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Have you ever wondered about the explicit formulas in analytic number theory? This short book provides a streamlined and rigorous approach to the explicit formulas of Riemann and …
New mathematics often comes about by probing what is already known. Mathematicians will change the parameters in a familiar calculation or explore the essential ingredients of a …
This new edition of Analytic Number Theory for Beginners presents a friendly introduction to analytic number theory for both advanced undergraduate and beginning graduate students, …
The circle method, pioneered by Ramanujan and Hardy in the early 20th century, has over the past 100 years become part of the standard tool chest of analytic number theory. Its …
This book is based on a capstone course that the author taught to upper division undergraduate students with the goal to explain and visualize the connections between different …
Welcome to diophantine analysis - an area of number theory in which we attempt to discover hidden treasures and truths within the jungle of numbers by exploring rational numbers. …
One of the great charms of mathematics is uncovering unexpected connections. In Numbers and Figures, Giancarlo Travaglini provides six conversations that do exactly that by talking …
Asymptotics in one form or another are part of the landscape for every mathematician. The objective of this book is to present the ideas of how to approach asymptotic problems that …
This book uses finite field theory as a hook to introduce the reader to a range of ideas from algebra and number theory. It constructs all finite fields from scratch and shows that …
How can you tell whether a number is prime? What if the number has hundreds or thousands of digits? This question may seem abstract or irrelevant, but in fact, primality tests are …