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