Gerhard Rosenberger's Books

Introduction to Abstract Algebra

From Rings, Numbers, Groups, and Fields to Polynomials and Galois Theory

By: Benjamin Fine,Anthony M. Gaglione,Gerhard Rosenberger

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Introduction to Abstract Algebra

From Rings, Numbers, Groups, and Fields to Polynomials and Galois Theory

By: Benjamin Fine,Anthony M. Gaglione,Gerhard Rosenberger

Presents a systematic approach to one of math's most intimidating concepts. Avoiding the pitfalls common in the standard textbooks, this title begins with familiar topics such as rings, numbers, and groups before introducing more difficult concepts.

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583

Publisher

JHU Press

Published Date

ISBN 10

1421411768

ISBN 13

9781421411767

The Fundamental Theorem of Algebra

By: Benjamin Fine,Gerhard Rosenberger

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The Fundamental Theorem of Algebra

By: Benjamin Fine,Gerhard Rosenberger

The fundamental theorem of algebra states that any complex polynomial must have a complex root. This book examines three pairs of proofs of the theorem from three different areas of mathematics: abstract algebra, complex analysis and topology. The first proof in each pair is fairly straightforward and depends only on what could be considered elementary mathematics. However, each of these first proofs leads to more general results from which the fundamental theorem can be deduced as a direct consequence. These general results constitute the second proof in each pair. To arrive at each of the proofs, enough of the general theory of each relevant area is developed to understand the proof. In addition to the proofs and techniques themselves, many applications such as the insolvability of the quintic and the transcendence of e and pi are presented. Finally, a series of appendices give six additional proofs including a version of Gauss'original first proof. The book is intended for junior/senior level undergraduate mathematics students or first year graduate students, and would make an ideal "capstone" course in mathematics.

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232

Publisher

Springer Science & Business Media

Published Date

ISBN 10

0387946578

ISBN 13

9780387946573

A Course in Mathematical Cryptography

By: Gilbert Baumslag,Benjamin Fine,Martin Kreuzer,Gerhard Rosenberger

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A Course in Mathematical Cryptography

By: Gilbert Baumslag,Benjamin Fine,Martin Kreuzer,Gerhard Rosenberger

Cryptography has become essential as bank transactions, credit card infor-mation, contracts, and sensitive medical information are sent through inse-cure channels. This book is concerned with the mathematical, especially algebraic, aspects of cryptography. It grew out of many courses presented by the authors over the past twenty years at various universities and covers a wide range of topics in mathematical cryptography. It is primarily geared towards graduate students and advanced undergraduates in mathematics and computer science, but may also be of interest to researchers in the area. Besides the classical methods of symmetric and private key encryption, the book treats the mathematics of cryptographic protocols and several unique topics such as Group-Based Cryptography Gröbner Basis Methods in Cryptography Lattice-Based Cryptography

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476

Publisher

Walter de Gruyter GmbH & Co KG

Published Date

ISBN 10

311038616X

ISBN 13

9783110386165

Topics in Infinite Group Theory

Nielsen Methods, Covering Spaces, and Hyperbolic Groups

By: Benjamin Fine,Anja Moldenhauer,Gerhard Rosenberger,Leonard Wienke

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Topics in Infinite Group Theory

Nielsen Methods, Covering Spaces, and Hyperbolic Groups

By: Benjamin Fine,Anja Moldenhauer,Gerhard Rosenberger,Leonard Wienke

This book gives an advanced overview of several topics in infinite group theory. It can also be considered as a rigorous introduction to combinatorial and geometric group theory. The philosophy of the book is to describe the interaction between these two important parts of infinite group theory. In this line of thought, several theorems are proved multiple times with different methods either purely combinatorial or purely geometric while others are shown by a combination of arguments from both perspectives. The first part of the book deals with Nielsen methods and introduces the reader to results and examples that are helpful to understand the following parts. The second part focuses on covering spaces and fundamental groups, including covering space proofs of group theoretic results. The third part deals with the theory of hyperbolic groups. The subjects are illustrated and described by prominent examples and an outlook on solved and unsolved problems.

