MATH 433-A	Abstract Algebra	9:00 A.M.	M,T, Q, F
Bryan Smith	Thompson 321-E	879-3562	bryans@ups.edu

1:00 - 2:00 P.M.	Monday	Tuesday		Thursday	Friday
2:30 - 4:30 P.M.			Wednesday

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 such 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.

• Analyze a given problem to determine which tools should be used in its solution,

• Select and use an appropriate strategy (e.g., direct proof, proving an equivalent result (contrapositive), contradiction, etc.) to determine a solution of the given problem,

• Follow accepted mathematical style to present a graceful and accurately written formal proof of your solution, and

• Know when your argument is correct and complete.

However, 25 problems will be collected and marked. When these problems are assigned, 20 of these 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 5 of the 25 problems as ``writing'' problems which I will mark for both mathematical accuracy and clarity of exposition (see below and my web page 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 3 of these problems to be turned in by October 19. Credit for a problem is earned when you turn in a complete and accurate solution. If you turn in an incomplete or inaccurate solution, I will make comments and return it. You may then re-submit the problem. This process may be repeated. To provide some reinforcement for being timely, I will not accept more than 5 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.

These ``writing'' problems are actually the mathematical equivalent of assigned papers in humanities courses. In particular, be sure to invest adequate time in analysis and research before you completely explain that analysis of the problem. You are also expected to follow standard mathematical style in your presentation. More detailed explanations of that style can be found at http://www.math.ups.edu/ bryans/JournalGuidelines.html . You can also peruse any copy of Mathematics Magazine or the American Mathematical Association Monthly to see how authors employ citations and references. Although you may not have much experience with mathematical writing, you will find it to be quite similar to other expository styles. In particular, you should write these problems:

• Using complete sentences
• In the first person plural
• With accurate punctuation
• For an audience consisting of students not in this class but with an equivalent background
• In a clear, easy to follow expository style

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.

Exam 1

September 28, 2001

Exam 2

November 9, 2001

Make-up examinations will be given only for appropriate reasons and if arrangements are made prior to the examination.

and 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.