Math 2600: Mathematical Reasoning & Proof
MAT 2600-004: MWF, 9:35-10:25, White Hall 116
Office Hours: TBA
MAT 2600-004: MWF, 9:35-10:25, White Hall 116
Office Hours: TBA
Announcements: Office hours week of Jan 19-23: Wednesday 12-1 and Thursday 10:45-11:30
Office hours week of Feb 2-6: Monday and Wednesday 12:50 - 1:50 (times slightly updated!)
Office Hours: TBA SAC 378
Overleaf Resources: Here is some information on how to type mathematics: overleaf primer and homework template. Both of these were generously given to me by the benevolent Dr. Kristin Heysse. Another useful guide is this blogpost by (Jeopardy! champion) Robert Won: https://blogs.gwu.edu/robertwon/2021/07/18/how-to-tex-your-homework/
List of learning objectives:
Syllabus: here: office hours to be added soon
Textbooks: Book of Proof by Hammack and An Introduction to Proof via Inquiry-Based Learning by Ernst. Both available online for free, links on blackboard.
Week 1 (Jan 12-16): introduction, beginning propositional logic, direct proof.
Definitions you should know: even, odd, statement, set, real numbers, integers, natural numbers, and, or, not, conditional statement
Useful reading: Hammack sections 2.1-2.3 and 4.3, Ernst Chapter 1, sections 2.1-2.3
Week 2 (Jan 19-23): no class Monday, divisibility and the division algorithm, more direct proof, using cases.
Definitions you should know: divisible by/multiple of, upper and lower bound
Useful reading: Hammack: 2.3, 4.1-4.4
Homework 1 presentations on Friday
Week 3 (Jan 26-30): De Morgan's laws, proof by contrapositive, modular arithmetic, biconditional statements. Homework 2 due Friday.
Definitions you should know: converse, biconditional statement, logically equivalent, contrapositive, congruent modulo n, prime, composite
Useful reading: Ernst 2.2 and 2.3, Hammack 2.4, 2.5, 2.6, 5.1
Week 4: (Feb 2-6) quantifiers, negating statements with quantifiers, proof by contradiction. Homework 3 due Friday with quiz.
Definitions you should know: greatest common divisor, rational/irrational
Useful reading: Hammack 2.7, 2.10, chapter 6, Ernst 2.4 and 2.5, Chapter 6
Week 5: (Feb 9-13) Proof by induction. Homework 4 due Friday.
Definitions you should know: base case and inductive hypothesis
Useful reading: Hammack 10.1, Ernst 4.1 and 4.2
Tentative exam dates: Friday Feb 27, Wednesday April 1
Homework 1 problem set : Due Friday January 23 with presentations
Homework 2 problem set : Due Friday January 30
Homework 3 problem set : Due Friday February 6 with quiz