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392

Publisher

Walter de Gruyter GmbH & Co KG

Published Date

ISBN 10

3110673371

ISBN 13

9783110673371

Numerical Differential Protection

Principles and Applications

By: Gerhard Ziegler

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Numerical Differential Protection

Principles and Applications

By: Gerhard Ziegler

Differential protection is a fast and selective method of protection against short-circuits. It is applied in many variants for electrical machines, trans-formers, busbars, and electric lines. Initially this book covers the theory and fundamentals of analog and numerical differential protection. Current transformers are treated in detail including transient behaviour, impact on protection performance, and practical dimensioning. An extended chapter is dedicated to signal transmission for line protection, in particular, modern digital communication and GPS timing. The emphasis is then placed on the different variants of differential protection and their practical application illustrated by concrete examples. This is completed by recommendations for commissioning, testing and maintenance. Finally the design and management of modern differential protection is explained by means of the latest Siemens SIPROTEC relay series. As a textbook and standard work in one, this book covers all topics, which have to be paid attention to for planning, designing, configuring and applying differential protection systems. The book is aimed at students and engineers who wish to familiarise themselves with the subject of differential protection, as well as the experienced user entering the area of numerical differential protection. Furthermore, it serves as a reference guide for solving application problems. For the new edition all contents have been revised, extended and updated to the latest state-of-the-art of protective relaying.

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287

Publisher

John Wiley & Sons

Published Date

ISBN 10

3895786705

ISBN 13

9783895786709

Germany and the Second World War

Volume VII: The Strategic Air War in Europe and the War in the West and East Asia, 1943-1944/5

By: Horst Boog,Gerhard Krebs,Detlef Vogel

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Germany and the Second World War

Volume VII: The Strategic Air War in Europe and the War in the West and East Asia, 1943-1944/5

By: Horst Boog,Gerhard Krebs,Detlef Vogel

By the spring of 1943, after the defeat at Stalingrad, the writing was on the wall. But while commanders close to the troops on Germany's various fronts were beginning to read it, those at the top were resolutely looking the other way. This seventh volume in the magisterial 10-volume series from the Militärgeschichtliches Forschungsamt [Research Institute for Military History] shows both Germany and her Japanese ally on the defensive, from 1943 into early 1945. It looks in depth at the strategic air war over the Reich and the mounting toll taken in the Battles of the Ruhr, Hamburg, and Berlin, and at the "Battle of the Radar Sets" so central to them all. The collapse of the Luftwaffe in its retaliatory role led to hopes being pinned on the revolutionary V-weapons, whose dramatic but ultimately fruitless achievements are chronicled. The Luftwaffe's weakness in defence is seen during the Normandy invasion, Operation overlord, an account of the planning, preparation and execution of which form the central part of this volume together with the landings in the south of France, the setback suffered at Arnhem, and the German counter-offensive in the Ardennes. The final part follows the fortunes of Germany's ally fighting in the Pacific, Burma, Thailand, and China, with American forces capturing islands ever closer to Japan's homeland, and culminates in her capitulation and the creation of a new postwar order in the Far East. The struggle between internal factions in the Japanese high command and imperial court is studied in detail, and highlights an interesting contrast with the intolerance of all dissent that typified the Nazi power structure. Based on meticulous research by MGFA's team of historians at Potsdam, this analysis of events is illustrated by a wealth of tables and maps covering aspects ranging from Germany's radar defence system and the targets of RAF Bomber Command and the US 8th Air Force, through the break-out from the Normandy beachhead, to the battles for Iwo Jima and Okinawa.

