MAT 200?nbsp;
Spring 2007 ?nbsp;

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Week

Topics

Homework

1/22

1 The Language of Mathematics?nbsp;

2 Implications?nbsp;

3 Proofs

4 Proof by Contradiction

Homework 1

Answer

1/29?nbsp;

5 Proof by Induction

6 The Language of Set Theory

HW 2 (due 2/7 or 2/8): Prove that if n is an integer, 2n+1 is odd.

On pages 53-54: problems 4 through 11. Answers

Text problems 2.1(p.19), 2.2(p.20), 3.2 and 3.3(p.29), 4.2 and 4.3(p.37) should be done, but won't be graded (since the answers are in the back).?nbsp;

?nbsp;2/5

7 Quantifiers

8 Functions

HW 3 (due 2/14 or 2/15)?nbsp; Ungraded problems (answers in back): 5.1 through 5.7 (p. 51-2)

On pages 55-57: problems 15,19,23,24

You should also hand in this problem.

Answers, Answers to extra problems

?nbsp;2/12

9 Injections, Surjections, and Bijections.

HW 4 (due 2/21 or 2/22)?nbsp; Ungraded problems (answers in back): 6.4 through 6.7 (p. 72-3), 7.1, 7.5 through 7.8 (p. 86-7).

On pages 115-117: problems 6,7,9,10,13, another problem.?nbsp; Answers

2/19?nbsp;

10 Counting.?nbsp;

?nbsp;HW 5 (due 3/7 or 3/8): Ungraded problems (answers in back): 10.2, 10.3 (p.132), 11.2, 11.4 (p. 143)

On pages 117-119: problems 14, 17, 21, answers, graphs

2/26

11 Properties of Finite Sets.

HW 6 (due 3/14 or 3/15): pages 182-4: 2,8,9,12,15, answers: page 1, page 2, the rest.

3/5?nbsp;

11 Properties of Finite Sets (continued)

12 Counting Functions and Subsets.

?nbsp;Exam I Answers (Lecture 2) (Monday/ Wednesday)

Both lectures: Redo this exam for extra credit.

3/12?nbsp;

12 Counting Functions and Subsets (continued)

13 Number Systems.

HW 7 (due 3/21 or 3/22): Ungraded problems (answers in back): 12.1 through 12.5.?nbsp;

pages 182-185: 4, 20, hints, answers

3/19

13 Number Systems (continued)

14 Counting Infinite Sets?nbsp;

Last day to drop (with "W"): March 23

HW 8 (due 3/28 or 3/29): ?nbsp; Ungraded problems (answers in back): 13.4, 14.1, 14.2, and 14.3.

On page 186: problems 23, 24, 25, 26. ?nbsp;Answers

3/26

Counting infinite sets (continued)

Geometry Notes: 1. Introduction through 3. Ruler Axiom.

HW 9 (due 4/11 or 4/19): Geometry notes: Exercises 2.3, 2.6, 3.1, 3.2, and 3.3. ?nbsp;Answers

4/2

Spring Break

?nbsp;4/9

Geometry notes:?nbsp;4.?nbsp; Protractor Axiom

HW 10:(due 4/18 or 4/26): Geometry notes: Exercises 4.3, 4.4, 4.7, and 4.8. Here are the solutions.

?nbsp;4/16

Geometry notes:?nbsp; 5. Triangles

HW 11: (Ungraded) Geometry notes: Exercises 5.2, 5.5, 5.6, Book: p. 269: 22.1,22.2,22.3, p.273: 17, Answers, answer to last question

?nbsp;4/23

Exam

Lecture 1 exam, lecture 2 exam, Lecture 1 answers, lecture 2 answers, lecture 2 bijection question                           

4/30

19 Modular Arithmetic.?nbsp;

21 Congruence Classes (continued).?nbsp;

22 Partitions and Equivalence Relations.