# Kevin Milans : Teaching : Spring 2016 Math293E/Math183

Kevin Milans (milans@math.wvu.edu)
Office: Armstrong Hall 408H
Office Hours: MTuTh 11:30am-12:30pm, and by appointment
Class Meetings: TuTh 10:00am-11:15am in Armstrong Hall 313

Home | Course Syllabus (PDF) | Homework

### Course Schedule

 No. Date Class Summary Section(s) Quiz Quiz Soln Comments 1 Jan 12 Introduction; Argument and Proof 1.1 - - HW1 assigned. 2 Jan 14 An extremal argument; Pythagorean Theorem 1.1 - - - 3 Jan 19 More "proofs" of the Pythagorean Theorem 1.1 - - HW1 due. HW2 assigned. 4 Jan 21 Primes; definitions; proof by contradiction 1.1.2 - - - 5 Jan 26 Irrational numbers 1.1.3 Q1 Q1-soln - 6 Jan 28 Irrational numbers; Algebra in mathematical arguments 1.2.2 - - HW3 assigned. 7 Feb 2 Language of math: or and implications 1.2.2-1.2.4 Q2 Q2-soln HW2 due. 8 Feb 4 Language of math: quantifiers; polynomials 1.2.4,1.3.3 - - HW3 due. HW4 assigned. 9 Feb 9 Roots and factors of polyomials 1.3.3 Q3 Q3-soln - 10 Feb 11 Quadratic formula 1.3,3,1.4 - - HW4 due. HW5 assigned. 11 Feb 16 Abstraction and examples; executing proofs; large gaps between primes - - - - 12 Feb 18 Test 1 1 T1 T1-soln HW5 assigned. 13 Feb 23 The sum 1+2+...+n 1.4 - - - 14 Feb 25 Sigma/Pi sum/product notation; application: how many regions are created by n lines? 1.4,2.2.2 - - HW5 due. HW6 assigned. 15 Mar 1 Patterns: a cautionary tale; Intro to sets 3.1 Q5 Q5-soln - 16 Mar 3 Set operations 3.5 - - HW6 due. HW7 assigned. 17 Mar 8 Proofs with sets; Russell's Paradox 3.3,3.9 Q6 Q6-soln - 18 Mar 10 Cartesian products; indexed operations 3.6,3.7 - - HW7 due. HW8 assigned. 19 Mar 15 Indexed operations; applications (bounds on n!, harmonic series); proofs 3.9 Q7 Q7-soln - 20 Mar 17 Mathematical logic: statements 4.1 - - HW8 due. 21 Mar 29 Mathematical logic: statements, variable propositions, quantifiers 4.1-4.3 - - HW9 assigned. 22 Mar 31 Negation of quantified statements, Logical connectives, implications 4.4-4.7 - - - 23 Apr 5 Proofs, sets, and mathematical logic 4.8-4.10 - - HW9 due. 24 Apr 7 Test 2 - T2 T2-soln - 25 Apr 12 Review Test 2; Converse and Contrapositive 4.8 - - HW10 assigned. 26 Apr 14 Proof techinique: no minimum counter-example - Q9 Q9-soln - 27 Apr 19 A combinatorial game; geometric coloring example 5 - - HW11 assigned. 28 Apr 21 Induction and the no minimum counter-example technique 5 - - - 29 Apr 26 Induction 5 - - - 30 Apr 28 Review Final Exam; Intro to Ramsey Theory - - - HW11 due. -- May 3 Final Exam: 7pm to 9pm - - - -

milans@math.wvu.edu