Rosenberger, Gerhard
Overview
Works:  61 works in 251 publications in 2 languages and 8,346 library holdings 

Genres:  Conference papers and proceedings Textbooks 
Roles:  Editor, Contributor, Author, Other, dgs, Dedicatee, htt 
Classifications:  QA212, 512.2 
Publication Timeline
.
Most widely held works by
Gerhard Rosenberger
Aspects of infinite groups : a festschrift in honor of Anthony Gaglione by
Benjamin Fine(
)
12 editions published in 2008 in English and held by 1,408 WorldCat member libraries worldwide
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 nonAbelian groupbased cryptography in particular. They also pinpoint the interactions between combinatorial group theory and mathematical logic, especially model theory
12 editions published in 2008 in English and held by 1,408 WorldCat member libraries worldwide
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 nonAbelian groupbased cryptography in particular. They also pinpoint the interactions between combinatorial group theory and mathematical logic, especially model theory
Discrete algebraic methods : arithmetic, cryptography, automata, and groups by
Volker Diekert(
)
10 editions published in 2016 in English and held by 1,143 WorldCat member libraries worldwide
The idea behind this book is to provide the mathematical foundations for assessing modern developments in the Information Age. It deepens and complements the basic concepts, but it also considers instructive and more advanced topics. The treatise starts with a general chapter on algebraic structures; this part provides all the necessary knowledge for the rest of the book. The next chapter gives a concise overview of cryptography. Chapter 3 on number theoretic algorithms is important for developping cryptosystems, Chapter 4 presents the deterministic primality test of Agrawal, Kayal, and Saxena. The account to elliptic curves again focuses on cryptographic applications and algorithms. With combinatorics on words and automata theory, the reader is introduced to two areas of theoretical computer science where semigroups play a fundamental role.The last chapter is devoted to combinatorial group theory and its connections to automata. Contents:Algebraic structuresCryptographyNumber theoretic algorithmsPolynomial time primality testElliptic curvesCombinatorics on wordsAutomataDiscrete infinite groups
10 editions published in 2016 in English and held by 1,143 WorldCat member libraries worldwide
The idea behind this book is to provide the mathematical foundations for assessing modern developments in the Information Age. It deepens and complements the basic concepts, but it also considers instructive and more advanced topics. The treatise starts with a general chapter on algebraic structures; this part provides all the necessary knowledge for the rest of the book. The next chapter gives a concise overview of cryptography. Chapter 3 on number theoretic algorithms is important for developping cryptosystems, Chapter 4 presents the deterministic primality test of Agrawal, Kayal, and Saxena. The account to elliptic curves again focuses on cryptographic applications and algorithms. With combinatorics on words and automata theory, the reader is introduced to two areas of theoretical computer science where semigroups play a fundamental role.The last chapter is devoted to combinatorial group theory and its connections to automata. Contents:Algebraic structuresCryptographyNumber theoretic algorithmsPolynomial time primality testElliptic curvesCombinatorics on wordsAutomataDiscrete infinite groups
Abstract algebra : applications to Galois theory, algebraic geometry, and cryptography by
Celine Carstensen(
)
18 editions published between 2011 and 2019 in English and held by 932 WorldCat member libraries worldwide
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 copublished with the Heldermann Verlag, and within Heldermann's Sigma Series in Mathematics. Celine Carstensen, Volkswohlbund Insurance, Dortmund, Germany;Benjamin Fine, Fairfield University, Connecticut, USA; Gerhard Rosenberger, Universität Hamburg, Germany
18 editions published between 2011 and 2019 in English and held by 932 WorldCat member libraries worldwide
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 copublished with the Heldermann Verlag, and within Heldermann's Sigma Series in Mathematics. Celine Carstensen, Volkswohlbund Insurance, Dortmund, Germany;Benjamin Fine, Fairfield University, Connecticut, USA; Gerhard Rosenberger, Universität Hamburg, Germany
A course in mathematical cryptography by
Gilbert Baumslag(
)
10 editions published between 2015 and 2016 in English and held by 836 WorldCat member libraries worldwide
"Cryptography has become essential as bank transactions, credit card information, contracts, and sensitive medical information are sent through insecure 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; GroupBased Cryptography; Gröbner Basis Methods in Cryptography; LatticeBased Cryptography."Publisher's description
10 editions published between 2015 and 2016 in English and held by 836 WorldCat member libraries worldwide
