Course Description and Grading BreakdownThis course is an introduction to number theory. No background in the topic is required, and all are welcome. Number theory is the study of the natural numbers. Although its ultimate scope is vast, in this course we will start at the very beginning. The topics covered will include: Primes and divisibility, Diophantine equations and Pythagorean triples, modular arithmetic, Euler's phi-function, solutions of congruence equations, Fermat and Mersenne primes, RSA encryption, Quadratic reciprocity, sums of squares, Gaussian integers, diophantine approximations, continued fractions, and binary quadratic forms. The final project will be a programming assignment. Students are encouraged to learn to use PARI, which is designed for number theoretic calculations. It is now incorporated into Sage, which is also very useful. See the notes section below for links to introductory guides. Course Meeting Time and LocationMonday, Wednesday and Friday 1:00 - 1:55 pm B111 Downs Laboratory of Physics (DWN) Course Instructor Contact Information and Office Hours221 Math Department (Building #15) Office Hours: Mondays 2-3pm TA Contact Information and Office Hours2-J Math Building Office Hours: Wednesdays 4-5pm, Common Room in the Math Department. Course Schedule and Textbook
Lecture NotesCourse PoliciesGrade will be based on six assignments, plus one final project. Assignments
Midterm and Final ExamCollaboration Table
* You may use a computer or calculator while doing the homework, but may not refer to this as justification for your work. For example, "by Mathematica" is not an acceptable justification for deriving one equation from another. Also, since computers and calculators will not be allowed on the exams, it's best not to get too dependent on them. |