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3789

Publisher

Oxford University Press

Published Date

ISBN 10

0191089842

ISBN 13

9780191089848

Analytic Theory of Polynomials

By: Qazi Ibadur Rahman,Gerhard Schmeisser

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Analytic Theory of Polynomials

By: Qazi Ibadur Rahman,Gerhard Schmeisser

Presents easy to understand proofs of same of the most difficult results about polynomials demonstrated by means of applications

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760

Publisher

Oxford University Press

Published Date

ISBN 10

0198534930

ISBN 13

9780198534938

Analysis by Its History

By: Ernst Hairer,Gerhard Wanner

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Analysis by Its History

By: Ernst Hairer,Gerhard Wanner

This book presents first-year calculus roughly in the order in which it was first discovered. The first two chapters show how the ancient calculations of practical problems led to infinite series, differential and integral calculus and to differential equations. The establishment of mathematical rigour for these subjects in the 19th century for one and several variables is treated in chapters III and IV. Many quotations are included to give the flavor of the history. The text is complemented by a large number of examples, calculations and mathematical pictures and will provide stimulating and enjoyable reading for students, teachers, as well as researchers.

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390

Publisher

Springer Science & Business Media

Published Date

ISBN 10

0387770364

ISBN 13

9780387770369

Corruption and the Secret of Law

A Legal Anthropological Perspective

By: Gerhard Anders

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Corruption and the Secret of Law

A Legal Anthropological Perspective

By: Gerhard Anders

This volume presents an anthropological perspective on the hidden continuities between corruption and law. The authors argue that the two opposites, corruption and law, are inextricably linked - with the possibility of the former already inscribed into the latter. Taking a critical stance towards the normative good governance agenda spearheaded by institutions such as Transparency International and the World Bank, this volume argues that by uncritically depicting corruption as an absolute evil, these anti-corruption programs disregard the close relationship that exists between corruption and state power. Addressing various aspects of a complex and ambivalent phenomenon, Corruption and the Secret of Law draws on studies from different parts of the world including Burundi, China, Indonesia, Italy, Japan, Mexico and the USA and provides a valuable resource for students, researchers and policy-makers working in this area.

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369

Publisher

Routledge

Published Date

ISBN 10

1351948342

ISBN 13

9781351948340

Numerical Distance Protection

Principles and Applications

By: Gerhard Ziegler

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Numerical Distance Protection

Principles and Applications

By: Gerhard Ziegler

Distance protection provides the basis for network protection in transmission systems and meshed distribution systems. This book covers the fundamentals of distance protection and the special features of numerical technology. The emphasis is placed on the application of numerical distance relays in distribution and transmission systems. This book is aimed at students and engineers who wish to familiarise themselves with the subject of power system protection, as well as the experienced user, entering the area of numerical distance protection. Furthermore it serves as a reference guide for solving application problems. For this fourth edition all contents, especially the descriptions of numerical protection devices and the very useful appendix have been revised and updated.

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419

Publisher

John Wiley & Sons

Published Date

ISBN 10

3895786675

ISBN 13

9783895786679

Mo Molybdenum

Physical Properties, Part 2. Electrochemistry

By: Gerhard Czack,Gerhard Kirschstein,Vera Haase,Wolf-Dietrich Fleischmann,Dieter Gras

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Mo Molybdenum

Physical Properties, Part 2. Electrochemistry

By: Gerhard Czack,Gerhard Kirschstein,Vera Haase,Wolf-Dietrich Fleischmann,Dieter Gras

As was announced two years ago, the description of the physical properties of molybde num has now been completed in the present volume up to page 124. Whereas most properties, e.g., the electrical, magnetic, and optical properties, are dealt with in the usual manner, the results of studies of the atom and ion emission had to be presented in a revised form, comprising not only the most recent data but having in mind also the corresponding data for tungsten, which will be represented in a supplement volume now in preparation. The various modes of electron emission have also been studied in great detail. Many more pages (exactly 226 pages, as contrasted to three pages in the Main Volume) were needed to present the electrochemical data for molybdenum, which were published to an astonishingly great extent by Russian workers. The large volume of literature is due to the extensive industrial application of the metaL, cf. "MoLybdän" Erg.-Bd. A 1, 1977, and to its occurrence in various oxidation states. Thus the equilibrium between an Mo eLectrode and Mo ions or between an inert eLectrode and Mo ions is deaLt with in the chapters "Standard PotentiaLs" and "PotentiaLs", whereas kinetics and reaction mechanisms of the reduction and oxidation of Mo ions on a dropping mercury electrode and other inert eLectrodes can be found in the chapter "Polarography/ Voltammetry.

