MATH 433-A | Abstract Algebra | 9:00 A.M. | M,T, Q, F |
Bryan Smith | Thompson 321-E | 879-3562 | bryans@ups.edu |
2:00 - 3:00 P.M. | Monday | Thursday | ||
5:00 - 6:15 P.M. | Tuesday |
I am also happy to make appointments for meetings at other times. Feel free to contact me: personally, by telephone or by electronic mail.
Since most of you are majoring in either mathematics or science, you should consider buying Scientific Notebook or some other technical word processor. Almost all of these products have student editions that are significantly less expensive than the standard editions.
Although there are few prerequisites, Abstract Algebra 433 is a senior level course. Faculty in mathematics consider this course a capstone for those of you pursuing either a career in secondary education or graduate studies in mathematics.
By taking Math 433, you will acquire a deeper knowledge of linear algebra as well as learn the fundamentals of group theory. This latter topic provides an exceptional example of the true power of algebra: take a useful, concrete example and abstract its basic concepts to such a level that the abstraction can be applied to many new situations. In particular, group theory has applications to quantum theory, molecular structure, symmetry (ranging from the structure of crystals to the mathematics describing attempts at ``Grand Unified Theories'' of everything), coding theory, the structure of complex numbers, the topology of the universe, etc.
Although most of the group theory we will cover is identical with that in chapters 0-11 of our text, we will not be closely following the structure of that book. In particular, we will be reviewing, and extending linear algebra as we weave it into our studies of group theory. Thus, you should not think of our text as the course bible, but rather as your primary resource for filling in details of the material covered in class. I also recommend that you take the time to find and use additional references. In particular, there are an abundance of useful books in the library and mathematics reading room.
By the time we finish this course, you should also have refined the following skills.
However, 25 problems will be collected and marked. When these problems are assigned, some of them will be designated as ``to be turned in'' and will be marked for mathematical accuracy. When you present these, you are to assume an audience of your Math 433 peers and provide justifications for every step in your argument that is not clear to this audience. In addition, over the course of the semester, you are to designate 7 of these as ``writing'' problems which I will mark for both mathematical accuracy and clarity of exposition (see below for some basic guidelines for writing mathematics). Do not turn in more than one of these writing problems in any week since their purpose is to provide feedback as you develop your mathematical writing style. I expect at least 4 of these problems to be turned in by October 24. You will not receive credit for any of these 25 problems until you turn in a complete and accurate solution. But you may submit a problem more than once. To provide some reinforcement for being timely, I will not accept more than 6 problems per week per student.
Feel free to use (or not) any technology that you like (e.g., Scientific Notebook, CABRI, Geometers Sketchpad, calculators, Mathematica, MATLAB, etc.). You may also work with others in solving these problems but there is to be no collaboration (other than consulting with me) in the writing of the solutions. Moreover, you must cite each resource you use. This includes: technological tools, texts read, participants in discussions and anything else other than your own thoughts. Citations are to occur in the text proper (in-line). Do not use footnotes or endnotes except in exceptional circumstances. Failure to include references is intellectual theft! Please see the ``Academic Honesty'' section of the Logger to see how serious this issue is to the university community.
It is best to think of these ``writing'' problems as officially assigned papers in which you completely explain your analysis of the problem. At the very least you should write these problems:
Since most of you are either science or mathematics majors, you should attempt to use a word processor to write your papers. One possibility is Scientific Notebook since it is not only an easy to use technical word processor but also contains a symbolic algebra package that can be useful for analyzing problems.
For more detail, see the Journal of Undergraduate Mathematics at Puget Sound ``Guidelines for Authors'' page at my web site.
The Journal of Undergraduate Mathematics at Puget Sound basic guidelines are as follows (But see the web page, especially the ``Guidelines for Authors'' page for more detail.)
Make-up examinations will be given only for appropriate reasons and if arrangements are made prior to the examination.
Homework | 45% |
Writing (Referees) | 3% |
Writing (Author) | 12% |
Examinations | 26% |
Final Examination | 14% |
TOTAL | 100% |
(http://www.math.ups.edu/ ®
faculty ® Bryan Smith)
and locate the Journal of Undergraduate Mathematics at Puget Sound ``Guidelines for Authors'' page. Then send an e-mail message to me at bryans@ups.edu indicating you have access to the internet and understand Beverly Smith (bsmith@ups.edu) does not appreciate receiving Bryan Smith's e-mail messages.