MAT 5400 (Elementary Theory of Numbers)
Fall 2009, Section 001, CRN 10453
Professor Drucker

COURSE INFORMATION
(last updated September 9, 2009)

Credits: 3  Prerequisites: MAT 2030 and 2250, or consent of instructor.
Class meetings: MWF 11:45 a.m. &ndash 12:40 p.m. in 135 State Hall.
Instructor: Daniel Drucker, Professor of Mathematics  Office: 1173 FAB
Phone: 313 577-3189 (my office), or call the Math Dept at 313 577-2479 and ask the staff member to leave a message in my box.
E-mail: drucker@math.wayne.edu   URL (World Wide Web): http://www.math.wayne.edu/~drucker
Office hours: WF 2:10 – 3:30 p.m. I suggest that you make an appointment before coming to the office. You can do that before or after class, or by phone or e-mail. (If you don’t make an appointment, I don’t guarantee to be in the office when you arrive. I may leave to make copies, take care of clerical work, return library books, etc.) I’m often available at other times and I’ll be happy to answer questions by e-mail, though it is sometimes hard to discuss calculations that way because of the difficulty of typing mathematics.

Text: Underwood Dudley, Elementary Number Theory, Second Edition, Dover paperback, ISBN 048646931X. Reprint of Second Edition published by Freeman in 1978.
Coverage: The core material is in Sections 1–12 and Appendix A, though the course will include some of the remaining material (and perhaps other material too).
Recommended software: Maple. Because I am recommending this software to the class, you will be able to buy your own personal download copy of Maple 13 for the specially discounted price of $75. For details, see the Maple Adoption Program flyer.
    Calculations in number theory can be cumbersome, especially when you are doing explorations in an attempt to find out what is true. Maple is a powerful tool for doing such calculations, and moreover it is useful in every branch of mathematics, so the one-time outlay will continue to yield benefits in future courses.
    Those of you who elect not to purchase Maple can use a calculator, different computer software, or other available resources (such as online Java applets).
Calculators and computers: Use of calculators and computers on homework is encouraged, provided you use them for exploration and numerical checks, rather than as a substitute for understanding. You are not required to own a calculator or computer, but if you wish to purchase a calculator that will be useful in this course, I would recommend a programmable model from Hewlett-Packard or Texas Instruments. (Come to my office hours for help with selecting a suitable model.) If you have trouble using your calculator and you have a manual for it, I’ll be glad to help.

About number theory: In this branch of mathematics, the objects (integers) are familiar, but the material is sometimes surprisingly abstract. At other times, it is purely computational. Initially, you may find that you feel quite comfortable when you can compute with specific numbers, but uncomfortable when you must reach conclusions or write proofs about integers in general. Likewise, if you are not used to reading abstract mathematics, you may have some trouble reading parts of the text on your own, especially the definitions and proofs. This is normal and not necessarily a cause for alarm. I will do my best to bring you “up to speed” in class and, if necessary, in my office hours. All I ask is that you work hard to overcome any obstacles you encounter. Just as in learning to ride a bicycle or to play a musical instrument, you will probably find that you don’t improve steadily, but in jumps separated by frustrating periods of slow progress.

Assignments: Problems from the text will be discussed in class as needed. Some will be graded. I may add some problems of my own. Notice that Dudley’s Section 23 provides additional problems for each section and 100 miscellaneous problems. For details on assignments, see the MAT 5400 Assignments web page.
Tests: In-class tests will consist of computational problems that can be solved by hand, plus some abstract material. Tentative exam dates: Fri., Oct. 2; Fri., Oct. 30; and Wed., Dec. 2. Quizzes as time permits. Cumulative final exam.
Final exam: Thursday, December 17, 10:40 a.m. – 1:10 p.m. in 135 State Hall.
Course Grade: Your two best exams will be worth 400 points each; the third exam will be worth 200 points. Quizzes (and projects, if any) will be worth 100 or 200 points each, depending on their length. Graded exercises will be worth a total of 400 points. The final exam will be worth 700 points. If you are near the boundary between two grades, then attendance, effort, and class participation will help determine your grade.
Letter Grades (as intervals of percentages): A [88, 100], A– [85, 88), B+ [82, 85), B [73, 82), B– [70, 73), C+ [67, 70), C [58, 67), C– [55, 58), D+ [53, 55), D [47, 53), D– [45, 47), E [0, 45). Qualitatively, being able to do the basic calculations is worth a C. Beyond that, an understanding of the main abstract concepts brings you up to the B level. For an A, you should have a firm grasp of both the concrete and abstract aspects of the course.
Changes in WSU’s Grading Policy (effective Fall 2006): I expect you to inform yourselves about WSU’s revised Grading Policy. For a more user friendly version, click here. The notation for a failing grade has been changed from “E” to “F”. There are no more “X” grades. If you sign up for a class, stop attending, and fail to withdraw, you will receive an F for the course. In addition, if you drop the course after 5 weeks, you will be assigned one of the following three grades: WP (withdrew but was passing at the time), WF (withdrew but was failing at the time), WN (withdrew and never attended class or had no graded work). Also, any “I” given to a student will automatically revert to an “F” if the work is not completed within one calendar year. There are no exceptions. The new policy also limits the number of times you may repeat a course.
    WARNING: Any student who stops attending this class without officially filing a withdrawal request via the Student tab in Pipeline will receive a course grade of F. As a courtesy, I request that you notify me of your intention to file for a withdrawal.

