Benjamin Baumslag's Books

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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Page Count

322

Publisher

Walter de Gruyter GmbH & Co KG

Published Date

ISBN 10

3110342030

ISBN 13

9783110342031

Topics in Infinite Group Theory

Nielsen Methods, Covering Spaces, and Hyperbolic Groups

By: Benjamin Fine,Anja Moldenhauer,Gerhard Rosenberger,Annika Schürenberg,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,Annika Schürenberg,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. New edition now includes the topics on universal free groups, quasiconvex subgroups and hyperbolic groups, and also Stallings foldings and subgroups of free groups. New results on groups of F-types are added.

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Page Count

424

Publisher

Walter de Gruyter GmbH & Co KG

Published Date

ISBN 10

311134004X

ISBN 13

9783111340043

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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Page Count

338

Publisher

CRC Press

Published Date

ISBN 10

0824703197

ISBN 13

9780824703196

Combinatorial Group Theory

Proceedings of the AMS Special Session in Combinatorial Group Theory-infinite Groups, April 23-24, 1988

By: Benjamin Fine

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Combinatorial Group Theory

Proceedings of the AMS Special Session in Combinatorial Group Theory-infinite Groups, April 23-24, 1988

By: Benjamin Fine

Eighteen papers presented during a special AMS session designed to draw together researchers in various areas of infinite group theory, especially combinatorial group theory, to share methods and results.

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Page Count

206

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821851160

ISBN 13

9780821851166

Aspects of Infinite Groups

A Festschrift in Honor of Anthony Gaglione

By: Benjamin Fine

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Aspects of Infinite Groups

A Festschrift in Honor of Anthony Gaglione

By: Benjamin Fine

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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Page Count

253

Publisher

World Scientific

Published Date

ISBN 10

9812793410

ISBN 13

9789812793416

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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Page Count

423

Publisher

Birkhäuser

Published Date

ISBN 10

3319438751

ISBN 13

9783319438757

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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Page Count

381

Publisher

Walter de Gruyter

Published Date

ISBN 10

311025008X

ISBN 13

9783110250084

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

Publisher

Walter de Gruyter GmbH & Co KG

Published Date

ISBN 10

3110605252

ISBN 13

9783110605259

Algebra and Number Theory

A Selection of Highlights

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

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Algebra and Number Theory

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 fundamental results in Algebra and Number Theory along with their proofs and their history. In the second edition, we include additional material on perfect and triangular numbers. We also added new sections on elementary Group Theory, p-adic numbers, and Galois Theory. A true collection of mathematical gems in Algebra and Number Theory, including the integers, the reals, and the complex numbers, along with beautiful results from Galois Theory and associated geometric applications. Valuable for lecturers, teachers and students of mathematics as well as for all who are mathematically interested.

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Page Count

513

Publisher

Walter de Gruyter GmbH & Co KG

Published Date

ISBN 10

3110790394

ISBN 13

9783110790399

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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Page Count

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

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Solve jigsaw puzzle

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Page Count

339

Publisher

Walter de Gruyter GmbH & Co KG

Published Date

ISBN 10

3110673401

ISBN 13

9783110673401

Book's by Benjamin Baumslag

The Elementary Theory of Groups

The Elementary Theory of Groups

Topics in Infinite Group Theory

Topics in Infinite Group Theory

Algebraic Generalizations of Discrete Groups

Algebraic Generalizations of Discrete Groups

Combinatorial Group Theory

Combinatorial Group Theory

Aspects of Infinite Groups

Aspects of Infinite Groups

Number Theory

Number Theory

Abstract Algebra

Abstract Algebra

Abstract Algebra

Abstract Algebra

Algebra and Number Theory

Algebra and Number Theory

A Course in Mathematical Cryptography

A Course in Mathematical Cryptography

Topics in Infinite Group Theory

Topics in Infinite Group Theory

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