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Essays in Constructive Mathematics, Edwards


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Автор: Edwards
Название:  Essays in Constructive Mathematics
ISBN: 9783030985578
Издательство: Springer
Классификация:




ISBN-10: 3030985571
Обложка/Формат: Hardback
Страницы: 322
Вес: 0.67 кг.
Дата издания: 14.10.2022
Язык: English
Издание: 2nd ed. 2022
Иллюстрации: 325 illustrations, color; 65 illustrations, black and white; xiv, 322 p. 390 illus., 325 illus. in color.
Размер: 235 x 155
Читательская аудитория: Professional & vocational
Основная тема: Mathematics
Ссылка на Издательство: Link
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Поставляется из: Германии
Описание: This collection of essays aims to promote constructive mathematics, not by defining it or formalizing it, but by practicing it. All definitions and proofs are based on finite algorithms, which pave illuminating paths to nontrivial results, primarily in algebra, number theory, and the theory of algebraic curves. The second edition adds a new set of essays that reflect and expand upon the first. The topics covered derive from classic works of nineteenth-century mathematics, among them Galois’s theory of algebraic equations, Gauss’s theory of binary quadratic forms, and Abel’s theorems about integrals of rational differentials on algebraic curves. Other topics include Newtons diagram, the fundamental theorem of algebra, factorization of polynomials over constructive fields, and the spectral theorem for symmetric matrices, all treated using constructive methods in the spirit of Kronecker. In this second edition, the essays of the first edition are augmented with new essays that give deeper and more complete accounts of Galois’s theory, points on an algebraic curve, and Abel’s theorem. Readers will experience the full power of Galois’s approach to solvability by radicals, learn how to construct points on an algebraic curve using Newton’s diagram, and appreciate the amazing ideas introduced by Abel in his 1826 Paris memoir on transcendental functions. Mathematical maturity is required of the reader, and some prior knowledge of Galois theory is helpful. But experience with constructive mathematics is not necessary; readers should simply be willing to set aside abstract notions of infinity and explore deep mathematics via explicit constructions.
Дополнительное описание: Part I.- 1. A Fundamental Theorem.- 2. Topics in Algebra.- 3. Some Quadratic Problems.- 4. The Genus of an Algebraic Curve.- 5. Miscellany. Part II.- 6. Constructive Algebra.- 7. The Algorithmic Foundation of Galois's Theory.- 8. A Constructive Definition



How to Prove It : A Structured Approach

Автор: Daniel J. Velleman
Название: How to Prove It : A Structured Approach
ISBN: 1108439535 ISBN-13(EAN): 9781108439534
Издательство: Cambridge Academ
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Цена: 5861.00 р.
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Описание: Proofs play a central role in advanced mathematics and theoretical computer science, and this bestselling text`s third edition will help students transition from solving problems to proving theorems by teaching them the techniques needed to read and write proofs, with a new chapter on number theory and over 150 new exercises.

Algebra

Автор: Lang
Название: Algebra
ISBN: 038795385X ISBN-13(EAN): 9780387953854
Издательство: Springer
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Цена: 8378.00 р.
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Описание: "Lang's Algebra changed the way graduate algebra is taught, retaining classical topics but introducing language and ways of thinking from category theory and homological algebra. It has affected all subsequent graduate-level algebra books."  NOTICES OF THE AMS"The author has an impressive knack for presenting the important and interesting ideas of algebra in just the right way, and he never gets bogged down in the dry formalism which pervades some parts of algebra." MATHEMATICAL REVIEWSThis book is intended as a basic text for a one-year course in algebra at the graduate level, or as a useful reference for mathematicians and professionals who use higher-level algebra. It successfully addresses the basic concepts of algebra.  For the revised third edition, the author has added exercises and made numerous corrections to the text.

Algebra

Автор: Paolo Aluffi
Название: Algebra
ISBN: 1108958230 ISBN-13(EAN): 9781108958233
Издательство: Cambridge Academ
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Цена: 5069.00 р.
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Описание: This conversational introduction to abstract algebra takes a modern, rings-first approach. In addition to its unconventional order of classical material, another key feature is the treatment of topics often neglected in undergraduate textbooks, such as modules. More than 400 exercises are included, 150 of which are carefully worked out.

Categories for the Working Mathematician

Автор: Mac Lane
Название: Categories for the Working Mathematician
ISBN: 0387984038 ISBN-13(EAN): 9780387984032
Издательство: Springer
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Цена: 7819.00 р.
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Описание: This second edition includes a number of revisions and additions, including new chapters on topics of active interest: symmetric monoidal categories and braided monoidal categories, and the coherence theorems for them, as well as 2-categories and the higher dimensional categories which have recently come into prominence.

