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.
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
Successful midterm + solutions
Handouts:
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
- For Wednesday 1/9:
- Discussion 1 [Tuesday, 1/8]: A Taste of Number Theory
- Lecture 2 [Wednesday, 1/9]: Conditional statements, Closure properties, and proofs (Section 1.2)
- Lecture 3 [Friday, 1/11]: Logical operators and truth tables (Section 2.1)
- IBL session 1 [Monday 1/14]: Logical equivalence (Sections 2.2 and 3.1)
- Lecture 5 [Wednesday 1/16]: Sets and quantifiers (Sections 2.3 and 2.4)
- Lecture 6 [Friday 1/18]: Negating quantifiers and proof by contradiction (Sections 2.4 and 3.3)
- 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:
- 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
- For Monday 1/28:
- Handout 3 [IBL Lecture on Monday 1/28]: Contradiction (Section 3.4)
- Lecture 8 [Wednesday 1/30]: There are infinitely many primes
- 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
- For Monday:
- 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
- For Wednesday:
- 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
- For Friday:
- 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
- For Wednesday:
- Lecture 12 [Wednesday 2/20]: Recursion (Section 4.3)
- Lecture 13 [Friday 2/22]: Basic set operations (Section 5.1)
- Handout 6 [IBL Lecture on Monday 2/25]: Basic operations on sets
- Lecture 14 [Wednesday 2/27]: Proving set relations (Section 5.2)
- 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
- For Monday 3/4:
- Handout 7 [IBL Lecture on Monday 3/4]: Proving set relations
- Lecture 16 [Wednesday 3/6]: Products and their subsets (Section 5.4)
- 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:
- 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
- For Friday 3/13:
- Lecture 19 [Friday 3/13]: Composition of functions