Richard A. Mollin's Books

Algebraic Number Theory

By: Richard A. Mollin

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Bringing the material up to date to reflect modern applications, this second edition has been completely rewritten and reorganized to incorporate a new style, methodology, and presentation. It offers a more complete and involved treatment of Galois theory, a more comprehensive section on Pollard's cubic factoring algorithm, and more detailed explanations of proofs to provide a sound understanding of challenging material. This edition also studies binary quadratic forms and compares the ideal and form class groups. The text includes convenient cross-referencing, a comprehensive index, and numerous exercises and applications.

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424

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CRC Press

Published Date

ISBN 10

1439845999

ISBN 13

9781439845998

Advanced Number Theory with Applications

By: Richard A. Mollin

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Advanced Number Theory with Applications

By: Richard A. Mollin

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

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440

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CRC Press

Published Date

ISBN 10

1420083295

ISBN 13

9781420083293

Fundamental Number Theory with Applications

By: Richard A. Mollin

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Fundamental Number Theory with Applications

By: Richard A. Mollin

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.

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382

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CRC Press

Published Date

ISBN 10

1420066617

ISBN 13

9781420066616

Quadratics

By: Richard A. Mollin

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Quadratics

By: Richard A. Mollin

The first thing you will find out about this book is that it is fun to read. It is meant for the browser, as well as for the student and for the specialist wanting to know about the area. The footnotes give an historical background to the text, in addition to providing deeper applications of the concept that is being cited. This allows the browser to look more deeply into the history or to pursue a given sideline. Those who are only marginally interested in the area will be able to read the text, pick up information easily, and be entertained at the same time by the historical and philosophical digressions. It is rich in structure and motivation in its concentration upon quadratic orders. This is not a book that is primarily about tables, although there are 80 pages of appendices that contain extensive tabular material (class numbers of real and complex quadratic fields up to 104; class group structures; fundamental units of real quadratic fields; and more!). This book is primarily a reference book and graduate student text with more than 200 exercises and a great deal of hints! The motivation for the text is best given by a quote from the Preface of Quadratics: "There can be no stronger motivation in mathematical inquiry than the search for truth and beauty. It is this author's long-standing conviction that number theory has the best of both of these worlds. In particular, algebraic and computational number theory have reached a stage where the current state of affairs richly deserves a proper elucidation. It is this author's goal to attempt to shine the best possible light on the subject.

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420

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CRC Press

Published Date

ISBN 10

1351420771

ISBN 13

9781351420778

An Introduction to Cryptography

By: Richard A. Mollin

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An Introduction to Cryptography

By: Richard A. Mollin

Continuing a bestselling tradition, An Introduction to Cryptography, Second Edition provides a solid foundation in cryptographic concepts that features all of the requisite background material on number theory and algorithmic complexity as well as a historical look at the field. With numerous additions and restructured material, this edition

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413

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CRC Press

Published Date

ISBN 10

1420011243

ISBN 13

9781420011241

Codes

The Guide to Secrecy From Ancient to Modern Times

By: Richard A. Mollin

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Codes

The Guide to Secrecy From Ancient to Modern Times

By: Richard A. Mollin

From the Rosetta Stone to public-key cryptography, the art and science of cryptology has been used to unlock the vivid history of ancient cultures, to turn the tide of warfare, and to thwart potential hackers from attacking computer systems. Codes: The Guide to Secrecy from Ancient to Modern Times explores the depth and breadth of the field, remain

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700

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CRC Press

Published Date

ISBN 10

1420035088

ISBN 13

9781420035087

RSA and Public-Key Cryptography

By: Richard A. Mollin

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RSA and Public-Key Cryptography

By: Richard A. Mollin

Although much literature exists on the subject of RSA and public-key cryptography, until now there has been no single source that reveals recent developments in the area at an accessible level. Acclaimed author Richard A. Mollin brings together all of the relevant information available on public-key cryptography (PKC), from RSA to the latest applic