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Page Count

370

Publisher

Springer Science & Business Media

Published Date

ISBN 10

366209293X

ISBN 13

9783662092934

Special Effect Pigments

Technical Basics and Applications

By: Gerhard Pfaff

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Special Effect Pigments

Technical Basics and Applications

By: Gerhard Pfaff

The Mission: To learn about the dynamic, technical advances occurring in special effect pigments and to know how to exploit them in specific coatings, plastics, printing inks and cosmetics applications while satisfying the demands of the market. The Audience: Colour designers, product developers and applications technologists in the coatings, plastics, printing inks and cosmetics industries, as well as all marketing and sales employees of these divisions who are seeking to instill coatings and pigment knowledge into their customers. The Value: Readers acquire a profound knowledge of the properties, manufacturing processes and specific application areas of special effect pigments. The latest advances in colorimetry ensure that products containing special effect pigments are subjected to state-of-the-art quality assurance methods.

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224

Publisher

Vincentz Network GmbH & Co KG

Published Date

ISBN 10

3866309058

ISBN 13

9783866309050

Algebra and Number Theory

A Selection of Highlights

By: Benjamin Fine,Anthony Gaglione,Anja Moldenhauer,Gerhard Rosenberger,Dennis Spellman

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Algebra and Number Theory

A Selection of Highlights

By: Benjamin Fine,Anthony Gaglione,Anja Moldenhauer,Gerhard Rosenberger,Dennis Spellman

This two-volume set collects and presents some fundamentals of mathematics in an entertaining and performing manner. The present volume examines many of the most important basic results in algebra and number theory, along with their proofs, and also their history. Contents The natural, integral and rational numbers Division and factorization in the integers Modular arithmetic Exceptional numbers Pythagorean triples and sums of squares Polynomials and unique factorization Field extensions and splitting fields Permutations and symmetric polynomials Real numbers The complex numbers, the Fundamental Theorem of Algebra and polynomial equations Quadratic number fields and Pell’s equation Transcendental numbers and the numbers e and π Compass and straightedge constructions and the classical problems Euclidean vector spaces

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342

Publisher

Walter de Gruyter GmbH & Co KG

Published Date

ISBN 10

3110516144

ISBN 13

9783110516142

Algebraic Generalizations of Discrete Groups

A Path to Combinatorial Group Theory Through One-Relator Products

By: Benjamin Fine,Gerhard Rosenberger

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Algebraic Generalizations of Discrete Groups

A Path to Combinatorial Group Theory Through One-Relator Products

By: Benjamin Fine,Gerhard Rosenberger

A survey of one-relator products of cyclics or groups with a single defining relation, extending the algebraic study of Fuchsian groups to the more general context of one-relator products and related group theoretical considerations. It provides a self-contained account of certain natural generalizations of discrete groups.

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338

Publisher

CRC Press

Published Date

ISBN 10

0824703197

ISBN 13

9780824703196

Abstract Algebra

Applications to Galois Theory, Algebraic Geometry, and Cryptography

By: Celine Carstensen,Benjamin Fine,Gerhard Rosenberger

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Abstract Algebra

Applications to Galois Theory, Algebraic Geometry, and Cryptography

By: Celine Carstensen,Benjamin Fine,Gerhard Rosenberger

A new approach to conveying abstract algebra, the area that studies algebraic structures, such as groups, rings, fields, modules, vector spaces, and algebras, that is essential to various scientific disciplines such as particle physics and cryptology. It provides a well written account of the theoretical foundations; also contains topics that cannot be found elsewhere, and also offers a chapter on cryptography. End of chapter problems help readers with accessing the subjects. This work is co-published with the Heldermann Verlag, and within Heldermann's Sigma Series in Mathematics.

