Kevin Milans : Teaching : Spring 2023 Math303

Kevin Milans (milans@math.wvu.edu)
Office: Armstrong Hall 408H
Office Hours: MW 2:00pm-3:00pm, and by appointment
Class Meetings: MWF 11:30am-12:20pm in Hodges Hall 307
Class Textbook: Book of Proof, by Richard Hammack
Home | Course Syllabus (PDF) | Homework

Course Schedule

No. Date Class Summary Sections(s) Quiz Quiz Soln Comments
1 Jan 9 Introduction; Sets: elements; equality 1.1 - - -
2 Jan 11 Set examples; Ordered pairs 1.1,1.2 - - HW1 assigned.
3 Jan 13 Cartesian Product; tuples 1.2 - - -
4 Jan 18 Subsets 1.3 - - HW1 due. HW2 assigned.
5 Jan 20 Power set 1.4 quiz1.pdf quiz1-soln.pdf Quiz 1 in class.
6 Jan 23 Union; Intersection; Set Difference 1.5 - - -
7 Jan 25 Complementation; Venn Diagrams; Equations with Sets 1.6,1.7 - - HW2 due. HW3 assigned.
8 Jan 27 Indexed Sets 1.8 quiz2.pdf quiz2-soln.pdf Quiz 2 in class.
9 Jan 30 Indexed Sets II; Russell's Paradox 1.8,1.10 - - HW3 due. HW4 assigned.
10 Feb 1 Statements 2.1,2.2 - - -
11 Feb 3 Test 1: 1.1-1.8, 1.10 - test1.pdf test1-soln.pdf Test 1 in class.
12 Feb 6 And, or, not 2.2 - - -
13 Feb 8 Conditional, Biconditional Statements 2.3,2.4 - - HW4 due. HW5 assigned.
14 Feb 10 Truth tables; statement equivalence 2.5,2.6 quiz4.pdf quiz4-soln.pdf Quiz 4 in class.
15 Feb 13 Quantified statements 2.7 - - -
16 Feb 15 Negating statements 2.10 - - HW5 due. HW6 assigned.
17 Feb 17 Negating statements, cont 2.10 quiz5.pdf quiz5-soln.pdf Quiz 5 in class.
18 Feb 20 Theorems and definitions 4.1 - - -
19 Feb 22 Even and odd definitions; proofs 4.2 - - HW6 due. HW7 assigned.
20 Feb 24 The division lemma, existence of q and r 4.2 quiz6.pdf quiz6-soln.pdf Quiz 6 in class.
21 Feb 27 Direct proof; proof critiques 4.3 - - -
22 Mar 1 Direct proof: AMGM inequality, case n = 2; proofs with cases 4.3,4.4 - - HW7 due. HW8 assigned.
23 Mar 3 Similar cases 4.5 quiz7.pdf quiz7-soln.pdf Quiz 7 in class.
24 Mar 6 Contrapositive proofs 5.1 - - -
25 Mar 8 Congruences 5.2 - - -
26 Mar 10 Test 2: 2.1-2.7, 2.9, 2.10, 4.1-4.5 - test2.pdf test2-soln.pdf Test 2 in class.
27 Mar 20 Proof by contradiction I 6.1,6.2 - - -
28 Mar 22 Proof by contradiction II 6.1,6.2 - - HW8 due. HW9 assigned.
29 Mar 24 Proof by contradiction III; factorials 6.3, 3.5 quiz8.pdf quiz8-soln.pdf Quiz 8 in class.
30 Mar 27 Binomial coefficients; Binomial theorem 3.5 - - -
31 Mar 29 Poker Hands; Binomial theorem; Pascal's Triangle 3.5, 3.6 - - HW9 due. HW10 assigned.
32 Mar 31 If and only if proofs; Equivalent statements 7.1,7.2 quiz9.pdf quiz9-soln.pdf Quiz 9 in class.
33 Apr 3 Existence and Uniqueness Proofs 7.3 - - -
34 Apr 5 Greatest Common Divisors, Integer Combinations 7.3 - - HW10 due. HW11 assigned.
- Apr 7 Holiday-- no class - - - -
35 Apr 10 Nonconstructive existence proofs; proofs with sets 7.4, Ch8 - - -
36 Apr 12 Proofs with sets; proof and disproof Ch8, Ch9 - - HW11 due. HW12 assigned.
37 Apr 14 Test 3: 3.5, 3.6, Ch5, Ch6, Ch7 - test3.pdf test3-soln.pdf Test 3 in class.
38 Apr 17 Proof and disproof: more examples Ch 9 - - -
39 Apr 19 No minimum counter-example proof technique 10.3 - - HW12 due. HW13 assigned.
40 Apr 21 No minimum counter-example and Induction 10.3, 10.1 quiz12.pdf quiz12-soln.pdf Quiz 12 in class.
41 Apr 24 Induction II: Sums of distinct powers of 2 10.2 - - -
42 Apr 26 Induction III 10.4,10.5 - - HW13 due.
43 Apr 28 Review Day - - - -
- May 4 Final Exam: Thurs, May 4, 11:00am-1:00pm - - - -
milans@math.wvu.edu