Students with disabilities: If you have a documented disability that requires accommodations, you will need to register with Student Disability Services (SDS). The SDS office is located at 1600 David Adamany Undergraduate Library in the Student Academic Success Services department. Their telephone number is 313 577-1851, or 313 577-3365 (TDD only). Once you have your accommodations in place, I will be glad to meet with you privately during my office hours to discuss your special needs. SDS’s mission is to assist the university in creating an accessible community where students with disabilities have an equal opportunity to fully participate in their educational experience.

Cheating: Cheating will not be tolerated. In particular, you are not permitted to represent someone else’s work as your own. Expect a zero on a test or assignment if you’re caught cheating. A repeat offense will earn you a failing grade in the course. NOTE:  I may change your seat during a test. I do this to give everyone as much room as possible and to keep others from having a clear view of your paper. It does not mean I think you’re cheating.
WHAT I EXPECT FROM YOU:

Check your WSU e-mail.
I expect all of you to check e-mail regularly, so that I can send you written messages. Click here for information on WSU e-mail. If you do not use the WSU e-mail address assigned to you, then set up your WSU e-mail so that it forwards e-mail to your preferred address. (Click here for instructions on how to forward your WSU mail to another e-mail address.)
   IMPORTANT: When you write to me, always include “MAT 5400” in the subject line of your e-mail message, and always sign the message with your full name. I don’t want to have to figure out who you are from your e-mail address.
Attend all classes.
If you MUST miss a class, tell me in advance if possible; otherwise contact me THAT DAY. (If you can’t reach me at my office, send me an e-mail message or call the Math Dept and leave a message as indicated above under the heading Phone. Be sure to mention your name and phone number, the course number, and the reason for your absence.) This is crucial with regard to tests, since I may let you take a test at a different time if you give me enough notice, but I won’t write make-up tests.
   Make a point of exchanging contact information with at least a couple of other students in the class, so that you’ll be able to obtain notes and assignments in the event that you have to miss a class.
  In class, I expect you to pay attention to what’s going on, and to participate whenever possible. Cell phones and pagers should be turned off before you enter the room.
Read the material in the text—carefully—before we discuss it in class.
I won’t discuss everything that’s in the book, nor will I always do things the way they’re done in the book. I’ll also add material that’s not in the book. You’re responsible for all the material in the sections we discuss (except material I specifically exclude) AND all the material covered in class.
IMPORTANT NOTE: When reviewing for tests, start with your class notes and give highest priority to things done only (or differently) in class. After that, study the text and the assigned exercises.
Keep up with the assignments.
Problems (and projects, if any) will be assigned well in advance. Do them as we get to them. DON’T FALL BEHIND! It’s tough to catch up in a math class. Solving lots of problems is the only way to learn mathematics. The assigned problems should be regarded as the MINIMUM you should do. Whenever possible, solve extra problems. Keep your homework separate from your class notes, in a binder that allows you to insert and remove pages, and organize it by section number and exercise number. If I assign other problems, I’ll name or number them separately. Be sure to put your name and the course number on each page.
Ask questions!
Write down the things that bother you while you’re reading the text or working on homework, so you’ll be ready with a list of questions when you come to class and/or office hours. I usually ask for questions at the beginning of each class. If a question arises during class, stop me right away. It’s hard to pay attention when something is bothering you. Don’t be afraid to ask questions; usually other members of the class have the same questions.
Think about the material and explore with your calculator and/or computer software (like Maple) and/or Java applets. Discuss it with classmates.
One of your goals is to learn how to speak and write mathematics. Another is to try to enjoy the process of thinking about mathematics and increasing your understanding of it. It’s much more satisfying to figure something out on your own than to memorize facts that someone else states for you.

Click to return to my home page.