# Math 220 – Introduction to Mathematical Reasoning.

MWF 9-9:50 & 11-11:50, Curtis 454.

Instructor: Anatolii Grinshpan
Office hours:  Mon 2-3, Wed 3-5 (Korman 247), or by appointment.

Outline

Mar 30. Introduction to the course. Definition.

Reading: preface, Sections 1 & 2. Problems: 1.1, 2.1-2.3, 2.6, 2.9(a). Homework 1: 2.5 (due April 6).

Apr 1.  Statements, axioms, and theorems.

Apr 3.  Quiz 1. Implication and equivalence.

Reading:  Section 3. Problems: 3.1-3.4, 3.8.

Apr 6.  Proof. Counterexample.

Week 1 answers. Reading: Sections 4 & 5. Problems: 4.2, 4.5, 4.8, 4.9, 5.1-5.9.  Homework 2: 4.13 (due April 13).

Apr 8.  Boolean Algebra.

Reading: Section 6. Problems: 6.1, 6.3, 6.4, 6.8, 6.9, 6.10, 6.11(a), 6.12(a).

Apr 10. Quiz 2. Lists.

Problems: Chapter 1 self test. Reading: Section 7.

Apr 13. Lists (continued). Factorial.

Week 2 answers. Problems: 7.1, 7.2, 7.4, 7.6, 7.7, 7.9, 7.10. Homework 3: 8.8 (due April 20).

Apr 15. Homework discussion. Factorial.

Reading: Section 8. Problems: 8.1, 8.3, 8.4, 8.5, 8.7.

Apr 17. Quiz 3. Sets.

Apr 20. Sets and subsets. Existential and universal quantifiers.

Week 3 answers. Problems: 9.1-9.3, 9.5-9.10. Homework 4: 11.15 (due April 27).

Apr 22. Quantifiers. Operations with sets.

Reading: Sections 10 & 11. Problems: 10.1, 10.4-10.6, 11.1-11.9.

Apr 24. Examples. Quiz 4.

Apr 27. Combinatorial proofs.

Week 4 answers. Reading: Section 12. Problems: 12.1, 12.2, 12.4, 12.5, Chapter 2 self test. Homework 5: none.

Apr 29. Review for the test – come armed with questions!

May 1. Midterm 1 (lectures of  March 30 – Apr 27).

May 4. Relations.

Reading: Section 13. Problems: 13.1, 13.2, 13.5-13.7, 13.12, 13.13. Homework 6: 16.10 (due May 11).

May 6. Equivalence relations.

Reading: Section 14, Section 15 (optional). Problems: 14.1, 14.3, 14.5, 14.7, 14.8.

May 8. Quiz 5. Binomial coefficients.

Reading: Section 16. Problems: 16.1-16.9, 16.11.

May 11. Binomial coefficients. Proofs: indirect arguments.

Week 6 answers. Reading: Sections 19. Problems: 19.1-19.3, 19.7, 19.10. Homework 7: 20.6 (due May 18).

May 13. Proofs by contrapositive and by contradiction.

Reading: Section 20. Problems: 20.1-20.5, 20.7.

May 15. Quiz 6. Induction.

May 18. Induction. Recurrence relations.

Week 7 answers. Reading: Sections 21 & 22 (optional: sequences generated by polynomials). Problems: 22.1, 22.2. Homework 8:  none.

May 20. Quiz 7. Recurrence relations.

May 22. Midterm 2. (lectures of May 4 – May 20).

May 25. No class (Memorial day). Homework 9: 23.11 (due June 1).

May 27. Functions.

Reading: Section 23. Problems: 23.1-23.5, 23.9, 23.12, 23.14.

May 29. The Pigeonhole principle.

Reading: Section 24. Problems: 24.1-24.7, 24.9.

June 1. Quiz 8. Cantor’s theorem.

June 3. Basics of Number Theory.

Reading: Section 34. Notes on the Euclidean Algorithm.

June 5. Greatest common divisor. The Euclidean Algorithm.

June 8. The Fundamental Theorem of Arithmetic.

Office hours: June 8, 2-3 P.M. (Korman 247)

June 9, 12-1+ P.M. (Korman 253)

June 12.  Final exam 10:30-12:30, Curtis 451.