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381

Publisher

Walter de Gruyter

Published Date

ISBN 10

311025008X

ISBN 13

9783110250084

Aspects of Infinite Groups

A Festschrift in Honor of Anthony Gaglione

By: Benjamin Fine,Gerhard Rosenberger,Dennis Spellman

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Aspects of Infinite Groups

A Festschrift in Honor of Anthony Gaglione

By: Benjamin Fine,Gerhard Rosenberger,Dennis Spellman

This book is a festschrift in honor of Professor Anthony Gaglione's sixtieth birthday. This volume presents an excellent mix of research and expository articles on various aspects of infinite group theory. The papers give a broad overview of present research in infinite group theory in general, and combinatorial group theory and non-Abelian group-based cryptography in particular. They also pinpoint the interactions between combinatorial group theory and mathematical logic, especially model theory.

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253

Publisher

World Scientific

Published Date

ISBN 10

9812793402

ISBN 13

9789812793409

The Elementary Theory of Groups

A Guide through the Proofs of the Tarski Conjectures

By: Benjamin Fine,Anthony Gaglione,Alexei Myasnikov,Gerhard Rosenberger,Dennis Spellman

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The Elementary Theory of Groups

A Guide through the Proofs of the Tarski Conjectures

By: Benjamin Fine,Anthony Gaglione,Alexei Myasnikov,Gerhard Rosenberger,Dennis Spellman

After being an open question for sixty years the Tarski conjecture was answered in the affirmative by Olga Kharlampovich and Alexei Myasnikov and independently by Zlil Sela. Both proofs involve long and complicated applications of algebraic geometry over free groups as well as an extension of methods to solve equations in free groups originally developed by Razborov. This book is an examination of the material on the general elementary theory of groups that is necessary to begin to understand the proofs. This material includes a complete exposition of the theory of fully residually free groups or limit groups as well a complete description of the algebraic geometry of free groups. Also included are introductory material on combinatorial and geometric group theory and first-order logic. There is then a short outline of the proof of the Tarski conjectures in the manner of Kharlampovich and Myasnikov.

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322

Publisher

Walter de Gruyter GmbH & Co KG

Published Date

ISBN 10

3110342030

ISBN 13

9783110342031

Combinatorial Group Theory, Discrete Groups, and Number Theory

A Conference in Honor of Gerhard Rosenberger, December 8-9, 2004, Fairfield University : AMS Special Session on Infinite Groups, October 8-9, 2005, Bard College

By: Benjamin Fine,Anthony M. Gaglione,Dennis Spellman

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Combinatorial Group Theory, Discrete Groups, and Number Theory

A Conference in Honor of Gerhard Rosenberger, December 8-9, 2004, Fairfield University : AMS Special Session on Infinite Groups, October 8-9, 2005, Bard College

By: Benjamin Fine,Anthony M. Gaglione,Dennis Spellman

This volume consists of contributions by participants and speakers at two conferences. The first was entitled Combinatorial Group Theory, Discrete Groups and Number Theory and was held at Fairfield University, December 8-9, 2004. It was in honor of Professor Gerhard Rosenberger's sixtieth birthday. The second was the AMS Special Session on Infinite Group Theory held at Bard College, October 8-9, 2005. The papers in this volume provide a very interesting mix of combinatorial group theory, discrete group theory and ring theory as well as contributions to noncommutative algebraic cryptography.

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282

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821839853

ISBN 13

9780821839850

Algebraic Generalizations of Discrete Groups

A Path to Combinatorial Group Theory Through One-Relator Products

By: Benjamin Fine,Gerhard Rosenberger

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Algebraic Generalizations of Discrete Groups

A Path to Combinatorial Group Theory Through One-Relator Products

By: Benjamin Fine,Gerhard Rosenberger

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338

Publisher

CRC Press

Published Date

ISBN 10

0824703197

ISBN 13

9780824703196

The Elementary Theory of Groups

A Guide through the Proofs of the Tarski Conjectures

By: Benjamin Fine,Anthony Gaglione,Alexei Myasnikov,Gerhard Rosenberger,Dennis Spellman

