MAT 200-02 - Logic, Language and Proof - Spring 2021
The class meets in person Monday/Wednesday/Friday 10:30-11:25am in Earth&Space 001. The math department is also offering online sections of the class this semester; see the department schedule.
Course information
Office hours: | Monday 12:00-1:00pm |
Wednesday 4:00-5:00pm (I may be slightly late because of my other class) | |
or by appointment | |
Office hours will be held on Zoom: | |
https://stonybrook.zoom.us/j/2482038879?pwd=TDVGcUU4UXhlNHEvdllnckdBb2VpZz09 | |
You also have the option to come to my office (Math Tower 4101B) by appointment. | |
Textbook: | Peter J. Eccles, An Introduction to Mathematical Reasoning: Numbers, Sets and Functions, Cambridge University Press, 2007. |
Course links
Lecture outline: part 1, part 2, part 3, part 4 | |
Tips for Learning Math | |
Overleaf Introduction to LaTeX | |
DeTeXify | |
Midterm 1 Key, Midterm 2 (Key), Midterm 3 (Key) | |
Piazza: | https://piazza.com/stonybrook/spring2021/mat200/home |
Gradescope: | https://www.gradescope.com/ (entry code GE32E7) |
Course schedule and assignments
The schedule here may be modified based on our progress through the material. The dates for the midterm exams are fixed. The sections covered may be modified if needed.
Each week’s homework assignment is due at the beginning of Wednesday's lecture (10:30 am) of the following week.
Week | Date | Sections | Assignment |
1 | Feb. 1 Feb. 3 Feb. 5 |
1 The language of mathematics 2 Implications 3 Proofs |
HW 1 1.1, 1.2, 1.4; 2.1, 2.3, 2.4; 3.2, 3.3 |
2 | Feb. 8 Feb. 10 Feb. 12 |
4 Proof by contradiction 4 Proof by contradiction 5 The induction principle |
HW 2 3.4, 3.5; 4.1, 4.2, 4.7; 5.1, 5.2, 5.5 |
3 | Feb. 15 Feb. 17 Feb. 19 |
5 The induction principle 6 The language of set theory 7 Quantifiers |
HW 3 5.7; 6.1, 6.4, 6.5, 6.6 |
4 | Feb. 22 Feb. 24 Feb. 26 |
7 Quantifiers 8 Functions 8 Functions |
HW 4 (Due Friday) 7.1, 7.2, 7.4, 7.6, 7.7 |
5 | Mar. 1 Mar. 3 Mar. 5 |
Midterm 1 Review MIDTERM 1 (Sections 1-7) 9 Injections, surjections and bijections |
HW 5 8.1, 8.2, 8.3, 8.5 |
6 | Mar. 8 Mar. 10 Mar. 12 |
9 Injections, surjections and bijections 10 Counting 10 Counting |
HW 6 9.1, 9.5, 9.7, PrII.21, 10.1, 10.2, 10.4 |
7 | Mar. 15 Mar. 17 Mar. 19 |
11 Properties of finite sets 11 Properties of finite sets 12 Counting functions and subsets |
HW 7 11.1, 11.3, 11.4 12.1, 12.3, 12.4, PrIII.10 |
8 | Mar. 22 Mar. 24 Mar. 26 |
13 Number systems 13 Number systems 14 Counting infinite sets |
HW 8 12.6, 13.1, 13.3, 13.5, PrIII.12 |
9 | Mar. 29 Mar. 31 Apr. 2 |
14 Counting infinite sets Midterm 2 Review MIDTERM 2 (Sections 8-13) |
HW 9 14.1, 14.2 |
10 | Apr. 5 Apr. 7 Apr. 9 |
15 The division theorem 16 The Euclidean algorithm 17 Consequences of the Euclidean algorithm |
HW 10 15.2, 15.6, 16.1, 16.4, PrIV.1 |
11 | Apr. 12 Apr. 14 Apr. 16 |
18 Linear diophantine equations 18 Linear diophantine equations 19 Congruence of integers |
HW 11 17.1, 17.3, 18.1, 18.2, 18.3, PrIV.13 |
12 | Apr. 19 Apr. 21 Apr. 23 |
20 Linear congruences 21 Congruence classes and the arithmetic of remainders 21 Congruence classes and the arithmetic of remainders |
HW 12 19.1, 19.3, 19.4, 20.1, 21.1, 21.4 |
13 | Apr. 26 Apr. 28 Apr. 30 |
22 Partitions and equivalence relations Review for Midterm 3 MIDTERM 3 (Sections 14-21) |
HW 13 21.3, 22.1 |
14 | May 3 May 5 May 7 |
23 The sequence of prime numbers 24 Congruence modulo a prime Final Exam Review |
HW 14 (not to be turned in) 23.2, 23.4, 24.1, 24.2, 24.4 |
May 17 | Final Exam
8:00-10:45am |
Cumulative All sections included in Midterms 1-3 plus 23-24 |
Sample Exams
Midterm 1 | Exam 1 (Spring 2020) |
Exam 2 (Fall 2019) | |
Exam 3 (Spring 2019) (Key) |
Note: ignore any questions not from Sections 1-7 of the book. Our exam will have roughly the following format: 10 short answer questions (2 points each) and three proof problems (10 points each).
Midterm 2 | Sample questions |
See also problems 5,6 on Exam 1 (Spring 2020). |
Midterm 3 | Sample questions |
Previous exam (Questions 1,2,3,6) |
Final | Sample Final 1 (Fall 2018) |
Sample Final 2 (Summer 2018) (Key) | |
Sample Final 3 (Fall 2017) |