Author Profile

Vahagn Aslanyan is a Dame Kathleen Ollerenshaw Fellow in the Department of Mathematics at the University of Manchester, also supported by an EPSRC Open Fellowship. From 2022 to 2023 he was a Leverhulme Trust Early Career Fellow at the University of Leeds. From 2019 to 2022 he was a senior research associate at the University of East Anglia. From 2017 to 2019 he was a postdoctoral associate at Carnegie Mellon University and concurrently a junior researcher at the National Academy of Sciences of Armenia. He did PhD (DPhil) at the University of Oxford from 2013 to 2017. He received bachelor's degree from Yerevan State University in 2013. His primary research interests are in Number Theory model, a branch of mathematical logic with a broad range of applications. More specifically, he is interested in applications of model theory in number theory, geometry, algebra, and analysis.

About The Book

Number theory is a branch of pure mathematics that deals with the study of natural numbers and integers. It focuses on the set of positive whole numbers which are called the set of natural numbers. The number theory helps in discovering interesting relationships between different sorts of numbers and in proving their legitimacy. It includes both experimental and theoretical aspects. The experimental aspect generates new questions and discovers their answer. The theoretical aspect tries to devise an argument that provides a conclusive answer to the questions. This book covers in detail some existent theories and innovative concepts revolving around number theory. Most of the topics introduced herein cover new techniques and applications of number theory. This book is appropriate for students seeking detailed information in this area as well as for experts. This book effectively builds a bridge from basic number theory to recent advances in applied number theory. Number theory is a branch of pure mathematics that deals with the study of natural numbers and integers. It focuses on the set of positive whole numbers which are called the set of natural numbers. The number theory helps in discovering interesting relationships between different sorts of numbers and in proving their legitimacy. It includes both experimental and theoretical aspects. The experimental aspect generates new questions and discovers their answer. The theoretical aspect tries to devise an argument that provides a conclusive answer to the questions. This book covers in detail some existent theories and innovative concepts revolving around number theory. Most of the topics introduced herein cover new techniques and applications of number theory. This book is appropriate for students seeking detailed information in this area as well as for experts. This textbook effectively builds a bridge from basic number theory to recent advances in applied number theory.

Table of Contents

Preface
Chapter 1. Introduction to Number Theory
Chapter 2. Modular Arithmetic and Congruences
Chapter 3. Diophantine Equations
Chapter 4. Arithmetic Functions and Multiplicativity
Chapter 5. Prime Numbers and Primality Testing
Chapter 6. Cryptography and Number Theory
Chapter 7. Quadratic Residues and Reciprocity
Chapter 8. Continued Fractions and Approximations
Chapter 9. Algebraic Number Theory Basics
Chapter 10. Geometry of Numbers
Bibliography
Index