{"title":"Benjamin Fine","description":"\u003cp\u003eDive into the captivating worlds crafted by Benjamin Fine, where thrilling mysteries and intricate plots await. Perfect for fans of intelligent suspense and gripping storytelling. Start your literary journey here.\u003c\/p\u003e","products":[{"product_id":"fundamental-theorem-of-algebra-book-benjamin-fine-9780387946573","title":"The Fundamental Theorem of Algebra","description":"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. It is ideal for a \"capstone\" course in mathematics for junior\/senior level undergraduate mathematics students or first year graduate students. 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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. 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Boards are a little rub worn, slight shelf wear to corners, s","brand":"WoB","offers":[{"title":"GB \/ GOOD \/ INTERNAL","offer_id":50074144211217,"sku":"1664279086ADA","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/1664279086ADA_1.jpg?v=1722882731"},{"product_id":"algebra-and-number-theory-book-benjamin-fine-9783110789980","title":"Algebra and Number Theory","description":"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.","brand":"WoB","offers":[{"title":"US \/ NEW \/ INGRAM","offer_id":51060636483857,"sku":"NIN9783110789980","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"GB \/ NEW \/ INGRAM","offer_id":52401252008209,"sku":"NLS9783110789980","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/3110789981.jpg?v=1775124303"},{"product_id":"number-theory-book-benjamin-fine-9783319829319","title":"Number Theory","description":"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.","brand":"WoB","offers":[{"title":"- \/ - \/ -","offer_id":51060777091345,"sku":"","price":0.0,"currency_code":"GBP","in_stock":true},{"title":"US \/ NEW \/ INGRAM","offer_id":51060779811089,"sku":"NIN9783319829319","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"GB \/ NEW \/ INGRAM","offer_id":52584190509329,"sku":"NLS9783319829319","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/3319829319.jpg?v=1751382681"},{"product_id":"topics-in-infinite-group-theory-book-benjamin-fine-9783111339566","title":"Topics in Infinite Group Theory","description":"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.","brand":"WoB","offers":[{"title":"- \/ - \/ -","offer_id":51064869585169,"sku":"","price":0.0,"currency_code":"GBP","in_stock":true},{"title":"US \/ NEW \/ INGRAM","offer_id":51064871878929,"sku":"NIN9783111339566","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/3111339564.jpg?v=1750998723"},{"product_id":"elementary-theory-of-groups-book-benjamin-fine-9783110341997","title":"The Elementary Theory of Groups","description":"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.","brand":"WoB","offers":[{"title":"- \/ - \/ -","offer_id":51187696730385,"sku":"","price":0.0,"currency_code":"GBP","in_stock":true},{"title":"US \/ NEW \/ INGRAM","offer_id":51187698991377,"sku":"NIN9783110341997","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"GB \/ NEW \/ INGRAM","offer_id":52135815053585,"sku":"NLS9783110341997","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/3110341999.jpg?v=1750967261"},{"product_id":"geometry-and-discrete-mathematics-book-benjamin-fine-9783110740776","title":"Geometry and Discrete Mathematics","description":"In the two-volume set ‘A Selection of Highlights’ we present basics of mathematics in an exciting and pedagogically sound way. 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Finally, a series of appendices give six additional proofs including a version of Gauss'original first proof.","brand":"WoB","offers":[{"title":"GB \/ NEW \/ INGRAM","offer_id":52089139757329,"sku":"NLS9781461273431","price":0.0,"currency_code":"GBP","in_stock":true},{"title":"US \/ NEW \/ INGRAM","offer_id":52750219215121,"sku":"NIN9781461273431","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9781461273431.jpg?v=1756905925"},{"product_id":"topics-in-infinite-group-theory-book-benjamin-fine-9783110673340","title":"Topics in Infinite Group Theory","description":"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. 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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.","brand":"WoB","offers":[{"title":"US \/ NEW \/ INGRAM","offer_id":52693011464465,"sku":"NIN9789004721548","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9789004721548.jpg?v=1768558579"},{"product_id":"in-and-against-development-book-ben-fine-9789004723504","title":"In and against Development","description":"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.","brand":"WoB","offers":[{"title":"US \/ NEW \/ INGRAM","offer_id":52693018444049,"sku":"NIN9789004723504","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9789004723504.jpg?v=1768560579"},{"product_id":"political-economy-of-south-africa-revisited-tracking-and-debating-the-minerals-e-book-ben-fine-9789004748323","title":"The Political Economy of South Africa Revisited: Tracking and Debating the Minerals-Energy and Financial Complex","description":"South Africa's political economy is commonly understood as a Minerals-Energy (and Financial) Complex, ME(F)C. 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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","brand":"WoB","offers":[{"title":"- \/ - \/ INTERNAL","offer_id":53005052444945,"sku":null,"price":0.0,"currency_code":"GBP","in_stock":true},{"title":"US \/ NEW \/ INGRAM","offer_id":53005052641553,"sku":"NIN9783110515848","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783110515848.jpg?v=1767853965"},{"product_id":"debating-economic-policy-for-south-africas-post-apartheid-transition-from-schola-book-ben-fine-9789004746565","title":"Debating Economic Policy for South Africa’s Post-apartheid Transition: From Scholarship and Ideology to Policy in Practice","description":"The reasons for South Africa's full and rapid post-apartheid embrace of neoliberal economic policy remain controversial. 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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.","brand":"WoB","offers":[{"title":"- \/ - \/ INTERNAL","offer_id":53398197469457,"sku":null,"price":0.0,"currency_code":"GBP","in_stock":true},{"title":"US \/ NEW \/ INGRAM","offer_id":53398197534993,"sku":"NIN9789004746565","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9789004746565.jpg?v=1775942889"}],"url":"https:\/\/www.worldofbooks.com\/en-au\/collections\/author-books-by-benjamin-fine.oembed","provider":"World of Books ","version":"1.0","type":"link"}