* MATH 108 (SECTION 31), 1020 Wickson, 8:00-9:15 a.m. MWF *

* Instructor: Dr. D. A. Kouba *

will be posted here by Thursday, August 22, 2002. If you would like to view your final exam or have questions about course grades, please stop by during Fall Quarter 2002. Enjoy the rest of your summer.

Text: A Transition to Advanced Mathematics (5th edition) by Smith, Eggen, and St. Andre

Office: 484 Kerr

Phone: (530) 752-1083

E-mail: * kouba@math.ucdavis.edu *

Office Hours (Subject to Change): 10-11 Tuesday, Thursday . . . . or by appointment

TA Office Hours (Subject to Change): Jeremy Dybdahl, 469 Kerr, 2-3 Monday, Wednesday

EXAM DATES :

- EXAM 1-- FRIDAY, July 12, 2002

- EXAM 2-- FRIDAY, August 2, 2002

- FINAL EXAM -- FRIDAY, August 16, 2002 ... FINAL EXAM WILL START AT 7:30 a.m. ON AUGUST 16, 2002, FOR THOSE WHO WOULD LIKE TO HAVE EXTRA TIME !

The course will likely cover the following sections in our textbook : 1.1-1.7, 2.1-2.5, 3.1-3.3, 4.1-4.3, 5.1-5.3, 7.1, 7.2

Here is the Course Syllabus

Here are Math 108 Lecture Notes , as part of The Proof Page, a webpage project partially funded by a UIIP grant from TRC.

Here are Practice Problems (Proofs) . . . page 1 , page 2

Here are Math 108 Homework and Exam Solutions .

Here are Practice Exam 1 . . . Page 1 , Page 2 , . . . and Solutions . . . Page 1 , Page 2 , Page 3 , Page 4 , Page 5

Here are Practice Exam 2 . . . Page 1 , Page 2 , . . . and Solutions . . . Page 1 , Page 2 , Page 3 , Page 4 , Page 5 , Page 6

The following homework assignments are subject to minor changes.

- HW #1 (Section 1.1) p. 7: 1bdfgi(optional), 2ei, 3fklm, 5befhi, 9, 10c, 11ce

TURN IN : All

- HW #2 (Section 1.2) p. 15: 1acdefgh, 2bh, 4acdg, 7cdg, 9bcf, 10bd, 12ab, 14bc, and
Mathematically Equivalent Statements

TURN IN : 7d, 9c, 10bd, 12ab, 14c, and Mathematically Equivalent Statements

- HW #3 (Section 1.3) p. 24: 1abdeik, 2cfk, 4acdh, 5bce, 6abdeh, 8 (optional), 9 (optional), 10bd (optional)

TURN IN : 2cfk, 4cdh, 5bce, 6be

- HW #4 (Section 1.4) p. 35: 4bde, 5a(cases)b(cases)d(direct proof and hint:|z| < or = M iff -M < or = z < or = +M), 6ad(cases)fgjk, 7, 8a(Change ``integers" to ``numbers.")bd, 10a

TURN IN : 4de, 5ab, 6adfj, 7, 8abd

- HW #5 (Section 1.5) P. 42: 3acfg, 4c, 6ad, 7ac, 9, 10, 11

TURN IN : All

- HW #6 (Section 1.6) p. 50: 1bcdh, 2ab, 3, 4(optional), 5acdh, 7a(proof by contrapositive)bfg, 8dgh

TURN IN : 1ch, 2ab, 3, 5cdh, 7abfg

- HW #7 (Section 1.7) p. 61: 1ac, 3abc, 6b, 7b, 11ce

TURN IN : 1ac, 3abc, 6b, 7b

- HW #8 (Section 2.1) p. 71: 1acf, 3, 4, 6ade, 8ac, 9abcdef, 11, 12, 17, 19bcfh

TURN IN : 4, 6ade, 8ac, 9abcdef, 11, 12, 17

- HW #9 (Section 2.2) p. 77: 1acdhj, 3cdegl, 4c, 6, 8nor, 9gh, 10bcf, 11d, 13b, 14a, 15b, 17adf

TURN IN : 8nor, 9gh, 10bf, 13b, 14a

- HW #10 (Section 2.3) p. 87: 1abfgikl, 2abfgikl, 4, 8(optional), 9, 11a, 12ab, 13, 17ef, 18, 19abc

TURN IN : 1gkl, 4, 9, 11a, 12ab, 13, 17ef

Exam 1 will cover sections 1.1-1.7 and 2.1-2.3 from the book, and homework assignments 1-10. The exam may include true/false questions, truth tables, proofs, prove/disprove problems, and other problems similar to the homework, practice exam, and examples from class.

THE GRADING SCALE FOR EXAM 1 2002 IS :

A+ ...... 100-110

A ...... 90-100

A-/B+ ...... 85-89

B ...... 68-84

C ...... 57-67

C-/D+ ...... 51-56

D ...... 46-50

F ...... 0-45

- HW #11 (Section 2.4) p. 100: 1abf, 2, 4, 6ace, 8acfh, 9bd, 10, 13

TURN IN : 4ab, 6ae, 8acfh, 9bd, 13

- HW #12 (Section 2.5) p. 109: 1(should say for all n greater than or equal to 1), 2(should say for all n greater than or equal to 1),3a, 4, 5a, 6ab, 7, 8a, 9, 12

TURN IN : ALL

- HW #13 (Section 3.1) p. 135: 1ac, 2, 3bcd, 4ac, 5, 6ce, 7eg, 8cg, 9abfg, 20ac (OMIT text material from bottom of page 132 through page 134.)