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The Elementary Theory of Groups

A Guide through the Proofs of the Tarski Conjectures

By: Benjamin Fine,Anthony Gaglione,Alexei Myasnikov,Gerhard Rosenberger,Dennis Spellman

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Page Count

333

Publisher

Walter de Gruyter GmbH & Co KG

Published Date

ISBN 10

3110382571

ISBN 13

9783110382570

Abstract Algebra

Applications to Galois Theory, Algebraic Geometry and Cryptography

By: Celine Carstensen,Benjamin Fine,Gerhard Rosenberger

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Abstract Algebra

Applications to Galois Theory, Algebraic Geometry and Cryptography

By: Celine Carstensen,Benjamin Fine,Gerhard Rosenberger

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381

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Walter de Gruyter

Published Date

ISBN 10

3110250098

ISBN 13

9783110250091

Geometry and Discrete Mathematics

A Selection of Highlights

By: Benjamin Fine,Anja Moldenhauer,Gerhard Rosenberger,Annika Schürenberg,Leonard Wienke

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Geometry and Discrete Mathematics

A Selection of Highlights

By: Benjamin Fine,Anja Moldenhauer,Gerhard Rosenberger,Annika Schürenberg,Leonard Wienke

In the two-volume set ‘A Selection of Highlights’ we present basics of mathematics in an exciting and pedagogically sound way. This volume examines many fundamental results in Geometry and Discrete Mathematics along with their proofs and their history. In the second edition we include a new chapter on Topological Data Analysis and enhanced the chapter on Graph Theory for solving further classical problems such as the Traveling Salesman Problem.

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412

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Walter de Gruyter GmbH & Co KG

Published Date

ISBN 10

3110740931

ISBN 13

9783110740936

Topics in Infinite Group Theory

Nielsen Methods, Covering Spaces, and Hyperbolic Groups

By: Benjamin Fine,Anja Moldenhauer,Gerhard Rosenberger,Leonard Wienke

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Topics in Infinite Group Theory

Nielsen Methods, Covering Spaces, and Hyperbolic Groups

By: Benjamin Fine,Anja Moldenhauer,Gerhard Rosenberger,Leonard Wienke

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392

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Walter de Gruyter GmbH & Co KG

Published Date

ISBN 10

3110673371

ISBN 13

9783110673371

Introduction to Abstract Algebra

From Rings, Numbers, Groups, and Fields to Polynomials and Galois Theory

By: Benjamin Fine,Anthony M. Gaglione,Gerhard Rosenberger

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Introduction to Abstract Algebra

From Rings, Numbers, Groups, and Fields to Polynomials and Galois Theory

By: Benjamin Fine,Anthony M. Gaglione,Gerhard Rosenberger

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583

Publisher

JHU Press

Published Date

ISBN 10

1421411768

ISBN 13

9781421411767

Abstract Algebra

Applications to Galois Theory, Algebraic Geometry, Representation Theory and Cryptography

By: Celine Carstensen-Opitz,Benjamin Fine,Anja Moldenhauer,Gerhard Rosenberger

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Abstract Algebra

Applications to Galois Theory, Algebraic Geometry, Representation Theory and Cryptography

By: Celine Carstensen-Opitz,Benjamin Fine,Anja Moldenhauer,Gerhard Rosenberger

A new approach to conveying abstract algebra, the area that studies algebraic structures, such as groups, rings, fields, modules, vector spaces, and algebras, that is essential to various scientific disciplines such as particle physics and cryptology. It provides a well written account of the theoretical foundations and it also includes a chapter on cryptography. End of chapter problems help readers with accessing the subjects.

