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.
 

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)