TURN IN : ALL

- HW #14 (Section 3.2) p. 142: 1bdfgik, 2dfg, 3dfg, 4abdgj, 8, 10ab, 12ab, 13

TURN IN : ALL

- HW #15 (Section 3.3) p. 150: 2ab, 5abce, 7, 9, 10, 11, 12, 13ad

TURN IN : ALL

- HW #16 (Section 4.1) p. 171: 1efhi, 2abfi, 3, 4c, 5ad, 8e, 9acd, 10, 13, 14 (See pages 141-142 and 175-176 in text), 15, 17ab

TURN IN : ALL

- HW #17 (Section 4.2) p. 187: 1bgi, 2bgi, 3acei, 4, 5, 7a, 8, 9, 11, 12abc, 14abcdg, 15abcef, 16abd, 18(optional)

TURN IN : 1i, 2i, 3ce, 5, 8, 9, 12b, 14cg, 15ac, 16a

- HW #18 (Section 4.3) p. 197: 1adjl(CHANGE (1, infinity) to [1, infinity)), 2ehil, 3ad, 4, 6, 8abdf, 9(Use Theorem 4.15 or prove using cases)abd, 11(Prove or find counterexamples for each), 12ab(and G:B to A), 13, 14a, 15, 16abcdf

TURN IN : 1jl, 2hl, 3ad, 4, 8bd, 9a, 11bd, 12a, 13, 15c, 16abcdef

Exam 2 will cover sections 2.4, 2.5, 3.1-3.3, and 4.1-4.3 from the book, and homework assignments 11-18. The exam may include true/false problems and problems similar to the homework and examples from class. Make sure that you know ALL of the definitions and statements of some theorems.

THE GRADING SCALE FOR EXAM 2 2002 IS :

A ...... 85 - 100

B ...... 70 - 84

B-/C+ ...... 66 - 69

C ...... 45 - 65

C-/D+ ...... 41 - 44

D ...... 36 - 40

F ...... 0 - 35

- HW #19 (Section 5.1) p. 213: 1, 2, 3, 4, 5cdhik, 6, 7, 8a(optional), 8b(Use the result from part a.), 9, 10, 12, 13, 14(Use Pigeonhole Principle), 15, (The following three problems are OPTIONAL.)16, 17, 18, 19acd

TURN IN : 1, 2, 4, 5cdk, 6(Use PMI), 7ab, 10, 12, 19cd

- HW #20 (Section 5.2) p. 219: 1acfg, 2abef, 3, 4a, 5, 6, 7, 8b, 10, 11

TURN IN : 1cf, 2af, 3, 4a, 6, 7, 10, 11

- HW #21 (Section 5.3) p. 228: 2, 3, 4, 5(Use PMI on the number of sets n.), 6, 8, 9(optional), 10a(Use method similar to proof of Theorem 5.17.), 10b(Use PMI on the number of elements n in set B.), 11(Set up function f:N to AXB and show f is 1-1 and onto AXB.), 12, 13a(Use method similar to that used to prove (0, 1) is an uncountable set.), 13b(optional), 14a(Set up function f:N to A and show f is 1-1 and onto A.), 14b(Set up function f:N to A and show f is 1-1 and onto A. See solution method for problem 11.), 15

TURN IN : 2, 3, 4, 5, 6, 8abdf, 10a, 12, 13a, 14a, 15

- HW #22 (Section 7.1) p. 290: 1abcdef, 2ac, 3ac, 4abdefi, 5ab, 7, 8a, 9a, 11abcd, 14

TURN IN : 1bc, 2c, 4bd, 5ab, 8a, 9a, 14

- HW #23 (Section 7.2) p. 300: 2, 3, 4abcdgh, 5acdegi, 6ac, 7abf, 8, 10abcd, 13, 14, 15, 16, 18

TURN IN : NONE-- All get 20 points.

THE FOLLOWING INFORMATION IS SUBJECT TO CHANGE. Exam 3 (Final Exam) will cover sections 1.1-1.7, 2.1-2.5, 3.1-3.3, 4.1-4.3, 5.1-5.3, 7.1, 7.2 from the book, and homework assignments 1-23. Roughly half of the exam will be on sections 1.1-1.6, 2.1-2.5, 3.1-3.3, 4.1-4.3 and homework assignments 1-18. The other half of the exam will be on sections 5.1-5.3, 7.1, 7.2 and homework assignments 19-23. The exam will include 10-13 True/False statements and 9-11 additional problems similar to the homework and examples from class and practice and regular exams. The PMI and PCI will be covered. The Well-Ordering Principle will NOT be covered ! You will be asked to rewrite English sentences in conditional form. You will be asked to prove that if A and B are open, then A intersect B is open. There will be one problem on compactness. The concepts of one-to-one and onto functions will be tested on this exam. Make sure that you know ALL of the definitions and statements of some theorems.

THE GRADING SCALE FOR EXAM 3 2002 WAS :

A ...... 135 - 150

A-/B+ ...... 125 - 134

B ...... 105 - 124

C ...... 80 - 104

C-/D+ ...... 75 - 79

D ...... 57 - 74

D- ...... 51 - 56

F ...... 0 - 50

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