Advanced Number Theory With Applications
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Author | : Richard A. Mollin |
Publisher | : CRC Press |
Total Pages | : 440 |
Release | : 2009-08-26 |
Genre | : Computers |
ISBN | : 1420083295 |
Exploring one of the most dynamic areas of mathematics, Advanced Number Theory with Applications covers a wide range of algebraic, analytic, combinatorial, cryptographic, and geometric aspects of number theory. Written by a recognized leader in algebra and number theory, the book includes a page reference for every citing in the bibliography and mo
Author | : Richard A. Mollin |
Publisher | : CRC Press |
Total Pages | : 382 |
Release | : 2008-02-21 |
Genre | : Mathematics |
ISBN | : 1420066617 |
An update of the most accessible introductory number theory text available, Fundamental Number Theory with Applications, Second Edition presents a mathematically rigorous yet easy-to-follow treatment of the fundamentals and applications of the subject. The substantial amount of reorganizing makes this edition clearer and more elementary in its coverage. New to the Second Edition • Removal of all advanced material to be even more accessible in scope • New fundamental material, including partition theory, generating functions, and combinatorial number theory • Expanded coverage of random number generation, Diophantine analysis, and additive number theory • More applications to cryptography, primality testing, and factoring • An appendix on the recently discovered unconditional deterministic polynomial-time algorithm for primality testing Taking a truly elementary approach to number theory, this text supplies the essential material for a first course on the subject. Placed in highlighted boxes to reduce distraction from the main text, nearly 70 biographies focus on major contributors to the field. The presentation of over 1,300 entries in the index maximizes cross-referencing so students can find data with ease.
Author | : Richard A. Mollin |
Publisher | : |
Total Pages | : 0 |
Release | : 2010 |
Genre | : Number theory |
ISBN | : |
"Exploring one of the most dynamic areas of mathematics, Advanced Number Theory with Applications covers a wide range of algebraic, analytic, combinatorial, cryptographic, and geometric aspects of number theory. Written by a recognized leader in algebra and number theory, the book includes a page reference for every citing in the bibliography and more than 1,500 entries in the index so that students can easily cross-reference and find the appropriate data. With numerous examples throughout, the text begins with coverage of algebraic number theory, binary quadratic forms, Diophantine approximation, arithmetic functions, p-adic analysis, Dirichlet characters, density, and primes in arithmetic progression. It then applies these tools to Diophantine equations, before developing elliptic curves and modular forms. The text also presents an overview of Fermat's Last Theorem (FLT) and numerous consequences of the ABC conjecture, including Thue-Siegel-Roth theorem, Hall's conjecture, the Erdos-Mollin--Walsh conjecture, and the Granville-Langevin Conjecture. In the appendix, the author reviews sieve methods, such as Eratothesenes', Selberg's, Linnik's, and Bombieri's sieves. He also discusses recent results on gaps between primes and the use of sieves in factoring. By focusing on salient techniques in number theory, this textbook provides the most up-to-date and comprehensive material for a second course in this field. It prepares students for future study at the graduate level." -- Publisher.
Author | : Henri Cohen |
Publisher | : Springer Science & Business Media |
Total Pages | : 591 |
Release | : 2012-10-29 |
Genre | : Mathematics |
ISBN | : 1441984895 |
Written by an authority with great practical and teaching experience in the field, this book addresses a number of topics in computational number theory. Chapters one through five form a homogenous subject matter suitable for a six-month or year-long course in computational number theory. The subsequent chapters deal with more miscellaneous subjects.
Author | : Harvey Cohn |
Publisher | : Courier Corporation |
Total Pages | : 289 |
Release | : 2012-05-04 |
Genre | : Mathematics |
ISBN | : 0486149242 |
Eminent mathematician/teacher approaches algebraic number theory from historical standpoint. Demonstrates how concepts, definitions, and theories have evolved during last two centuries. Features over 200 problems and specific theorems. Includes numerous graphs and tables.
Author | : H. E. Rose |
Publisher | : Oxford University Press |
Total Pages | : 420 |
Release | : 1995 |
Genre | : Mathematics |
ISBN | : 9780198523765 |
This textbook covers the main topics in number theory as taught in universities throughout the world. Number theory deals mainly with properties of integers and rational numbers; it is not an organized theory in the usual sense but a vast collection of individual topics and results, with some coherent sub-theories and a long list of unsolved problems. This book excludes topics relying heavily on complex analysis and advanced algebraic number theory. The increased use of computers in number theory is reflected in many sections (with much greater emphasis in this edition). Some results of a more advanced nature are also given, including the Gelfond-Schneider theorem, the prime number theorem, and the Mordell-Weil theorem. The latest work on Fermat's last theorem is also briefly discussed. Each chapter ends with a collection of problems; hints or sketch solutions are given at the end of the book, together with various useful tables.
Author | : Abhijit Das |
Publisher | : CRC Press |
Total Pages | : 614 |
Release | : 2016-04-19 |
Genre | : Computers |
ISBN | : 1482205823 |
Developed from the author's popular graduate-level course, Computational Number Theory presents a complete treatment of number-theoretic algorithms. Avoiding advanced algebra, this self-contained text is designed for advanced undergraduate and beginning graduate students in engineering. It is also suitable for researchers new to the field and pract
Author | : Oystein Ore |
Publisher | : Courier Corporation |
Total Pages | : 404 |
Release | : 2012-07-06 |
Genre | : Mathematics |
ISBN | : 0486136434 |
Unusually clear, accessible introduction covers counting, properties of numbers, prime numbers, Aliquot parts, Diophantine problems, congruences, much more. Bibliography.
Author | : Satyabrota Kundu |
Publisher | : CRC Press |
Total Pages | : 275 |
Release | : 2022-02-03 |
Genre | : Mathematics |
ISBN | : 1000562581 |
Number Theory and its Applications is a textbook for students pursuing mathematics as major in undergraduate and postgraduate courses. Please note: Taylor & Francis does not sell or distribute the print book in India, Pakistan, Nepal, Bhutan, Bangladesh and Sri Lanka.
Author | : James Andrew Anderson |
Publisher | : Pearson |
Total Pages | : 584 |
Release | : 1997 |
Genre | : Mathematics |
ISBN | : |
For undergraduate courses in Number Theory for mathematics, computer science, and engineering majors. Ideal for students of varying mathematical sophistication, this text provides a self-contained logical development of basic number theory, supplemented with numerous applications and advanced topics.