## Math 465 Number Theory, Spring 2021

Number theory is central to the whole of mathematics and much of
modern society, in particular because of connections with security
of communications and digital information. The most important
problem in mathematics is the Riemann
Hypothesis which fundamentally is a problem about the
distribution of primes. Another of the Millennium
Prize problems is the Birch
and Swinnerton-Dyer conjecture which is also a question in
number theory

Syllabus

We will follow closely Vaughan, A Course of
Elementary Number Theory

Other good textbooks are

Andrews, Number Theory, ISBN-10: 0486682528, ISBN-13: 978-0486682525

Burton, Elementary Number Theory, ISBN-10: 9781259025761, ISBN-13:
978-1259025761

Davenport, The Higher Arithmetic, CUP, ISBN--10:0521722365,
ISBN--13:978-0521722360

Hardy & Wright, An Introduction to the Theory of Numbers,
ISBN-10: 9780199219865, ISBN-13: 978-0199219865

Landau, Elementary Number Theory, ISBN-10: 0821820044, ISBN-13:
978-0821820049

LeVeque, Fundamentals of Number Theory, Dover, ISBN--10:0486689069,
ISBN--13:978-0486689067

Niven, Zuckerman & Montgomery, An Introduction to the Theory of
Numbers, ISBN-10: 9788126518111, ISBN-13: 978-8126518111

Hardy & Wright, Landau, and Niven, Zuckerman & Montgomery,
cover much more material, but are iconic. There are other
excellent books out there, by Carmichael, Dickson, Dudley,
Silverman, Jones & Jones, Vinogradov but they don't cover
everything I plan to cover.

Homeworks and Practice Exams