Mathematics 437/537, Elementary Number Theory

Term 1, 2006, MWF 1-2

  • Instructor : David Boyd
    Office: 200 Mathematics
    Office hours: Mon 10:30-11:30 & 2:00-2:30, Wed 10:30-11:30, Fri 10:30-11:30
    Other times may be arranged by appointment (e-mail).
    e-mail: boyd at math dot ubc dot ca
    URL of this web page:

  • Textbook:
    I. Niven, H. S. Zuckerman and H. L. Montgomery,
    An Introduction to the Theory of Numbers
    It is definitely worth purchasing the text (see below).
    There will be one copy of the text on one day loan in the Mathematics Library.

  • Course description:
    The course is intended to be a self-contained first introduction to number theory for well motivated students. The first few weeks will be spent quickly covering the foundations of elementary number theory: divisibility, congruences, prime numbers, etc. You may have seen some of this material in your reading or in an earlier course. After that, the course will branch out to cover a variety of topics as indicated on the detailed outline below. The course does not require any particular background in number theory. What is required is some previous experience in discovering and writing proofs.
    Corequisite for Math 437: one of Math 320 or Math 322. UBC Calendar entry.
    Note that credit will be given for only one of Math 312 or Math 437. Students who have taken Math 312 can take Math 437 but will not receive credit for both. A similar remark applies to Math 313. Credit Exclusion list.

  • Marking:
    The course mark will be based on six assignments (60%) which will be assigned at regular intervals and on a final examination (40%). Be sure to do the assignments and hand them on on time!
    Many of the exercises on the assignments will be taken from the text or adapted from those in the text. The text has a wonderful collection of problems, some quite challenging. You are encouraged to try some of these in addition to the assigned problems.
    You may discuss the problems with the other students in the class but your submitted solutions must be written by you in your own words.

  • Announcements:
    Nov 15, Offer concerning final exam: If you are satisfied with a mark based on the best 5 marks of the 6 assignments (each assignment counting for 20% of the final mark) then you need not write the final examination. If you decide not to write the exam, please let me know by e-mail before the day of the exam.
    If you do decide to write the final exam, then your mark will be computed as indicated in the Marking section above (i.e. each of the best 5 assignments counting 12% of the final mark and the final exam 40%), or else be based on the best 5 assignments, whichever produces the higher mark.

  • Assignments and Supplementary course material:
    There will be no paper handouts in class. Any such material will be linked to this web page and be in pdf format. To read pdf you need Adobe's free acrobat reader.
    Assignment #1, due Monday, September 18
    Assignment #2, due Monday, October 2
    Assignment #3, due Monday, October 16
    Assignment #4, due Monday, October 30
    Assignment #5, due Wednesday, November 15
    Assignment #6, due Wednesday, November 29

  • Final Examination: Monday, Dec 11, 12:00 PM - 2:30 PM, room MATH 103
    You may bring the textbook and your course notes to the examination.
    Final Exam, posted December 12

  • Course outline (chapter references to the text in parentheses):
    1. Divisibility, the Euclidean algorithm (1)
    2. Congruences, the theorems of Fermat and Euler, RSA cryptosystem (2)
    3. Quadratic reciprocity (3) (Some other proofs of quadratic reciprocity)
    4. Some diophantine equations of order 1 and 2 (5)
    5. Farey fractions and continued fractions (6,7)
    6. Pell's equation (7)
    7. Quadratic number fields (9)
    8. Elementary prime number theory (8)