Benjamin Fine - Böcker
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24 produkter
24 produkter
856 kr
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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 prooof 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 trascendence 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. 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 mathmatics teachers.
340 kr
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In the preface of this new book, Dr. Fine states, “In the extensive literature on human and sexual liberation, there is a startling omission--the psychology of man.” In response to this enormous oversight, Dr. Fine has written The Forgotten Man, an important book that clearly demonstrates how many dimensions of the male's psychic structure and psychodynamics have either been neglected and/or misunderstood by many psychoanalytically oriented clinicians. As a result, professionals of all persuasions and non-professionals have “forgotten” about many of the male's dilemmas and stresses. This frank, controversial, sometimes startling book covers the topics of sexuality, aggression, social roles, and love as they influence the development of the male psyche. Dr. Fine, a world-renowned psychologist comments on man's loves and hates; his sexual desires, practices, and conflicts; his problems with aggression; his anxieties, trials, and tribulations with women; and his difficulties in maturing.In addition to his brilliant theoretical formulations, Dr. Fine provides us with penetrating analyses of men from all walks of life--politicians, businessmen, psychologists, athletes, and many more. He shows us healthy men, ill men, loving men, hateful men, those who are too uptight and those who are too loose, winners and losers.Thorough scholarship and detailed research distinguish this landmark volume. Readable, insightful, and desperately needed, The Forgotten Man tells of the rocky roads to manhood and fatherhood, the myths about men promulgated by the women's movement, and the relationship between aggression and sexual performance. The book contains references, chapter notes, and discussions by 10 recognized critics that alone cover 54 pages.
Introduction to Abstract Algebra
From Rings, Numbers, Groups, and Fields to Polynomials and Galois Theory
Inbunden, Engelska, 2014
1 092 kr
Skickas inom 7-10 vardagar
Introduction to Abstract Algebra presents a breakthrough approach to teaching one of math's most intimidating concepts. Avoiding the pitfalls common in the standard textbooks, Benjamin Fine, Anthony M. Gaglione, and Gerhard Rosenberger set a pace that allows beginner-level students to follow the progression from familiar topics such as rings, numbers, and groups to more difficult concepts. Classroom tested and revised until students achieved consistent, positive results, this textbook is designed to keep students focused as they learn complex topics. Fine, Gaglione, and Rosenberger's clear explanations prevent students from getting lost as they move deeper and deeper into areas such as abelian groups, fields, and Galois theory. 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.Topics covered include: rings; integral domains; the fundamental theorem of arithmetic; fields; groups; Lagrange's theorem; isomorphism theorems for groups; fundamental theorem of finite abelian groups; the simplicity of A n for n=5; Sylow theorems; the Jordan-Holder theorem; Ring isomorphism theorems; Euclidean domains; principal ideal domains; the fundamental theorem of algebra; Vector spaces; Algebras; field extensions: algebraic and transcendental; the fundamental theorem of Galois theory; and the insolvability of the quintic.
612 kr
Skickas inom 10-15 vardagar
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.
Elementary Theory of Groups
A Guide through the Proofs of the Tarski Conjectures
Inbunden, Engelska, 2014
2 547 kr
Skickas inom 5-8 vardagar
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.
632 kr
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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
Abstract Algebra
Applications to Galois Theory, Algebraic Geometry, Representation Theory and Cryptography
Häftad, Engelska, 2019
676 kr
Skickas inom 5-8 vardagar
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 1-2, 2018
Inbunden, Engelska, 2020
1 858 kr
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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.
Topics in Infinite Group Theory
Nielsen Methods, Covering Spaces, and Hyperbolic Groups
Häftad, Engelska, 2021
936 kr
Skickas inom 5-8 vardagar
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.
682 kr
Skickas inom 3-6 vardagar
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.
794 kr
Skickas inom 5-8 vardagar
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.
Topics in Infinite Group Theory
Nielsen Methods, Covering Spaces, and Hyperbolic Groups
Häftad, Engelska, 2024
1 081 kr
Skickas inom 3-6 vardagar
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.
636 kr
Skickas
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 TheoremConcise treatment of algebraic number theory, including a complete presentation of primes, prime factorizations in algebraic number fields, and unique factorization of idealsDiscussion of the AKS algorithm, which shows that primality testing is one of polynomial time, a topic not usually included in such textsMany interesting ancillary topics, such as primality testing and cryptography, Fermat and Mersenne numbers, and Carmichael numbersThe 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.
718 kr
Skickas inom 10-15 vardagar
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 TheoremConcise treatment of algebraic number theory, including a complete presentation of primes, prime factorizations in algebraic number fields, and unique factorization of idealsDiscussion of the AKS algorithm, which shows that primality testing is one of polynomial time, a topic not usually included in such textsMany interesting ancillary topics, such as primality testing and cryptography, Fermat and Mersenne numbers, and Carmichael numbersThe 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.
Del 273 - Studies in Critical Social Sciences
Cliometrics as Economics Imperialism: Across the Watershed
Critical Reconstructions of Political Economy, Volume 3
Inbunden, Engelska, 2023
2 443 kr
Skickas inom 5-8 vardagar
In Cliometrics as Economics Imperialism, Ben Fine traces the cliometric revolution, from before its emergence through three phases of the new, the newer and the newest economic history. These phases are shown to correspond to those of “economics imperialism”, the colonisation of topics and fields by mainstream economics, moving successively through as if there were perfectly working markets, as if imperfectly working markets, and these combined plus arbitrary inclusion of other variables.The text draws upon case studies, for example of the putative eighteenth-century consumer revolution, Douglass North, path dependence, and the British coal industry, and through exposing the reduction of economic theory and economic history deployed within them and giving rise to a corresponding reduction in the presence of the social, the historical and political economy.
