# Math 220 – Introduction to Mathematical Reasoning.

MWF 11-11:50,  Korman 245.

Instructor: Anatolii Grinshpan
Office hours:  Mon, Wed 3-4 (Korman 247), Tue 4-5 (Korman 266) or by appointment.

Outline

Mar 31. Introduction to the course. Truth tables.

Reading: Chapter 1. Problems: 1.1-1.12. Homework 1: 1.5 (due April 7).

Apr 2.  Logic of proof: forward and backward.

Reading: Chapter 2. Problems: 2.1-2.11, 2.13, 2.15, 2.17, … , 2.25.

Apr 4. Definitions and math terminology.

Reading: Chapter 3. Problems: 3.1-3.10.

Apr 7. Quiz 1 (material of week 1). Problem discussion.

Homework and quiz answers. Homework 2: give a proof of 3.1 e (due April 14).

Apr 9. The existential quantifier and construction method.

Reading: Chapter 4. Problems: 4.1-4.10, 4.13.

Apr 11. The universal quantifier and choose method.

Reading: Chapter 5. Problems: 5.1-5.17 (odds).

Apr 14. Quiz 2 (material of week 2). Specialization. Homework and quiz answers.

Homework 3: 5.2 (due April 21). Reading: Chapter 6.

Apr  16. Reasoning with quantifiers (construction, choice, specialization).

Problems: 6.1-6.10.

Apr  18. Nested quantifiers. Negation of composite statements.

Reading: Chapters 7 and 8. Problems: 7.1-7.11 (odds), 8.1-8.8.

Apr 21. Quiz 3 (material of week 3). Homework and quiz discussion.

Apr 23. Problem discussion. Euclidean algorithm in brief.

Apr 25. Midterm 1 (Chapters 1-8). Midterm answers.

Apr 28. Division of integers. Homework 4: midterm question 5 (due May 5).

May 5. Quiz 4 (Euclidean algorithm). Proof by contradiction.

Reading: Chapter 9. Problems: 9.1-9.21 (odds). Homework 5: 9.10 (due May 12).

May 7. The contrapositive method.

Reading: Chapter 10. Problems: 10.1-10.15 (odds).

May 9. Problem discussion: # 22, 31, 32 from the handout.

May 12. Quiz 5 (Chapters 9 and 10). Uniqueness arguments.

May 14. Uniqueness arguments. Mathematical induction.

Reading: Chapter 11. Problems: 11.1-11.15 (odds). Homework 6: 11.4 (due May 21).

May 16. Mathematical induction.

May 19. Quiz 6 (uniqueness arguments and induction). Proof by cases, proof by elimination.

Reading: Chapter 12. Problems: 12.1-12.13 (odds). Homework 7: 12.9 (due May 26).

May 21. Max/min arguments. Problem discussion. Homework and quiz answers.

May 23. Midterm 2 (Chapters 9-13, Euclidean algorithm). Midterm answers.

May 28. Examples from Discrete Mathematics. Reading: Appendix A.

May 30. Examples from Linear Algebra. Reading: Appendix B.

Homework 8: B.9 (due June 6).

June 2.  Examples from Number Theory and Group Theory.

June 4. Examples from Group Theory (continued).

June 6. Examples from Real Analysis. Reading: Appendix D. Homework answers

June 9. Office hours:  1-2 P.M.

Focus: homework, quizzes, midterms, exercises and examples from class.