 4ab, 7, 9
• Lecture 22 [Wednesday 11/21]: Compositions of functions
  • For Monday 11/26:
    • Watch videos: 6.5.2 and 6.5.4
    • Do preview activities for Section 6.5
  • Problems for HW 9 from Section 6.4: 1, 4b, 5b, 7dh
  • Recommended problems from Section 6.4: 2, 3, 4a, 5a, 7abf
• Lecture 23 [Monday 11/26]: Inverse functions
  • For Wednesday 11/28:
    • Do preview activities for Section 6.6: 6c, 8
    • Recommended problems from Section 6.5: 2, 3, 6ab, 7
• Lecture 24 [Wednesday 11/28]: Images and preimages
  • For Friday 11/30:
    • Do preview activities for Section 7.1
    • Videos 7.1.1 and 7.1.2
  • Problems for HW 10 from Section 6.6: 8, 13
  • Recommended problems from Section 6.6: 1adfh, 2bdef, 3ab, 4a, 9
• Lecture 25 [Friday 11/30]: Relations
  • For Monday 12/3:
    • Do preview activities for Section 7.2
    • Videos 7.2.1 and 7.2.2
  • Problems for HW 10 from Section 7.1: 5, 10
  • Recommended problems from Section 7.1: 1, 2, 3, 4, 6, 9
• Lecture 26 [Monday 12/3]: Equivalence relations
  • For Wednesday 12/5:
    • Do preview activities for Section 7.3
    • Videos 7.3.1 and 7.3.3
  • Problems for HW 10 from Section 7.2: 11, 16
  • Recommended problems from Section 7.2: 1, 3, 4, 6
• Lecture 27 [Wednesday 12/5]: Equivalence classes
  • For Friday 12/7:
    • Do preview activities for Section 7.4
  • Problems for HW 10 from Section 7.3: 7
  • Recommended problems from Section 7.3: 1, 2, 3, 5a, 11
• Lecture 28 [Friday 12/7]: Modular arithmetic
  • This section is not on the exam.
  • For the final on Wednesday 12/12: Study :-)