"Cryptography has become essential as bank transactions, credit card information, contracts, and sensitive medical information are sent through insecure 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; GroupBased Cryptography; Gröbner Basis Methods in Cryptography; LatticeBased Cryptography."Publisher's description
Algebra and number theory a selection of highlights by
Benjamin Fine(
)
9 editions published in 2017 in English and held by 799 WorldCat member libraries worldwide
This twovolume 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. ContentsThe natural, integral and rational numbersDivision and factorization in the integersModular arithmeticExceptional numbersPythagorean triples and sums of squaresPolynomials and unique factorizationField extensions and splitting fieldsPermutations and symmetric polynomialsReal numbersThe complex numbers, the Fundamental Theorem of Algebra and polynomial equationsQuadratic number fields and Pell{u2019}s equationTranscendental numbers and the numbers e and sCompass and straightedge constructions and the classical problemsEuclidean vector spaces
9 editions published in 2017 in English and held by 799 WorldCat member libraries worldwide
This twovolume 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. ContentsThe natural, integral and rational numbersDivision and factorization in the integersModular arithmeticExceptional numbersPythagorean triples and sums of squaresPolynomials and unique factorizationField extensions and splitting fieldsPermutations and symmetric polynomialsReal numbersThe complex numbers, the Fundamental Theorem of Algebra and polynomial equationsQuadratic number fields and Pell{u2019}s equationTranscendental numbers and the numbers e and sCompass and straightedge constructions and the classical problemsEuclidean vector spaces
The fundamental theorem of algebra by
Benjamin Fine(
Book
)
17 editions published between 1996 and 2009 in English and German and held by 717 WorldCat member libraries worldwide
"The Fundamental Theorem of Algebra states that any complex polynomial must have a complex root. This basic result, whose first accepted proof was given by Gauss, lies really at the intersection of the theory of numbers and the theory of equations and arises also in many other areas of mathematics. The purpose of this book is to examine 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 lends itself to generalizations which in turn lead 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 [rho] and [pi] are presented. Finally, a series of appendices give six additional proofs including a version of Gauss's original first proof." "The book is intended for junior/seniorlevel undergraduate mathematics students or firstyear graduate students. It is ideal for a "capstone" course in mathematics. It could also be used as an alternative approach to an undergraduate abstract algebra course. Finally, because of the breadth of topics it covers it would also be ideal for a graduate course for mathematics teachers."Jacket
17 editions published between 1996 and 2009 in English and German and held by 717 WorldCat member libraries worldwide
"The Fundamental Theorem of Algebra states that any complex polynomial must have a complex root. This basic result, whose first accepted proof was given by Gauss, lies really at the intersection of the theory of numbers and the theory of equations and arises also in many other areas of mathematics. The purpose of this book is to examine 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 lends itself to generalizations which in turn lead 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 [rho] and [pi] are presented. Finally, a series of appendices give six additional proofs including a version of Gauss's original first proof." "The book is intended for junior/seniorlevel undergraduate mathematics students or firstyear graduate students. It is ideal for a "capstone" course in mathematics. It could also be used as an alternative approach to an undergraduate abstract algebra course. Finally, because of the breadth of topics it covers it would also be ideal for a graduate course for mathematics teachers."Jacket
Number theory : an introduction via the distribution of primes by
Benjamin Fine(
)
25 editions published between 2006 and 2016 in English and held by 687 WorldCat member libraries worldwide
"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."Jacket
25 editions published between 2006 and 2016 in English and held by 687 WorldCat member libraries worldwide
"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."Jacket
Number theory : an introduction via the density of primes by
Benjamin Fine(
)
16 editions published between 2007 and 2016 in English and German and held by 338 WorldCat member libraries worldwide
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 padic numbers, Hensel's lemma, multiple zetavalues, 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 userfriendly 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 selfstudy 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
16 editions published between 2007 and 2016 in English and German and held by 338 WorldCat member libraries worldwide
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 padic numbers, Hensel's lemma, multiple zetavalues, 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 userfriendly 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 selfstudy 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
