Math 2600: Mathematical Reasoning & Proof
MAT 2600-004: MWF, 9:35-10:25, White Hall 116
Office Hours: MW 1-2 or by appointment, SAC 378
MAT 2600-004: MWF, 9:35-10:25, White Hall 116
Office Hours: MW 1-2 or by appointment, SAC 378
Announcements: The first midterm will be Friday February 27
Office Hours: Monday and Wednesday 1-2, SAC 378. Other times by appointment.
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
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
Week 6: (Feb 16-20) All horses are the same color, strong induction, proof by smallest counterexample, Unique factorization theorem
Week 7: (Feb 23-27) Introduction to sets. First exam, Friday February 27
SPRING BREAK
Week 8: (March 9-13) Sets and associated definitions. Distributive-type laws. Definitions quiz on Friday.
Definitions you should know: set, well-defined, empty set, set-builder notation, subset, equality of sets, intersection, union, set difference, disjoint
Useful reading: Hammack Chapter 1 and 8.1-8.3
Week 9: (March 16-20) Cartesian products and power sets, perfect numbers. Homework 6 due Wednesday (quiz or presentations)
Definitions you should know: Cartesian product, power set.
Useful reading: Ernst Chapter 3
Week 10: (March 23-27) Relations, equivalence relations, functions. Homework 6 presentations Monday. Homework 7 due Wednesday.
Definitions you should know: relation, reflexive, symmetric, transitive, anti-symmetric, partial order, total order, equivalence relation, equivalence class
Useful reading: Hammack Chapter 11 or Ernst Chapter 7
Week 11: (March 30 and April 1): No class Friday for Easter break. Exam Wednesday April 1. Homework 8 due Wednesday.
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
Homework 4 problemt set : Due Friday February 13 with presentations
Homework 5 problem set : Due Friday February 20 with quiz
Homework 6 problem set : Due Wednesday March 18
Homework 7: Due Wednesday March 25
Homework 8: Due Wednesday April 1