The branch of pure mathematics devoted primarily to the study of integers and integer-valued functions is known as number theory. The concepts of prime numbers as well as the properties of mathematical objects made out of integers such as rational numbers or generalizations of the integers, and algebraic integers are studied within this field. Some of the main subdivisions of number theory are elementary number theory, analytic number theory, algebraic number theory, Diophantine geometry, probabilistic number theory, arithmetic combinatorics, and computational number theory. Number theory has applications in discrete mathematics courses for computer science, numerical analysis, and cryptography. This book will help new researchers by foregrounding their knowledge in this branch. The various sub-fields of number theory along with technological progress that have future implications are glanced at herein. This book aims to equip students and experts with the advanced topics and upcoming concepts in this area.
The branch of pure mathematics devoted primarily to the study of integers and integer-valued functions is known as number theory. The concepts of prime numbers as well as the properties of mathematical objects made out of integers such as rational numbers or generalizations of the integers, and algebraic integers are studied within this field. Some of the main subdivisions of number theory are elementary number theory, analytic number theory, algebraic number theory, Diophantine geometry, probabilistic number theory, arithmetic combinatorics, and computational number theory. Number theory has applications in discrete mathematics courses for computer science, numerical analysis, and cryptography. This book will help new researchers by foregrounding their knowledge in this branch. The various sub-fields of number theory along with technological progress that have future implications are glanced at herein. This book aims to equip students and experts with the advanced topics and upcoming concepts in this area.
This edition has been called 'startlingly up-to-date', and in this corrected second printing you can be sure that it's even more contemporaneous. It surveys from a unified point of view both the...
For a regular 17-gon, the formulas above give the x-coordinate of the first vertex in the upper half plane.The first formula goes back to Gauss. The second formula is obtained by a more elementary...
This book has been growing over the years out of several resources. Firstly, the courses in number theory and modern algebra I had occasionally been teaching at UNC Charlotte. Secondly, my interest...
This well-developed, accessible text details the historical development of the subject throughout. It also provides wide-ranging coverage of significant results with comparatively elementary proofs,...
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