Outline
Lectures:
Mondays, Wednesdays, and Fridays, 1011 AM, room MATX 1118 (Mathematics Annex)
Course textbook: Niven, Zuckerman, and Montgomery, An Introduction to the Theory of Numbers, Wiley, 1991 (5th edition). Please let me know if you encounter problems buying the textbook from the UBC bookstore. Course description: The first few weeks will be spent quickly covering the foundations of elementary number theory: divisibility, congruences, prime numbers, and so on, some of which might already be familiar to you. Once we have this foundation, many different subjects will be open to us, such as: finding roots of polynomial congruences; quadratic reciprocity; multiplicative functions. Topics that might also be covered include: running times of numbertheoretic algorithms; RSA cryptography; writing numbers as sums of squares; Farey fractions and continued fractions; binary quadratic forms. I will also indicate the connections between these topics and other advanced areas of number theory (algebraic number theory, analytic number theory, diophantine approximation, etc.). Notes to undergraduates: MATH 437 treats roughly the same material as MATH 312 and 313 combined. Note that a student cannot have credit for both MATH 312 and MATH 437, nor for both MATH 313 and MATH 437. To enroll in MATH 437, an undergraduate student must have already taken, or be taking simultaneously, one of MATH 320 or MATH 322. The word “elementary” in the title does not mean the course isn't difficult; rather it means that the course doesn't use techniques from real or complex analysis or from abstract algebra. The course will not require any particular background in number theory. What is required is “mathematical sophistication”, which certainly includes being able to understand and write proofs. Be forewarned that this course will be taught at the level of a graduate course. Honours students typically will be wellequipped to succeed in this course. Evaluation: The course mark will be based on six homework assignments (75% of the final mark), due approximately every two weeks, and one midterm exam (25% of the final mark) which will be held on Monday evening, November 17. In the case of extreme disparity between the homework and exam marks, the instructor may use his discretion in assigning a final course mark. Your homework will be marked on correctness, completeness, rigor, and elegance. A correct answer will not earn full marks unless it is completely justified, in a rigorous manner, and written in a logical sequence that is easy to follow and confirm. Students are allowed to consult one another concerning the homework problems, but your submitted solutions must be written by you in your own words. If two students submit virtually identical answers to a question, both can be found guilty of plagiarism. Use of the web: After the first day, no handouts will be distributed in class. All homework assignments and other course materials will be posted on this course web page. All documents will be posted in PDF format and can be read with the free Acrobat reader. You may download the free Acrobat reader at no cost. You may access the course web page on any public terminal at UBC or via your own internet connection. Accounts for the Mathematics department undergraduate computer lab (located in the MSRC building) will be given to any enrolled student who requests one; please email or visit the instructor to request an account. DownloadsAll homeworks are due at the beginning of class (10:00 AM) on the indicated days. The links below lead to the most uptodate versions of the homework (reflecting any needed corrections, for example).