Del 290 - Studies in Critical Social Sciences
Financialisation of Social Reproduction in the Age of Neoliberalism: From Theory to Case Studies
Critical Reconstructions of Political Economy, Volume 4
Inbunden, Engelska, 2024
2 058 kr
Skickas inom 3-6 vardagar
Drawing upon comprehensive research across five countries, including case studies of housing, water, and health, comprehensive theoretical and empirical accounts are offered of the impact of financialisation on economic and social reproduction, alongside the corresponding material cultures of neoliberalism. Economic is understood as embedded within social reproduction, with neoliberalism, as the current stage of capitalism, fundamentally underpinned by, but not reducible to, the financialisation of everyday life. Considerable emphasis is placed upon the variegated outcomes attached to the neoliberalisation of social reproduction, as highlighted by the comparative study of economic and social provisioning across different countries and sectors.
Del 312 - Studies in Critical Social Sciences
In and against Development: From New to Newest Development Economics
Critical Reconstructions of Political Economy, Volume 5
Inbunden, Engelska, 2025
1 928 kr
Skickas inom 3-6 vardagar
The Economics of Everything, or Economics Imperialism, now has a dominant presence in development economics, and an agenda-setting role in development studies, with the World Bank taking a leading, if contested, role. This volume examines how this happened, charting the evolution from the old or classic development economics through the new, newer and newest development economics. Drawing critically upon the Kuhnian notions of paradigm shifts, corresponding changes are contextualised materially, intellectually and policy-wise. Covering key issues such as famine, the developmental state, and trade and industrial policy, detailed attention is paid to the potential for alternatives for economics and economic policies.
Del 314 - Studies in Critical Social Sciences
In and against Development
The World Bank behind the Looking Glass
Inbunden, Engelska, 2025
1 560 kr
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Long self-proclaimed as “Knowledge Bank”, the World Bank is as active as criticised in its endeavours across scholarship, ideology and policy in practice, serving US interests in the age of globalisation, neoliberalism and financialisation. This Volume focuses on the Bank’s scholarship, meticulously criticising it and assessing alternatives. Its analytical framing draws upon economics imperialism in general, and its evolution through three phases. Corresponding phases of new, newer and newest development economics are identified, with the World Bank taking a leading role in each, with implications for the expanding scope of development economics and its contestations with development studies.
Del 344 - Studies in Critical Social Sciences
Debating Economic Policy for South Africa’s Post-apartheid Transition: From Scholarship and Ideology to Policy in Practice
Critical Reconstructions of Political Economy, Volume 8
Inbunden, Engelska, 2025
2 295 kr
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The reasons for South Africa’s full and rapid post-apartheid embrace of neoliberal economic policy remain controversial. Drawing on the author’s own participation in policy debates, this volume establishes there were alternatives available that were either dismissed or not even considered. Explanations for policy failings have to be sought in determinants such as globalisation, financialisation, capital flight, corporate restructuring and Black Economic Empowerment. The text offers extensive surveys of relevant literature including the developmental state, industrial and social policy, privatisation, trade policy, the Harvard School, comparative experience and the deficiencies in the country’s National Development Plan and New Growth Path.
Del 350 - Studies in Critical Social Sciences
Political Economy of South Africa Revisited: Tracking and Debating the Minerals-Energy and Financial Complex
Critical Reconstructions of Political Economy, Volume 9
Inbunden, Engelska, 2025
2 317 kr
Skickas inom 3-6 vardagar
South Africa’s political economy is commonly understood as a Minerals-Energy (and Financial) Complex, ME(F)C. But the MEC has been misunderstood. Specifying the MEFC as a system of accumulation and drawing upon extensive research and engaging in critical debates, the originator of the term, traces the MEFC from apartheid origins, through the ANC’s failure to adopt coherent and coordinated policies, ultimately leading to degeneration into state capture and beyond. Emphasis is placed upon the interaction between South African specificities and globalisation, neoliberalisation and financialisation, anchoring economic and social reproduction in “five lows” across investment, productivity, wages, employment and social provision.
- Nyhet
From Orthodox to Heterodox Economics and Beyond: How Mainstream Neoclassical Economics Got to Be the Way It Is and How It Needs to Change: Critical Re
Inbunden, Engelska, 2026
1 719 kr
Kommande
- Nyhet
From Value in Production to Value in Exchange: Marxist Political Economy Revisited: Critical Reconstructions of Political Economy, Volume 11
Inbunden, Engelska, 2026
1 872 kr
Kommande
Del 1 - Algebra And Discrete Mathematics
Aspects Of Infinite Groups: A Festschrift In Honor Of Anthony Gaglione
Inbunden, Engelska, 2008
1 417 kr
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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.
1 105 kr
Skickas
The development of algebraic geometry over groups, geometric group theory and group-based cryptography, has led to there being a tremendous recent interest in infinite group theory. This volume presents a good collection of papers detailing areas of current interest.