Combinatorial group theory, discrete groups, and number theory : a conference in honor of Gerhard Rosenberger, December 89,
2004, Fairfield University : AMS Special Session on Infinite Groups, October 89, 2005, Bard College by
AMS Special Session on Infinite Groups(
Book
)
13 editions published between 2006 and 2012 in English and held by 235 WorldCat member libraries worldwide
13 editions published between 2006 and 2012 in English and held by 235 WorldCat member libraries worldwide
Algebraic generalizations of discrete groups : a path to combinatorial group theory through onerelator products by
Benjamin Fine(
Book
)
8 editions published in 1999 in English and held by 219 WorldCat member libraries worldwide
"Building on the achievements of combinatorial group theory, first established as a response to infinite discrete groups used in topological studies by Poincare, this reference/text thoroughly surveys onerelator groups and onerelator products of cyclic groups  extending the algebraic study of Fuchsian groups to the more general context of onerelator products and related group theoretical constructions."BOOK JACKET. "Algebraic Generalizations of Discrete Groups is an indispensable reference for pure and applied mathematicians, algebraist, and number theorists, and a superb text for graduate students in these disciplines."Jacket
8 editions published in 1999 in English and held by 219 WorldCat member libraries worldwide
"Building on the achievements of combinatorial group theory, first established as a response to infinite discrete groups used in topological studies by Poincare, this reference/text thoroughly surveys onerelator groups and onerelator products of cyclic groups  extending the algebraic study of Fuchsian groups to the more general context of onerelator products and related group theoretical constructions."BOOK JACKET. "Algebraic Generalizations of Discrete Groups is an indispensable reference for pure and applied mathematicians, algebraist, and number theorists, and a superb text for graduate students in these disciplines."Jacket
Computational and combinatorial group theory and cryptography : AMS Special Sessions: Computational Algebra, Groups, and Applications,
April 30May 1, 2011, University of Nevada, Las Vegas, NV, Mathematical Aspects of Cryptography and Cyber Security, September
1011, 2011, Cornell University, Ithaca, NY(
Book
)
14 editions published in 2012 in English and held by 204 WorldCat member libraries worldwide
14 editions published in 2012 in English and held by 204 WorldCat member libraries worldwide
Diskrete algebraische Methoden Arithmetik, Kryptographie, Automaten und Gruppen by
Volker Diekert(
)
8 editions published between 2013 and 2016 in German and English and held by 135 WorldCat member libraries worldwide
From basic algebraic structures to cryptography, arithmetic with elliptic curves, and automata  this textbook contains a modern introduction to discrete algebraic methods as required by mathematicians and computer scientists in the age of the internet. It lays foundations for theoretical computer science and is suitable for master students with a basic background in mathematics
8 editions published between 2013 and 2016 in German and English and held by 135 WorldCat member libraries worldwide
From basic algebraic structures to cryptography, arithmetic with elliptic curves, and automata  this textbook contains a modern introduction to discrete algebraic methods as required by mathematicians and computer scientists in the age of the internet. It lays foundations for theoretical computer science and is suitable for master students with a basic background in mathematics
Elemente der diskreten Mathematik Zahlen und Zählen, Graphen und Verbände by
Volker Diekert(
)
7 editions published in 2013 in German and held by 134 WorldCat member libraries worldwide
The fundamental aim of this book is to communicate the knowledge necessary for a competent mathematical assessment of modern developments in the age of the Internet. Most crucially, this includes an understanding of very large graphs, calculating with large numbers, and calculating using prime number bases
7 editions published in 2013 in German and held by 134 WorldCat member libraries worldwide
The fundamental aim of this book is to communicate the knowledge necessary for a competent mathematical assessment of modern developments in the age of the Internet. Most crucially, this includes an understanding of very large graphs, calculating with large numbers, and calculating using prime number bases
Introduction to abstract algebra : from rings, numbers, groups, and fields to polynomials and Galois theory by
Benjamin Fine(
Book
)
6 editions published in 2014 in English and held by 113 WorldCat member libraries worldwide
"This textbook will help bring about the day when abstract algebra no longer creates intense anxiety but instead challenges students to fully grasp the meaning and power of the approach."Publisher's description
6 editions published in 2014 in English and held by 113 WorldCat member libraries worldwide