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305

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CRC Press

Published Date

ISBN 10

142003524X

ISBN 13

9781420035247

A Combinatorial Approach to Matrix Theory and Its Applications

By: Richard A. Brualdi,Dragos Cvetkovic

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A Combinatorial Approach to Matrix Theory and Its Applications

By: Richard A. Brualdi,Dragos Cvetkovic

Unlike most elementary books on matrices, A Combinatorial Approach to Matrix Theory and Its Applications employs combinatorial and graph-theoretical tools to develop basic theorems of matrix theory, shedding new light on the subject by exploring the connections of these tools to matrices. After reviewing the basics of graph theory, elementary counting formulas, fields, and vector spaces, the book explains the algebra of matrices and uses the König digraph to carry out simple matrix operations. It then discusses matrix powers, provides a graph-theoretical definition of the determinant using the Coates digraph of a matrix, and presents a graph-theoretical interpretation of matrix inverses. The authors develop the elementary theory of solutions of systems of linear equations and show how to use the Coates digraph to solve a linear system. They also explore the eigenvalues, eigenvectors, and characteristic polynomial of a matrix; examine the important properties of nonnegative matrices that are part of the Perron–Frobenius theory; and study eigenvalue inclusion regions and sign-nonsingular matrices. The final chapter presents applications to electrical engineering, physics, and chemistry. Using combinatorial and graph-theoretical tools, this book enables a solid understanding of the fundamentals of matrix theory and its application to scientific areas.

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288

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CRC Press

Published Date

ISBN 10

1420082248

ISBN 13

9781420082241

Cryptology

Classical and Modern with Maplets

By: Richard E. Klima,Neil P. Sigmon

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Cryptology

Classical and Modern with Maplets

By: Richard E. Klima,Neil P. Sigmon

Easily Accessible to Students with Nontechnical Backgrounds In a clear, nontechnical manner, Cryptology: Classical and Modern with Maplets explains how fundamental mathematical concepts are the bases of cryptographic algorithms. Designed for students with no background in college-level mathematics, the book assumes minimal mathematical prerequisites and incorporates student-friendly Maplets throughout that provide practical examples of the techniques used. Technology Resource By using the Maplets, students can complete complicated tasks with relative ease. They can encrypt, decrypt, and cryptanalyze messages without the burden of understanding programming or computer syntax. The authors explain topics in detail first before introducing one or more Maplets. All Maplet material and exercises are given in separate, clearly labeled sections. Instructors can omit the Maplet sections without any loss of continuity and non-Maplet examples and exercises can be completed with, at most, a simple hand-held calculator. The Maplets are available for download at www.radford.edu/~npsigmon/cryptobook.html. A Gentle, Hands-On Introduction to Cryptology After introducing elementary methods and techniques, the text fully develops the Enigma cipher machine and Navajo code used during World War II, both of which are rarely found in cryptology textbooks. The authors then demonstrate mathematics in cryptology through monoalphabetic, polyalphabetic, and block ciphers. With a focus on public-key cryptography, the book describes RSA ciphers, the Diffie–Hellman key exchange, and ElGamal ciphers. It also explores current U.S. federal cryptographic standards, such as the AES, and explains how to authenticate messages via digital signatures, hash functions, and certificates.

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558

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CRC Press

Published Date

ISBN 10

1439872414

ISBN 13

9781439872413

Unsolved Problems in Number Theory

By: Richard Guy

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Unsolved Problems in Number Theory

By: Richard Guy

Mathematics is kept alive by the appearance of new, unsolved problems. This book provides a steady supply of easily understood, if not easily solved, problems that can be considered in varying depths by mathematicians at all levels of mathematical maturity. This new edition features lists of references to OEIS, Neal Sloane’s Online Encyclopedia of Integer Sequences, at the end of several of the sections.

