Math 144
Set Theory
- 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)
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
- For Monday 10/1:
- Lecture 2 [Monday, 10/1]: Truth tables, number systems, and our first (direct) proof
- Lecture 3 [Wednesday, 10/3]: Compound Statements and Logical equivalence (Sections 2.1 and 2.2)
- Lecture 4 [Friday, 10/5]: More logical equivalence; Sets (Sections 2.2-2.3)
- Lecture 5 [Monday, 10/8]: Sets (Section 2.3)
- Lecture 6 [Wednesday, 10/10]: Quantifiers and quantified statements (Section 2.4)
- Lecture 7 [Friday, 10/12]: Negating multiple quantifiers, proof by contrapositive (Sections 2.4, 3.1, and 3.2)
- Lecture 8 [Monday 10/15]: Proving biconditional statements, proof by contradiction (Sections 3.2 and 3.3)
- Lecture 9 [Wednesday 10/17]: Proof by cases, the division algorithm and congruence (Section 3.4 and 3.5)
- For Friday 10/19:
- 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
- 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
- For Wednesday 10/24:
- 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
- For Friday 10/26:
- Lecture 13 [Friday 10/26]: 2nd PMI
- For Monday 10/29:
- Prepare questions for review session from 5-7p in Skye 284
- For Monday 10/29:
- 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
- For Wednesday 10/31:
- 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
- Lecture 16 [Monday 11/5]: Proving set relations
- 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
- For Friday 11/9:
- 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
- For Wednesday 11/14:
- Lecture 19 [Wednesday 11/14]: Indexed sets
- Lecture 20 [Friday 11/16]: Functions
- 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
- For Wednesday 11/21:
- Lecture 22 [Wednesday 11/21]: Compositions of functions
- 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
- For Wednesday 11/28:
- Lecture 24 [Wednesday 11/28]: Images and preimages
- Lecture 25 [Friday 11/30]: Relations
- Lecture 26 [Monday 12/3]: Equivalence relations
- 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
- For Friday 12/7:
- Lecture 28 [Friday 12/7]: Modular arithmetic
- This section is not on the exam.
- For the final on Wednesday 12/12: Study :-)