# Matthew Romney

### MAT 200-02 - Logic, Language and Proof - Spring 2021

Course Syllabus

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.

 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 CumulativeAll sections included in Midterms 1-3plus 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)