Math 108 Website

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

Instructor: Dr. D. A. Kouba

Last Updated: August 22, 2002

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

Instructor: Dr. D. A. Kouba

Your comments, questions, or suggestions can be sent via e-mail to Kouba by clicking on the following address : kouba@math.ucdavis.edu .

Your comments, questions, or suggestions can be sent via e-mail to Kouba by clicking on the following address :
kouba@math.ucdavis.edu .