``If it be then your Pleasure, ye Lovers of Study, come always; be not restrained through any Fear, nor retarded by too much Modesty, what you may do by your Right, you shall make me do willingly, nay gladly and joyfully. Ask your Questions, make your Enquiries, bid and command; you shall neither find me averse nor refractory to your Commands, but officious and obedient. If you meet with any Obstacles or Difficulties, or are retarded with any Doubts while you are walking in the cumbersome Road of this Study of Mathematics, I beg you to impart them, and I shall endeavour to remove every Hindrance out of your Way to the best of my Knowledge and Ability.''
Isaac Barrow, March 14, 1664
I'll be using the book by Stan Wagon and myself: A Course in Computational Number Theory. We'll cover the standard topics: the Euclidean algorithm, modular arithmetic, linear congruences, Chinese remainder theorem, Fermat's Little Theorem, primality testing using pseudoprime tests, Euler's phi function, perfect numbers, Euler's theorem, primitive roots, the distribution of prime numbers, how to certify that a number is prime, RSA cryptosystems, check digit schemes, factoring algorithms, and quadratic residues. Throughout the course, we will be using the computer (using Mathematica programs that will be supplied) to explore patterns in the integers, use those explorations to guess what is happening and motivate the theory, and then use the theory to show what to explore next.
All assignments for this course and reminders of what is coming due will be posted on a Moodle site that will be set up before class starts in September.
Reading the textbook: Read the assigned section(s) of the textbook (see moodle site) before each class. You must submit answers to any two of the following questions by noon of the day we will be talking about that reading. Answer two of the following questions
Answers can be very brief. Five points are available for advance reading. If you submit answers for at least 25 of the readings, you will earn all five points. 20–24 earns four points. 15–19 earns three points. 10–14 earns two points. 5–9 earns one point. Less than 5 earns no points.
Counts 5% of the final grade. There are 28 days for which you will need to submit answers. You'll earn the full 5% if you send messages for at least 22 of these days, 4% for at least 18 days, 3% for at least 14 days, 2% for at least 10 days, and 1% for at least 6 days.
Homework: There will be weekly homework assignments that are due on Mondays. Assignments may be turned in in class or by 5:00 pm on the door to my office. Homework counts for 22% of your final grade. Late work will be penalized 10% if less than one day late and an additional 5% for each day late after that.
Project. There will be one major project on a topic of your choice. A brief description of your topic is due on Wednesday, November 1 when you will have to be able to dsescribe your topic to the rest of the class. The first draft is due Wednesday, November 22. The final version is due Wednesday, December 13. 19% of total grade. Late work will be penalized 10% if less than one day late and an additional 5% for each day late after that.
Mid-term examinations. There will be two take-home mid-term examinations, the first due on on Monday, October 9 and the second on Monday, November 10. Each exam is 18% of the total grade.
Final examination. There will be a take-home final examination due by 5pm on Monday, December 18. 18% of total grade.
Grades will be assigned on a straight 90% = A, 80% = B, 70% = C, 60% = D, although I reserve leeway in the assignment of + and -.
A Course in Computational Number Theory, by Bressoud and Wagon, Key College Press.