Kevin Milans : Teaching : Spring 2024 Math303

Kevin Milans (milans@math.wvu.edu)
Office: Armstrong Hall 408H
Office Hours: M 12:30pm-1:30pm, W 2:00pm-3:00pm and by appointment
Class Meetings: MWF 11:30am-12:20pm in Hodges Hall 321
Class Textbook: Book of Proof, by Richard Hammack
Class Workshop: M 5:00pm-6:30pm in Hodges Hall 221
Home | Course Syllabus (PDF) | Homework

Course Schedule

No. Date Class Summary Sections(s) Quiz Quiz Soln Comments
1 Jan 8 Introduction; Pythagorean Theorem - - - -
2 Jan 10 Intro to sets 1.1 - - HW1 assigned.
3 Jan 12 Ordered pairs; Cartesian product 1.2 - - -
4 Jan 17 Review HW1; Generalized Cartesian product 1.2 - - HW1 due. HW2 assigned.
- Jan 19 Class Canceled (snow) - - - -
5 Jan 22 Subsets, Powersets 1.3, 1.4 quiz1.pdf quiz1-soln.pdf Quiz 1 in class. Workshop this evening.
6 Jan 24 Union, Intersection, Set Difference 1.5 - - HW2 due. HW3 assigned [available now].
7 Jan 26 Union, Intersection, Set Difference; Complementation 1.5,1.6 quiz2.pdf quiz2-soln.pdf Quiz 2 in class.
8 Jan 29 Venn Diagrams; Indexed Sets 1.7, 1.8 - - -
9 Jan 31 Indexed Sets; Russell's Paradox 1.8, 1.10 - - HW3 due. HW4 assigned [available now].
10 Feb 2 Test 1: sections 1.1-1.8 - test1.pdf test1-soln.pdf Test 1 in class.
11 Feb 5 Statements and open sentences 2.1 - - -
12 Feb 7 And, or, not; conditional statements 2.2,2.3 - - HW4 due. HW5 assigned [available now].
13 Feb 9 Biconditional Statements 2.4 quiz4.pdf quiz4-soln.pdf Quiz 4 in class.
14 Feb 12 Truth tables; statement equivalence 2.5,2.6 - - -
15 Feb 14 Quantified statements, Translation 2.7,2.9 - - HW5 due. HW6 assigned [available now].
16 Feb 16 Negating statements 2.10 quiz5.pdf quiz5-soln.pdf Quiz 5 in class.
17 Feb 19 More on negation; Intro to Proofs; importance of definitions 2.10,4 - - -
18 Feb 21 Termonology; definitions 4.1,4.2 - - HW6 due. HW7 assigned [available now].
19 Feb 23 Even and odd definitions; direct proofs 4.2,4.3 quiz6.pdf quiz6-soln.pdf Quiz 6 in class.
20 Feb 26 The division lemma, direct proof exxamples 4.2, 4.3 - - -
21 Feb 28 Proof critiques 4.3 - - HW7 due. HW8 assigned [available now].
22 Mar 1 Test 2: 1.10, 2.1-2.7, 2.9, 2.10, 4.1-4.3 - test2.pdf test2-soln.pdf Test 2 in class.
23 Mar 4 More proof critiques 4.3 - - -
24 Mar 6 Proofs with cases; combining similar cases 4.4,4.5 - - HW8 due. HW9 assigned [available now].
25 Mar 8 Proof by contrapositive; congruences 5.1,5.2 quiz8.pdf quiz8-soln.pdf Quiz 8 in class.
26 Mar 18 Congruences, Proof by Contradiction 5.2, 6.1 - - -
27 Mar 20 Proof by contradiction II 6.1,6.2 - - HW9 due. HW10 assigned [available now].
28 Mar 22 Proof by contradiction III 6.1,6.2 quiz9.pdf quiz9-soln.pdf Quiz 9 in class.
29 Mar 25 Permutations; Binomial Coefficients; Binomial Theorem 3.4-3.6 - - -
30 Mar 27 Combinatorial Arguments; Algebraic vs Combinatorial Proof 3.4-3.6 - - HW10 due.
- Mar 29 No Class; spring recess - - - No Quiz 10.
31 Mar 31 Sierpinski's Triangle; If and only if proofs; Equivalent statements 7.1,7.2 - - -
32 Apr 3 Existence and Uniqueness Proofs 7.3 - - HW11 assigned [available now].
33 Apr 5 Test 3: 4.4, 4.5, 5.1, 5.2, 6.1-6.3, 3.4-3.6, 7.1 - test3.pdf test3-soln.pdf Test 3 in class
- Apr 8 No class (eclipse) - - - -
34 Apr 10 Integer combinations and gcd's 7.3 - - HW11 due. HW12 assigned [available now].
35 Apr 12 Nonconstructive existence proofs; proofs with sets 7.4, Ch8 quiz11.pdf quiz11-soln.pdf Quiz 11 in class.
36 Apr 15 Proofs with sets II; proof and disproof Ch8, Ch9 - - -
37 Apr 17 Induction Introduction Ch 10 - - HW12 due. HW13 assigned [available now].
38 Apr 19 Cake revisited 10.3 quiz12.pdf quiz12-soln.pdf Quiz 12 in class.
39 Apr 22 No minimum counter-example proof technique; Induction I: summation identities Ch 10 - - -
41 Apr 24 Induction II: Binet's formula; Harmonic series inequality; graphs without cycles Ch 10 - - -
42 Apr 26 Induction III: tromino tilings, Ramsey theory Ch 10 - - HW13 due.
- Apr 30 Review Session, 12pm-1:30pm, in our regular room Hodges Hall 321 - - - -
- May 2 Final Exam: Thurs, May 2, 11:00am-1:00pm - - - -
milans@math.wvu.edu