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455

Publisher

Springer Science & Business Media

Published Date

ISBN 10

0387266771

ISBN 13

9780387266770

Handbook of Product Graphs

By: Richard Hammack,Wilfried Imrich,Sandi Klavžar

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Handbook of Product Graphs

By: Richard Hammack,Wilfried Imrich,Sandi Klavžar

This handbook examines the dichotomy between the structure of products and their subgraphs. It also features the design of efficient algorithms that recognize products and their subgraphs and explores the relationship between graph parameters of the product and factors. Extensively revised and expanded, this second edition presents full proofs of many important results as well as up-to-date research and conjectures. It illustrates applications of graph products in several areas and contains well over 300 exercises. Supplementary material is available on the book's website.

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537

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CRC Press

Published Date

ISBN 10

1439813051

ISBN 13

9781439813058

Applications of Abstract Algebra with Maple and MATLAB, Second Edition

By: Richard Klima,Neil P. Sigmon,Ernest Stitzinger

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Applications of Abstract Algebra with Maple and MATLAB, Second Edition

By: Richard Klima,Neil P. Sigmon,Ernest Stitzinger

Eliminating the need for heavy number-crunching, sophisticated mathematical software packages open the door to areas like cryptography, coding theory, and combinatorics that are dependent on abstract algebra. Applications of Abstract Algebra with Maple and MATLAB®, Second Edition explores these topics and shows how to apply the software programs to abstract algebra and its related fields. Carefully integrating MapleTM and MATLAB®, this book provides an in-depth introduction to real-world abstract algebraic problems. The first chapter offers a concise and comprehensive review of prerequisite advanced mathematics. The next several chapters examine block designs, coding theory, and cryptography while the final chapters cover counting techniques, including Pólya's and Burnside's theorems. Other topics discussed include the Rivest, Shamir, and Adleman (RSA) cryptosystem, digital signatures, primes for security, and elliptic curve cryptosystems. New to the Second Edition Three new chapters on Vigenère ciphers, the Advanced Encryption Standard (AES), and graph theory as well as new MATLAB and Maple sections Expanded exercises and additional research exercises Maple and MATLAB files and functions available for download online and from a CD-ROM With the incorporation of MATLAB, this second edition further illuminates the topics discussed by eliminating extensive computations of abstract algebraic techniques. The clear organization of the book as well as the inclusion of two of the most respected mathematical software packages available make the book a useful tool for students, mathematicians, and computer scientists.

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536

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CRC Press

Published Date

ISBN 10

1584886102

ISBN 13

9781584886105

Algebraic Number Theory

By: Richard A. Mollin

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Algebraic Number Theory

By: Richard A. Mollin

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Page Count

424

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CRC Press

Published Date

ISBN 10

1439845999

ISBN 13

9781439845998

RSA and Public-Key Cryptography

By: Richard A. Mollin

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RSA and Public-Key Cryptography

By: Richard A. Mollin

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305

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CRC Press

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ISBN 10

142003524X

ISBN 13

9781420035247

Fundamental Number Theory with Applications, Second Edition

By: Richard A. Mollin

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Fundamental Number Theory with Applications, Second Edition

By: Richard A. Mollin

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Page Count

384

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Chapman and Hall/CRC

Published Date

ISBN 10

1420066595

ISBN 13

9781420066593

Book's by Richard A. Mollin

Algebraic Number Theory

Algebraic Number Theory

Advanced Number Theory with Applications

Advanced Number Theory with Applications

Fundamental Number Theory with Applications

Fundamental Number Theory with Applications

Quadratics

Quadratics

An Introduction to Cryptography

An Introduction to Cryptography

Codes

Codes

RSA and Public-Key Cryptography

RSA and Public-Key Cryptography

A Combinatorial Approach to Matrix Theory and Its Applications

A Combinatorial Approach to Matrix Theory and Its Applications

Cryptology

Cryptology

Unsolved Problems in Number Theory

Unsolved Problems in Number Theory

Handbook of Product Graphs

Handbook of Product Graphs

Applications of Abstract Algebra with Maple and MATLAB, Second Edition

Applications of Abstract Algebra with Maple and MATLAB, Second Edition

Algebraic Number Theory

Algebraic Number Theory

RSA and Public-Key Cryptography

RSA and Public-Key Cryptography

Fundamental Number Theory with Applications, Second Edition

Fundamental Number Theory with Applications, Second Edition

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