Course information (Spring 2001)Course information (Spring 2001)Welcome to Math 522! Here you will find homework assignments, the course syllabus, and guidelines.
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Dr. Farshid Hajir. Office: Craven 6239. Phone: 750-8031. e-mail: fhajir@csusm.edu.
Monday & Wednesday 6:00-7:50, ACD 317.
M W 4:30-5:30 and by appointment.
Silverman and Tate, Rational Points on Elliptic Curves, Springer.
Introduction to number theory from the algebraic and/or analytic point of view. Includes some of the following: congruences, finite fields and rings and quadratic reciprocity; quadratic forms and Diophantine equations; elliptic curves; the Gaussian integers, the Eisenstein integers, and unique factorization in these rings; other quadratic and cyclotomic fields and ideal factorization; introduction to analytic number theory, primes in arithmetic progressions, and the prime number theorem. This course meets four hours per week. Prerequisite: MATH 470 or consent of instructor.
This year, we are concentrating on elliptic curves. These are given by cubic equations, so it is easy to compute with them; on the other hand, their arithmetic is very deep: elliptic curves were fundamental, for instance, in the solution of Fermat's last theorem. Also, elliptic curves can be used for devising efficient factoring algorithms. We will get our hands dirty with many individual elliptic curves as a way of becoming friends with them. They are among the most beautiful objects in mathematics at the intersection of algebra, number theory, analysis, and geometry.
Midterm 1: 20%; Midterm 2: 20%; Homework: 20%; Class participation: 10%; Final Exam: 30%. The Final is on Wed May 30
Homework will be due each week at the start of class on Wednesday. Your 2500-word writing requirement will be met by these assignments, and therefore you will be graded on your writing style as well as the correctness of the mathematics. Learning to present mathematical ideas clearly and concisely is an important aspect of this course: your solutions should be written with this in mind.
You are welcome, indeed encouraged, to work together on homework assignments, as long as you adhere strictly to the following rules:
1) for each problem, you must always acknowledge your sources, e.g. indicate with whom you collaborated on a certain problem, or indicate the books (complete reference with page numbers) you consulted, and
2) you should always do your write-up completely independently.
Make sure you give a problem plenty of thought on your own first before working on it with someone else. If you are stuck on a problem and seek help from an instructor or a fellow student, you owe it to yourself to aim for an understanding of the concepts and ideas that come up in the discussion (don't just memorize the series of steps leading to the solution), then go home and reconstruct the argument for yourself to make sure you are not merely reproducing mindlessly something you have not thought through. Remember that you will be called upon at times to explain your solution to the class (see "Class Participation" below), and that during the tests, you will have to rely on your own understanding of the material.
The policy on late assignments and make-up exams is simple. Homework is expected to be turned in on the assigned date at the assigned time. Late homework will be accepted only in exceptional cases where a valid excuse exists. Similarly, make-up exams will be given only for valid reasons. If you know in advance that you cannot take an exam on the scheduled date, please arrange in advance for an alternate test date. Make-up tests may be somewhat harder than the original tests, in fairness to those who take the test on time.
On the first page of each of your homework assignments, indicate the problems which you believe are solved correctly. Your score will be calculated as follows: approximately 1/5 of the homework problems will be graded, at random, chosen from the problems you have indicated. (If there are 7 or fewer problems, one will be graded, and if there are more than 7, two will be graded.) The maximum score for the graded problems will be 5. For each additional problem that you indicated as correct, you will receive 1 additional point.
You are expected to participate actively in class by asking and answering questions.
Any evidence of cheating (including plagiarism -- presenting the words or ideas of others as your own) will result in a failing grade for that assignment and possibly a failing grade for the course. Please familiarize yourself with the regulations on academic honesty as stated in Appendix O of the CSUSM catalogue, and speak with me if you have any questions about what exactly constitutes plagiarism.
You may reach me via e-mail at fhajir@csusm.edu