Updated: November 10, 2005
This course is meant for students who wish to pursue a Master of
Arts in Mathematics (MAM). Please
contact me in
order to find out whether this course is suitable for you and/or your degree plan.
For further info about MAM, please visit
http://www.math.uh.edu/
and follow the link to MAM.
Notice that this course cannot be used for MATH 3336, DISCRETE MATHEMATICS. An ONLINE VERSION of MATH 3336 has been planned for the near future.
Book: Discrete Mathematics and Its Applications, Kenneth H.
Rosen, fifth edition. McGraw Hill, ISBN 0-07-242434-6
Plus: My own Notes on Basic Set Theory, an axiomatic approach. These notes will soon be posted on this site.
I also recommend "Introduction to Set Theory" by Karel Hrbacek and Thomas Jech, Second Edition, ISBN 0-8247-7074-9
This is a more informal exposition of formal set theory. The book is still in print ($69) but used copies are available through amazon.com for $50.
Syllabus: Chapter 1, Chapter 3 (3.3), Chapter 7 (7.1, 7.4, 7.5, 7.6) from the Rosen
book.
The Zermelo Fraenkel Axioms; Cardinals, Ordinals and the Axiom of Choice
in form of my notes.
Notes, Comments and HW:
Chapter 1 (SN LaTex file); Chapter 1 (PDF file)
Chapter 3 (SN LaTeX file); Chapter 3 (PDF file)
Chapter 7 (SN LaTeX file); Chapter 7 (PDF file)
HW 1, due Sunday, September 4, before Midnight
Section 1.1, Problems 1, 3, 13, 21
Section 1.2, Problems 14, 21, 22, 23
HW 2, due Sunday, September 11, before Midnight
Section 1.3, Problems 16, 41, 43, 44, 45
Section 1.4, Problems 9, 19
Section 1.5, Problems 1,5
HW 3, due Sunday, September 18, before Midnight
Section 1.6, Problems 1, 2, 3, 17, 18
Section 1.7, Problems 18, 37, 47, 48
HW 4, due Sunday, September 25, before Midnight
Section 1.8, Problems
1, 10, 12, 14, 16, 36
Because of Rita, all HW dates have been postponed by one week. The test date remains the same.
HW 5, due Sunday, October 9, before Midnight
Section 3.3, Problems 11, 20, 23, 51, 54
Section 7.1, Problems 1, 5, 24, 30, 31, 53
HW 6, due Sunday October 16, before Midnight
Section 7.4, Problems 1, 2, 3, 22, 23
Test, Saturday, October 22, 11-13 o'clock
HW 7, due Sunday October 23, before Midnight
Section 7.5, Problems 3,10, 29, 41, 43
Section 7.6, Problems 1, 6, 9, 27, 56, 58
HW 8, due Sunday November 13, before midnight
Do the problems at the end of the Zermelo-Fraenkel notes
HW 9, due Sunday November 27, before midnight
Do the problems at the end of the Equivalence of Sets notes
Final: Saturday, December 3, 11-14 o'clock
All homework has to be submitted by e-mail to
klaus@math.uh.edu
as a Scientific Notebook (SN) attachment. For details concerning SN, scroll further down.
Your e-mail message should have the subject field completed like
Subject: Your name 5397, HW # for example
Subject: John Smith 5397, HW 1
Homework has to be submitted by the deadline. I do not accept late homework. Always submit what you got, and on time. If you miss three homeworks, you will be dropped.
If you have problems, feel free to contact me by e-mail. Always include your name in the subject field.
Your HW file will be returned with comments and correction marks.
Organization of the course: You will receive on a regular basis reading assignments together with homework. For most sections of the book, I will add some comments. They are meant to add a graduate course perspective and help you with the reading. All homework has to be submitted by e-mail. Your grade will depend heavily on your HW. However, there will be at least a midterm and a final.
Homework has to be submitted by e-mail.
The file format for submitting homework must be TeX. In order for doing so, you will need
Scientific Notebook (SN): This program is available for $99 through MacKichan Software at http://www.mackichan.com/
SN is a rather simple word processor meant for text entry together with math. Files are saved in LaTeX but for SN you don't need to know any LaTeX. With SN you can also perform all sorts of mathematical calculations through MuPad. This makes SN a reasonable buy at the price of a graphics calculator.
Of course, if you have already access to TeX then you don't need SN. However, then you have to know some LaTeX. But even if you have access to a TeX implementation, I still recommend SN as a convenient front-end for LaTeX.
However, I do not recommend buying one of the "upgrades" of SN, namely Scientific Word (SW) or Scientific Workplace (SP). If for some reason you wish to get a full TeX program, there are better choices. SW as well as SWP offer only limited compatibility with LaTeX.
Why don't we use MS Word with the Equation Editor? Because this is an awful combination and sooner or later I would be forced to accept handwritten HW. It just would take you too long to get any math typed. And there are many other reasons why we should not use Word for documents that contain a nontrivial amount of mathematical formulas.