"This textbook will help bring about the day when abstract algebra no longer creates intense anxiety but instead challenges students to fully grasp the meaning and power of the approach."Publisher's description
The elementary theory of groups : a guide through the proofs of the Tarski conjectures by
Benjamin Fine(
Book
)
4 editions published in 2014 in English and held by 96 WorldCat member libraries worldwide
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. This book is an examination of the material on the general elementary theory of groups that is necessary to begin to understand the proofs. B. Fine, Fairfield U.; A. Gaglione, US Naval Academy; A. Myasnikov, McGill U.; G. Rosenberger, U. of Passau;D. Spellman, Temple U
4 editions published in 2014 in English and held by 96 WorldCat member libraries worldwide
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. This book is an examination of the material on the general elementary theory of groups that is necessary to begin to understand the proofs. B. Fine, Fairfield U.; A. Gaglione, US Naval Academy; A. Myasnikov, McGill U.; G. Rosenberger, U. of Passau;D. Spellman, Temple U
Einführung in die kombinatorische und die geometrische Gruppentheorie by
Thorsten Camps(
Book
)
2 editions published in 2008 in German and held by 46 WorldCat member libraries worldwide
2 editions published in 2008 in German and held by 46 WorldCat member libraries worldwide
Einführung in die mengentheoretische und die algebraische Topologie by
Thorsten Camps(
Book
)
1 edition published in 2006 in German and held by 43 WorldCat member libraries worldwide
1 edition published in 2006 in German and held by 43 WorldCat member libraries worldwide
Elementary Theory of Groups and Group Rings, and Related Topics : Proceedings of the Conference held at Fairfield University
and at the Graduate Center, CUNY, November 12, 2018 by
Vladimir Shpilrain(
)
7 editions published in 2020 in English and Undetermined and held by 39 WorldCat member libraries worldwide
This proceedings volume documents the contributions presented at the conference held at Fairfield University and at the Graduate Center, CUNY in 2018 celebrating the New York Group Theory Seminar, in memoriam Gilbert Baumslag, and to honor Benjamin Fine and Anthony Gaglione. It includes several expert contributions by leading figures in the group theory community and provides a valuable source of information on recent research developments
7 editions published in 2020 in English and Undetermined and held by 39 WorldCat member libraries worldwide
This proceedings volume documents the contributions presented at the conference held at Fairfield University and at the Graduate Center, CUNY in 2018 celebrating the New York Group Theory Seminar, in memoriam Gilbert Baumslag, and to honor Benjamin Fine and Anthony Gaglione. It includes several expert contributions by leading figures in the group theory community and provides a valuable source of information on recent research developments
Geometry and discrete mathematics a selection of highlights by
Benjamin Fine(
Book
)
5 editions published in 2018 in English and held by 37 WorldCat member libraries worldwide
"This twovolume set collects and presents the fundamentals of mathematics in an exciting and pedagogically sound way. The present volume examines the most important basic results in geometry and discrete mathematics, along with their proofs, and also their history."
5 editions published in 2018 in English and held by 37 WorldCat member libraries worldwide
"This twovolume set collects and presents the fundamentals of mathematics in an exciting and pedagogically sound way. The present volume examines the most important basic results in geometry and discrete mathematics, along with their proofs, and also their history."
ČSSR, [19621968] : Dokumentation und Kritik by
F Roell(
Book
)
6 editions published in 1968 in German and Undetermined and held by 29 WorldCat member libraries worldwide
6 editions published in 1968 in German and Undetermined and held by 29 WorldCat member libraries worldwide
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Related Identities
 Fine, Benjamin 1948 Other Contributor Author Editor
 Spellman, Dennis 1945 Other Editor Contributor Author
 Gaglione, Anthony M. Other Editor
 Kufleitner, Manfred Other Author
 Hertrampf, Ulrich Author
 Moldenhauer, Anja Other Author Editor
 Carstensen, Celine Author
 Kreuzer, Martin Contributor
 Baumslag, Gilbert Performer Author Contributor
 Gaglione, Anthony Contributor
Associated Subjects
Algebra Algebra, Abstract Algebraic topology Algorithms Coding theory Combinatorial analysis Combinatorial group theory Communism Computer scienceMathematics Cryptography CryptographyMathematics Czechoslovakia Data encryption (Computer science) Data structures (Computer science) Discrete groups Engineering mathematics Fundamental theorem of algebra Galois theory Geometry Geometry, Algebraic Global analysis (Mathematics) Group theory Infinite groups Logic, Symbolic and mathematical Mathematical analysis Mathematics Numbers, Prime Number theory Ordered algebraic structures Politics and government Proof theory Public key cryptography Representations of groups Tarski, Alfred, Topological spaces Topology United States