Section 003: Tuesday Thursday, 10-11:15, John Barry Hall 202B
Section 004: Tuesday Thursday, 11:30-12:45, John Barry Hall 202B
Office Hours: Wednesday 2-3:45 pm. Most days by appointment (more notice = higher chance we can make your preferred time work!)
Announcements: You may come to either section's final to take your final exam (see the schedule for days/times)
Office Hours: Wednesday 2-3:45 pm, any day after class, or by appointment (most afternoons and some mornings can work)
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: This will be updated throughout the semester. A current draft is here
Syllabus: Section 003 , Section 004
Textbooks: on blackboard
Week 1: 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: Ernst Chapter 1, Hammack Sections 2.1-2.3, Ernst 2.1-2.3, 4.3
Week 2: divisibility and the division algorithm, more direct proof, using cases. Homework 1 due Thursday.
Definitions you should know: divisible by/multiple of, upper and lower bound
Useful reading: Ernst 4.3, 1.9, 4.1, Hammack: 2.3, 2.1
Week 3: De Morgan's laws, proof by contrapositive, modular arithmetic, biconditional statements. Homework 2 due Thursday.
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
Week 4: quantifiers, negating statements with quantifiers, proof by contradiction. Homework 3 due Thursday.
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: Proof by induction. Homework 4 due Thursday
Definitions you should know: base case and inductive hypothesis
Useful reading: Hammack 10.1, Ernst 4.1 and 4.2
Week 6: Strong induction. Proof of the Fundamental Theorem of Arithmetic. All horses are the same color. Homework 5 due Thursday
Week 7: review, FIRST EXAM Thursday February 27
Spring Break March 3-7
Week 8 (March 11 and 13): Sets and associated definitions. Distributive-type laws. Group quiz on Thursday
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: Cartesian products and power sets, Perfect numbers. Definition Quiz on Tuesday. No lecture on Thursday March 20
Definitions you should know: Cartesian product, power set.
Useful reading: Ernst Chapter 3
Week 10: Relations, equivalence relations, functions. Homework 6 quiz and written homework due on Tuesday (March 25).
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: More on relations, equivalence relations, functions. Homework 7 due Thursday (April 3) with presentations
Week 12: Functions, injections and surjections and bijections, Homework 8 due Thursday (April 10)
Definitions you should know: function, image pre-image, domain, co-domain, range, injective, surjective, bijective
Useful reading: Hammack 12.1, 12.2, and 12.6 or Ernset 8.1, 8.2, and 8.4
Week 13: Exam before Easter break, Tuesday April 15
Week 14: Cardinalities of sets, different types of infinities, Cantor diagonalization, Homework 9 due Thursday (April 24)
Week 15: No class Tuesday (Friday class schedule), Homework 10 due Thursday May 1
Final exams: Section 003 on Saturday May 3 10:45-1:15, Section 004 on Tuesday May 6 from 8:30-11
Homework 1 problem set: due Thursday January 23 with presentations
Homework 2 problem set : due Thursday January 30 with presentations
Homework 3 problem set : due Thursday February 6 with presentations
Homework 4 problem set : due Thursday February 13 with presentations
Homework 5 problem set : due Thursday February 20 with presentations or quiz
Homework 6 problem set : due Tuesday March 25 with a quiz
Homework 7 problem set : Due Thursday April 3 with presentations
Homework 8 problem set : Due Thursday April 10
Homework 9 problem set : Due Thursday April 24
Homework 10 problem set : Due Thursday May 1