Courses:

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Required

Niven, Ivan, Herbert S. Zuckerman, and Hugh L. Montgomery. An Introduction to the Theory of Numbers. 5th ed. New York: Wiley Text Books, 1991. ISBN: 0471625469.

Suggested

Davenport, Harold. The Higher Arithmetic: An Introduction to the Theory of Numbers. 7th ed. Cambridge; New York: Cambridge University Press, 1999. ISBN: 0521634466.

Prerequisites

I will not assume any results from abstract algebra, and so there are no formal prerequisites beyond basic linear algebra and calculus. However, familiarity with reading, writing, and understanding proofs will be assumed.

Exams

There will be two midterms and a final.

Homework

There will be weekly homework which will be turned in at the beginning of lecture on the due date. No late homework will be accepted without prior permission of the instructor. However, the lowest homework score will be dropped when computing the final grades.

Remark on Collaboration

Collaboration on homework is encouraged, but all write-ups should be done independently and proper credit should be given (that is, if someone explains a problem to you, it should be noted in the write-up). Also, taking notes while someone is explaining a problem to you is strongly discouraged as it leads to students writing up other people's solutions without understanding them (which is plagiarism!). Rather you should discuss the problem and then write up the solution later alone to make sure you understand the solution.

Grading

The grades will be calculated roughly as follows:

It is impossible to cover all the topics in the textbook in one semester. My goal is to go through chapter 1-3 (Divisibility-Congruences-Quadratic Reciprocity and Quadratic Forms) carefully, and then do as much of chapters 4-7 (Some Functions of Number Theory-Some Diophantine Equations-Farey Fractions and Irrational Numbers-Simple Continued Fractions) as time permits. This goal is very ambitious, and most likely we will only be able to study one or two of chapters 4-7.