MATH 7900 (Azoff) 
Foundations for Graduate Mathematics
Fall 2007

This website was last updated on November 25.

The last assignment is due on Tuesday December 4.

The final exam is scheduled for Noon - 3 PM on Friday December 14 in our usual classroom. It will be comprehensive.
 

Contents

  • Texts and References
  • Exams
  • Assignments
  • e-mail Addresses and Phone Numbers of Class Members
  • Course Objective
  • Course Syllabus
    •

    Texts and References

    Author
    		 Title
    		 Web Link or Publisher
    		 Comments
    Zakon, Elias
    		 Basic Concepts of  Mathematics
    		 http://www.trillia.com/zakon1.html For logic and set theory (Chapter 1)
    Bond, R. J.;  Keane, W. J.
    		 Intro to Abstract Mathematics
    		 Brooks/Cole
    		 Logic/set theory reference
    Spivak, Michael
    		 Calculus, 4th Edition
    		 Publish or Perish
    		 Free prepublication version
    Azoff, Edward
    		 Sequences and Series
    		 http://www.math.uga.edu/%7Eazoff/courses/3100s05.pdf
    		 For Taylor series & uniform conv
    Halmos, Paul R
    		 How to Write Mathematics
    		 http://www.math.uga.edu/%7Eazoff/courses/halmos.pdf
    		 Expository suggestions
    Shifrin, Theodore
    		 Multivariable Mathematics Wiley, 2005;  ISBN 0-471-52638-X Main text

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    Exams

    The final exam is scheduled for Noon - 3 PM on Friday December 14 in our usual classroom. It will be comprehensive.

    There were two "hour" exams during the term.  The first covered Chapter 1 of the Zakon text and Chapters 1 through 14 of the Spivak text.
    The second test covered the sequence/series notes and the first four chapters of Shifrin's text.

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    Assignment Summary

    Assign
    		 Due
    		 Text
    		 Reading
    		 Pages for Problems
    		 Problems to Hand In
    		 Extra Problems for
    Practice/Class Discussion
    1
    		 F 24 Aug
    		 Zakon
    		 Chap 1
    		 9-11
    		 4, 11i, 17ii
    20-22
    		 2ix, 6, 12, 18
    26-27
    		 7ii, 9, 11iii
    30-31
    		 7, 8i, 12i
    35
    		 2, 11
    Worksheet  on  Symbolization: online at
    http://www.math.uga.edu/%7Eazoff/courses/7900symb.pdf
    		1, 2, 3, 4
    2
    		 F 7 Sept
    		 Spivak
    		 Chap 1
    		 13-19
    		 5iv,6ab,11iii,12v,14
    		 3ii,22
    Chap 2
    		 32
    		 19
    Chap 3
    		 51-53
    		 13,21,26
    Chap 4
    		 72-73
    		 17v
    		 20
    Chap 5
    		 108
    		 3,8,12,13,24,37b
    		 10cd,18,21b, 31
    3
    		 F 14 Sept
    		Spivak
    		 Chap 6
    		 119-121
    		 3ab,6,12
    		 4,10c,16abc
    Chap 7
    		 130-131
    		 7,10,17
    		 3,5
    Chap 8
    		 140-141
    		 6c,12
    		 1,6ab
    8 Appendix
    		 146
    		 1b,2bc
    		 1c
    Chap 9
    		 163-166
    		 14,22a
    		 3,7
    Chap 10
    		 181-186
    		 9,16,28
    		 1
    4
    		 M 24 Sept
    		 Spivak
    		 Chap 11
    		 207-215
    		 11,20,28,38,43,49,55
    		 1vi,2vi,5,31,33,41,53
    Chap 12
    		 242-243
    		 23
    		 5
    Chap 13
    		 274-280
    		 13,19,20,23ab,37
    		 5,16,29,33,36
    Chap 14
    		 298-299
    		 8,18
    		 3,4,16
    5
    		 F 5 Oct
    		 Azoff
    		 Chap 2
    		 36-39
    		 27,38,43
    		 11,17,24,33,36,41
    Chap 3
    		 52-56
    		 18,28,36,37
    		 24,32,38
    Chap 4
    		 62-64
    		 5,20,25 4,15,32
    Chap 5
    		 74-76
    		 6,9,16
    		 3,15,17
    Chap 6
    		 84-85
    		 7,10
    		 1,4,5,9
    Chap 7
    		 89-90
    		 8
    		 13
    6
    		 W 17 Oct
    		 Shifrin
    		 Section 1.1
    		 7-8
    		 10
    		 9,13
    Section 1.2 13-16
    		 2g
    		 4,5,7,11,15,17
    Section 1.3 22-23
    		 1hi,7,12
    		 3,5,6,8,9,10
    Section 1.4 39-43
    		 8,20,30,33
    		 2,3,5,6,17,19,
    26,32,34,37
    Section 1.5 50-52
    		 2,7b,9
    		 6b,12,13,14
    Section 2.1 61-64
    		4
    Section 2.2 70-71
    		 3,9,14c
    		 1,2,8,15
    Section 2.3 78-80
    		 2,4,8bgi,9,12
    		 3,6,7b,10,11,13
    7
    		 W Oct 24
    		 Shifrin
    		 Section 3.1
    		 85-86
    		 5,9,11,13
    		 3b,4,8
    Section 3.2
    		 95-97
    		 6,7,11,14,15,18
    		 1b,2b,3b,5,17
    8
    		 W Oct 31
    		 Shifrin
    		 Section 3.3 102-104
    		 8,12,17
    		 3,5,11,13
    Section 3.4 106-109
    		 6,11
    		 2,10,14
    Section 3.5 117-119
    		 1,5,8c
    		 2,6,7b
    Section 3.6 124-126
    		 1,11
    		 4,7
    9
    		 F Nov 9
    		 Shifrin
    		 Section 4.1
    		 142-146
    		 6b,12a,15,16,18
    		 11a,23
    Section 4.2 155-156
    		 4
    		 1b,2a,3c,5
    Section 4.3 168-171
    		 1,3,6,8,9,10,13,15,
    16,19,20,21,23
    		 5,14c,22,25,26
    Section 4.4 184-186
    		 2,6,15,16,17
    		 3d,4,7,9,12
    Section 4.5 193-195
    		2,5,7,11
    10
    		 W 28 Nov
    		 Shifrin
    		 Section 7.5
    		 321-324
    		 5,6,12
    		 1ac,11,19,21
    Section 9.1
    		 420-422
    		 3,4,9def,10
    		 9,11
    Section 9.2
    		 433-436
    		 2,4,5,6,9,12gh,13,18
    		 3,7,8,19,20abc,22,23,24,25
    Section 9.3
    		 452-455
    		 1,5
    		 2
    Section 9.4
    		 463-466
    		 1e,3,9
    		 4,5,6,8,13,14
    11
    		 Tu Dec 4
    		 Shifrin
    		 Section 8.3
    		 362-366
    		 3ac,6bc,10b
    		 2,8,12,21
    Section 5.1
    		 201-202
    		 2,3,6
    		 4a,5,7,8,9,10
    Section 5.2
    		 207-208
    		 2,8,14
    		 3,6,7,10,13
    Section 5.3 215-216
    		 2,4,6ad
    		 6c,7
    Section 5.4 222-225
    		 1,7,10,29
    		 2,5,6,9,15,16,23
    Section 5.5 240-243
    		 3,5,8,10
    		 4,7,11,13,17,20

