Math 206
Spring '04
Rhonda Hughes
332 PSB
x5351; rhughes@brynmawr.edu



COURSE INFORMATION


TEXT: Diane Driscoll Schwartz, Conjecture and Proof: An Introduction to Mathematical Thinking

COURSE REQUIREMENTS: There will be two exams, on Wednesday, February 25th and Friday, April 2nd, each worth 25% of your grade, and a self-scheduled final exam worth 30%. Homework will be collected regularly. In addition, there will be a project on the last day of written work; details will be handed out later. Homework and the project will be worth 20% of your grade.

HOMEWORK: Homework will be graded. You are encouraged to work together on the homework, but you should write up your own solutions. Homework that is more than a week late will not be graded. You are allowed two late homeworks (late = after the due date, but less than or equal to one week after the due date!).

OFFICE HOURS (Room 332): Mondays and Wednesdays, 2:30 - 3:30 p.m.; and by appointment. There will be Problem Sessions each week (TBA), conducted by TA Jill Jordan.

EXTENSIONS: Tests may not be taken late without advance permission. Extensions are usually granted ONLY for family emergencies, infirmary or hospital stays, or similar major crises.

SPECIAL ACCOMMODATIONS: Students who think they may need accommoda-tions in this course because of the impact of a disability are encouraged to meet with me privately early in the semester. Students should also contact Stephanie Bell, Coordinator of Accessibility Services, at 610-526-7351 in Canwyll House, as soon as possible, to verify their eligibility for reasonable accommodations. Early contact will help to avoid unnecessary inconvenience and delays.

 


Reading Assignments

1.   Sections 1.3, 2.1-2.3, 4.1: Warm-Up, Set Theory, Logic.
2.   Sections 2.4-2.5, 3.1: Truth Tables, Proofs, and Quantifiers.
3.   Appendix C, Sections 3.2-3.3: Deductive Proofs, Proof by Induction.
4.   Sections 4.2-4.6: Set Operations, Families of Sets, Cartesian Products.
5.   Sections 5.1-5.3: Functions, Injective and Surjective Functions.
6.   Sections 5.4-5.7: Functions, Composition, Image and Inverse Image.
7.   Sections 6.1-6.3: Relations, Equivalence Relations, and Equivalence Classes.
8.   Sections 10.1-10.2: Analysis, The Real Numbers, Sequences.
9.   Sections 10.3-10.4: Analysis, Limits of Functions and Continuity.
10. Sections 8.1-8.2: Cardinality, Finite and Infinite Sets, Countable and Uncountable Sets.
11. Sections 9.1-9.3: Groups.
12. Sections 9.4-9.6: Groups, Integers modm, subgroups, homomorphisms.

 

Homework Assignments

1.   Section 1.3, Problems 4, 5.
2.   Section 2.1, Problems 1; 3a,b,d; 5c,d; 7e,f; 8.
3.   Section 2.3, Problems 1a,c,d,g; 2.
4.   Section 4.1, Problems 1-13, odd.
5.   Section 2.4, Problems 4,a,b,c; 6a,c,e,g.
6.   Section 2.5, Problems 1, 2"odd'', 3, 6a,c; 8.
7.   Section 3.1, Problems 1, 3, 4, 8; 15a,b; 17.
8.   Section 3.2, Problems 1, 3, 4, 5.
9.   Section 3.2, Problems 7, 8, 13.
10. Section 3.3, Problems 6, 7, 10, 14, 16.
11. Section 4.2, Problems 2, 5.
12. Section 4.3, Problems 2, 3, 4.
13. Section 4.4, Problems 9, 11, 12.
14. Section 4.6, Problems 1, 2 "odd''.
15. Section 5.1, Problems 2a,b,c,g.i.j.k; 3, 4, 5.
16. Section 5.2, Problems 1, 4, 5.
17. Section 5.3, Problems 1 "odd'', 3a,b; 5.
18. Section 5.5, Problems 6a-c; 7, 8.
19. Section 5.6, Problems 2, 3.
20. Section 6.1, Problems 1, 6.
21. Section 6.2, Problems 1 "odd''.
22. Section 6.3, Problems 1 "odd'', 2, 4a,b.
23. Section 10.1, Problems 1, 6.
24. Section 10.2, Problems 1, 6.
25. Section 10.3, Problems 1, 2, 4, 5, 8a.
26. Section 10.4, Problems 1-4.
27. Section 8.1, Problems 2, 3, 5, 8.
28. Section 8.2, Problems 1, 2, 4.
29. Section 9.1, Problems 1, 2.
30. Section 9.2, Problems 3a,c,e.
31. Section 9.3, Problems 1, 5, 6, 7.
32. Section 9.4, Problems 4, 5.
33. Section 9.5, Problems 3,5,6,7.
34. Section 9.6, Problems 2a,b,c,f; 6.