Kevin Milans : Teaching : Fall 2018 Math283: Introduction to Concepts of Mathematics

Kevin Milans (milans@math.wvu.edu)
Office: Armstrong Hall 408H
Office Hours: M,W,Th 11:30am-12:30pm, and by appointment
Class Meetings: M,W,F 10:30am-11:30am in Armstrong Hall 207
Home | Course Syllabus (PDF) | Homework

Course Schedule

No. Date Class Summary Sections(s) Quiz Quiz Soln Comments
1 Jan 8 Introduction; Sets: elements; equality 1.1 - - HW1 assigned.
2 Jan 10 Set examples; Ordered pairs 1.1,1.2 - - -
3 Jan 12 Cartesian Product; tuples 1.2 pdf pdf Quiz 1 in class. HW1 due. HW2 assigned.
- Jan 15 MLK Day - - - -
4 Jan 17 Subsets; power set 1.3,1.4 - - -
5 Jan 19 Union; intersection; set difference 1.5 pdf pdf Quiz 2 in class. HW2 due. HW3 assigned.
6 Jan 22 Set operation examples; Complementation; Venn Diagrams 1.5--1.7 - - -
7 Jan 24 Indexed Sets 1.8 - - -
8 Jan 26 Russell's paradox 1.10 pdf pdf Quiz 3 in class. HW3 due. HW4 assigned.
9 Jan 29 Statements; And, or, not 2.1,2.2 - - -
10 Jan 31 Conditional, Biconditional Statements 2.3,2.4 - - -
11 Feb 2 Truth tables 2.5 pdf pdf Quiz 4 in class. HW4 due. HW5 assigned.
12 Feb 5 Truth tables; statement equivalence 2.5,2.6 - - -
13 Feb 7 Quantifiers 2.7 - - -
14 Feb 9 Negating Statements 2.10 pdf pdf Quiz 5 in class. HW5 due.
15 Feb 12 Review; theorems 4.1 - - -
16 Feb 14 Test 1: Ch1 and Ch2 - pdf pdf -
17 Feb 16 Theorems and definitions 4.1 - - HW6 assigned.
18 Feb 19 The division algorithm 4.2 - - -
19 Feb 21 Proof Critiques - - - -
20 Feb 23 Direct proof: AMGM inequality, case n = 2 4.3 pdf pdf Quiz 6 in class. HW6 due. HW7 assigned.
21 Feb 26 Cases; Proof by contrapositive 4.4,4.5,5.1 - - -
22 Feb 28 Congruences 5.2 - - -
23 Mar 2 HW \#7, problem 3 discussion; factorials 3.2 pdf pdf Quiz 7 in class. HW7 due. HW8 assigned.
24 Mar 5 Binomial coefficients; Pascal's triangle; Binomial theorem 3.3,3.4 - - -
25 Mar 7 Proof by contradiction 6.1,6.2 - - -
26 Mar 9 Proof by contradiction II 6.2,6.3 pdf pdf Quiz 8 in class. HW8 due. HW9 assigned.
27 Mar 19 Proof by contradiction III; combining techniques 6.1,6.3 - - -
28 Mar 21 Proving biconditional statements; equivalent statements 7.1,7.2 - - -
29 Mar 23 Review for Test 2 - pdf pdf Quiz 9 in class. HW9 due.
30 Mar 26 Test 2: 3.2-3.4, Ch4, Ch5, Ch6, 7.1-7.2 - pdf pdf -
31 Mar 28 Existence and uniqueness proofs; greatest common divisors 7.3 - - HW10 assigned.
- Mar 30 University closed - - - -
32 Apr 2 Non-constructive existence proofs; proofs with sets 7.4,Ch 8 - - -
33 Apr 4 Proof and disproof I Ch 9 - - -
34 Apr 6 Proof and disproof II Ch 9 pdf pdf Quiz 10 in class. HW10 due. HW11 assigned.
35 Apr 9 The "no smallest counterexample" technique 10.2 - - -
36 Apr 11 The "no smallest counterexample" technique II 10.2 - - -
37 Apr 13 Induction I 10.1 pdf pdf Quiz 11 in class. HW11 due. HW12 assigned.
38 Apr 16 Induction II; Fibonacci Numbers 10.1, 10.3 - - -
39 Apr 18 Relations 11.0, 11.1 - - -
40 Apr 20 Review Induction Ch10 pdf pdf Quiz 12 in class. HW12 due. HW13 assigned.
41 Apr 23 Equivalence Relations 11.2 - - -
42 Apr 25 Functions 12.1,12.2 - - -
43 Apr 27 - - - - HW13 due.
milans@math.wvu.edu