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    Phone Numbers and e-mail Addresses

    Go By Family Name e-mail
    Phone
    Michael
    		 Berglund
    		 berglund@math.uga.edu
    Joe
    		 Brown
    		 jbrown@math.uga.edu
    		 706-614-3513
    Larousse
    		 Charlot
    		 gamb2002@uga.edu
    		 706-224-6835
    Jennifer
    		 Muskovin
    		 muskovin@math.uga.edu
    		 630-404-0649
    Kate
    		 Thompson
    		 thompson@math.uga.edu
    Bill
    		 Triplett
    		 triplett@math.gua.edu

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    Course Objective

    From the Bulletin: "An intensive review of techniques and material essential for graduate study in mathematics, including background in calculus and linear algebra".

    The main text, by Shifrin, will be used for topics in linear algebra and multivariate calculus.

    Handouts and outside references will be provided for preliminary discussions involving logic, limits, and continuity.  Depth and length of this part of the course will depend on background of class members.

    MATH 7900 
    Foundations for Graduate Mathematics
    Course Syllabus

    Call Number
    		 01-685



    Web Page  http://www.math.uga.edu/~azoff/courses/7900.html 



    Time & Place  1:15 - 2:05  MWF 
    		524 Boyd



    Texts  Logic:  First Chapter of  E. Zakon's  Basic Concepts of Mathematics, available online at http://www.trillia.com/zakon1.html
    Main Text:  Multivariable Mathematics, by Theodore Shifrin, Wiley, 2005;  ISBN 0-471-52638-X. 



    Grading Homework 
    Hour Tests (2 @ 100 pts) 
    Final Exam    		 100 points 
    200 points 
    200 points




    		Homework will be collected once or twice a week;  no late work will be accepted.   The final exam is scheduled for
    Noon - 3 PM on Friday December 14;  it will be comprehensive. 



    Instructor  E. Azoff
         e-mail 
         Phone 
         Office 
    		azoff@math.uga.edu
    542-2608 
    443 Boyd 
    Office Hours MTuWTh:         3:30 - 4:30 PM
    F:                      2:30 - 3:30 PM 
    		No Office Hours on:
    Th - F  September 13 - 14
    Th - F  September 27 - 28
    Th - F  October 4 - 5

    Assignment on Logic and Set Theory

    Due Friday August 24

    1.  Read Chapter 1 of  Elias Zakon's online text, Basic Concepts of Mathematics, available online at http://www.trillia.com/zakon1.html. 
    2.  Work the following problems from that text:

    Pages
    		 Problems
    9-11
    		 4, 11i, 17ii
    20-22
    		 2ix, 6, 12, 18
    26-27
    		 7ii, 9, 11iii
    30-31
    		 7, 8i, 12i
    35
    		 2, 11

    3. Read the Symbolization Worksheet located online at http://www.math.uga.edu/%7Eazoff/courses/7900symb.pdf. and work the problems at the end of the  worksheet..

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