All the Math You Missed

Автор: Thomas A. Garrity
Название: All the Math You Missed
ISBN: 1009009192 ISBN-13(EAN): 9781009009195
Издательство: Cambridge Academ
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Цена: 3960.00 р.
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Описание: The second edition of this bestselling book provides an overview of the key topics in undergraduate mathematics, allowing beginning graduate students to fill in any gaps in their knowledge. With numerous examples, exercises and suggestions for further reading, it is a must-have for anyone looking to learn some serious mathematics quickly.

Numerical linear algebra

Автор: Trefethen, Lloyd N. Bau, David, Iii
Название: Numerical linear algebra
ISBN: 0898713617 ISBN-13(EAN): 9780898713619
Издательство: Mare Nostrum (Eurospan)
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Цена: 9656.00 р.
Наличие на складе: Нет в наличии.

Описание: Numerical Linear Algebra is a concise, insightful, and elegant introduction to the field of numerical linear algebra.

A Course in Algebra Graduate Studies in Mathematics, Volume: 56

Автор: E.B. Vinberg
Название: A Course in Algebra Graduate Studies in Mathematics, Volume: 56
ISBN: 0821834134 ISBN-13(EAN): 9780821834138
Издательство: Mare Nostrum (Eurospan)
Рейтинг:
Цена: 5174.00 р.
Наличие на складе: Есть (более 5-х шт.)
Описание: Presents modern algebra. This book includes such topics as affine and projective spaces, tensor algebra, Galois theory, Lie groups, and associative algebras and their representations. It is suitable for independent study for advanced undergraduates and graduate students.

Conceptual Mathematics

Автор: F. William Lawvere
Название: Conceptual Mathematics
ISBN: 052171916X ISBN-13(EAN): 9780521719162
Издательство: Cambridge Academ
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Цена: 7762.00 р.
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Описание: Conceptual Mathematics introduces the concept of category to beginning students and practising mathematical scientists based on a leisurely introduction to the important categories of directed graphs and discrete dynamical systems. The expanded second edition approaches more advanced topics via historical sketches and a concise introduction to adjoint functors.

Alan M. Turing

Автор: Turing
Название: Alan M. Turing
ISBN: 1107524229 ISBN-13(EAN): 9781107524224
Издательство: Cambridge Academ
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Цена: 2533.00 р.
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Описание: To commemorate the centenary of Turing`s birth, this republication of his mother`s biography contains a new foreword by Martin Davis and a never-before-published memoir by Alan`s brother. The contrast between this memoir and the original biography sheds new light on Turing`s relationship with his family, and on the man himself.

A Primer of Algebraic Geometry

Автор: Li, Huishi
Название: A Primer of Algebraic Geometry
ISBN: 082470374X ISBN-13(EAN): 9780824703745
Издательство: Taylor&Francis
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Цена: 19906.00 р.
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Functional interpretations: from the dialectica interpretation to interpretations of classical and constructive set theory

Автор: Diller, Justus (univ Of Munster, Germany)
Название: Functional interpretations: from the dialectica interpretation to interpretations of classical and constructive set theory
ISBN: 9814551392 ISBN-13(EAN): 9789814551397
Издательство: World Scientific Publishing
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Цена: 14256.00 р.
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Описание: This book gives a detailed treatment of functional interpretations of arithmetic, analysis, and set theory. The subject goes back to G del's Dialectica interpretation of Heyting arithmetic which replaces nested quantification by higher type operations and thus reduces the consistency problem for arithmetic to the problem of computability of primitive recursive functionals of finite types. Regular functional interpretations, in particular the Dialectica interpretation and its generalization to finite types, the Diller-Nahm interpretation, are studied on Heyting as well as Peano arithmetic in finite types and extended to functional interpretations of constructive as well as classical systems of analysis and set theory. Kreisel's modified realization and Troelstra's hybrids of it are presented as interpretations of Heyting arithmetic and extended to constructive set theory, both in finite types. They serve as background for the construction of hybrids of the Diller-Nahm interpretation of Heyting arithmetic and constructive set theory, again in finite types. All these functional interpretations yield relative consistency results and closure under relevant rules of the theories in question as well as axiomatic characterizations of the functional translations.

Noncommutative Polynomial Algebras of Solvable Type and Their Modules: Basic Constructive-Computational Theory and Methods

Автор: Li Huishi
Название: Noncommutative Polynomial Algebras of Solvable Type and Their Modules: Basic Constructive-Computational Theory and Methods
ISBN: 1032079886 ISBN-13(EAN): 9781032079882
Издательство: Taylor&Francis
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Цена: 24499.00 р.
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Описание: This is the first book to systematically introduce the basic constructive-computational theory and methods developed for investigating solvable polynomial algebras and their modules. This book is perfectly suited to researchers and postgrads researching noncommutative computational algebra.


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