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563

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Walter de Gruyter GmbH & Co KG

Published Date

ISBN 10

3110605252

ISBN 13

9783110605259

Abstract Algebra

With Applications to Galois Theory, Algebraic Geometry, Representation Theory and Cryptography

By: Gerhard Rosenberger,Annika Schürenberg,Leonard Wienke

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Abstract Algebra

With Applications to Galois Theory, Algebraic Geometry, Representation Theory and Cryptography

By: Gerhard Rosenberger,Annika Schürenberg,Leonard Wienke

Abstract algebra is the study of algebraic structures like groups, rings and fields. This book provides an account of the theoretical foundations including applications to Galois Theory, Algebraic Geometry and Representation Theory. It implements the pedagogic approach to conveying algebra from the perspective of rings. The 3rd edition provides a revised and extended versions of the chapters on Algebraic Cryptography and Geometric Group Theory.

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564

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Walter de Gruyter GmbH & Co KG

Published Date

ISBN 10

3111142841

ISBN 13

9783111142845

Algebra and Number Theory

A Selection of Highlights

By: Benjamin Fine,Anthony Gaglione,Anja Moldenhauer,Gerhard Rosenberger,Dennis Spellman

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Algebra and Number Theory

A Selection of Highlights

By: Benjamin Fine,Anthony Gaglione,Anja Moldenhauer,Gerhard Rosenberger,Dennis Spellman

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342

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Walter de Gruyter GmbH & Co KG

Published Date

ISBN 10

3110516144

ISBN 13

9783110516142

Number Theory

An Introduction via the Density of Primes

By: Benjamin Fine,Gerhard Rosenberger

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Number Theory

An Introduction via the Density of Primes

By: Benjamin Fine,Gerhard Rosenberger

Now in its second edition, this textbook provides an introduction and overview of number theory based on the density and properties of the prime numbers. This unique approach offers both a firm background in the standard material of number theory, as well as an overview of the entire discipline. All of the essential topics are covered, such as the fundamental theorem of arithmetic, theory of congruences, quadratic reciprocity, arithmetic functions, and the distribution of primes. New in this edition are coverage of p-adic numbers, Hensel's lemma, multiple zeta-values, and elliptic curve methods in primality testing. Key topics and features include: A solid introduction to analytic number theory, including full proofs of Dirichlet's Theorem and the Prime Number Theorem Concise treatment of algebraic number theory, including a complete presentation of primes, prime factorizations in algebraic number fields, and unique factorization of ideals Discussion of the AKS algorithm, which shows that primality testing is one of polynomial time, a topic not usually included in such texts Many interesting ancillary topics, such as primality testing and cryptography, Fermat and Mersenne numbers, and Carmichael numbers The user-friendly style, historical context, and wide range of exercises that range from simple to quite difficult (with solutions and hints provided for select exercises) make Number Theory: An Introduction via the Density of Primes ideal for both self-study and classroom use. Intended for upper level undergraduates and beginning graduates, the only prerequisites are a basic knowledge of calculus, multivariable calculus, and some linear algebra. All necessary concepts from abstract algebra and complex analysis are introduced where needed.

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423

Publisher

Birkhäuser

Published Date

ISBN 10

3319438751

ISBN 13

9783319438757

The Fundamental Theorem of Algebra

By: Benjamin Fine,Gerhard Rosenberger

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The Fundamental Theorem of Algebra

By: Benjamin Fine,Gerhard Rosenberger

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220

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Springer Science & Business Media

Published Date

ISBN 10

1461219280

ISBN 13

9781461219286

Number Theory

An Introduction via the Distribution of Primes

By: Benjamin Fine,Gerhard Rosenberger

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Number Theory

An Introduction via the Distribution of Primes

By: Benjamin Fine,Gerhard Rosenberger

This book provides an introduction and overview of number theory based on the distribution and properties of primes. This unique approach provides both a firm background in the standard material as well as an overview of the whole discipline. All the essential topics are covered: fundamental theorem of arithmetic, theory of congruences, quadratic reciprocity, arithmetic functions, and the distribution of primes. Analytic number theory and algebraic number theory both receive a solid introductory treatment. The book’s user-friendly style, historical context, and wide range of exercises make it ideal for self study and classroom use.

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Page Count

350

Publisher

Springer Science & Business Media

Published Date

ISBN 10

0817645411

ISBN 13

9780817645410

Book's by Gerhard Rosenberger

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