Algebra II

Chapters 4 - 7

Author: N. Bourbaki

Publisher: Springer Science & Business Media

ISBN: 3642616984

Category: Mathematics

Page: 453

View: 7315

This is a softcover reprint of chapters four through seven of the 1990 English translation of the revised and expanded version of Bourbaki’s Algebre. Much material was added or revised for this edition, which thoroughly establishes the theories of commutative fields and modules over a principal ideal domain.
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Automorphic Forms and L-Functions for the Group GL(n,R)

Author: Dorian Goldfeld

Publisher: Cambridge University Press

ISBN: 1139456202

Category: Mathematics

Page: N.A

View: 442

L-functions associated to automorphic forms encode all classical number theoretic information. They are akin to elementary particles in physics. This 2006 book provides an entirely self-contained introduction to the theory of L-functions in a style accessible to graduate students with a basic knowledge of classical analysis, complex variable theory, and algebra. Also within the volume are many new results not yet found in the literature. The exposition provides complete detailed proofs of results in an easy-to-read format using many examples and without the need to know and remember many complex definitions. The main themes of the book are first worked out for GL(2,R) and GL(3,R), and then for the general case of GL(n,R). In an appendix to the book, a set of Mathematica functions is presented, designed to allow the reader to explore the theory from a computational point of view.
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Weil Conjectures, Perverse Sheaves and l’adic Fourier Transform

Author: Reinhardt Kiehl,Rainer Weissauer

Publisher: Springer Science & Business Media

ISBN: 9783540414575

Category: Mathematics

Page: 375

View: 9193

In this book the authors describe the important generalization of the original Weil conjectures, as given by P. Deligne in his fundamental paper "La conjecture de Weil II". The authors follow the important and beautiful methods of Laumon and Brylinski which lead to a simplification of Deligne's theory. Deligne's work is closely related to the sheaf theoretic theory of perverse sheaves. In this framework Deligne's results on global weights and his notion of purity of complexes obtain a satisfactory and final form. Therefore the authors include the complete theory of middle perverse sheaves. In this part, the l-adic Fourier transform is introduced as a technique providing natural and simple proofs. To round things off, there are three chapters with significant applications of these theories.
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The American Mathematical Monthly

The Official Journal of the Mathematical Association of America

Author: N.A

Publisher: N.A

ISBN: N.A

Category: Mathematicians

Page: N.A

View: 8892

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Integration II

Chapters 7–9

Author: N. Bourbaki

Publisher: Springer Science & Business Media

ISBN: 9783540205852

Category: Mathematics

Page: 326

View: 2392

Integration is the sixth and last of the books that form the core of the Bourbaki series; it draws abundantly on the preceding five Books, especially General Topology and Topological Vector Spaces, making it a culmination of the core six. The power of the tool thus fashioned is strikingly displayed in Chapter II of the author's Théories Spectrales, an exposition, in a mere 38 pages, of abstract harmonic analysis and the structure of locally compact abelian groups. The first volume of the English translation comprises Chapters 1-6; the present volume completes the translation with the remaining Chapters 7-9. Chapters 1-5 received very substantial revisions in a second edition, including changes to some fundamental definitions. Chapters 6-8 are based on the first editions of Chapters 1-5. The English edition has given the author the opportunity to correct misprints, update references, clarify the concordance of Chapter 6 with the second editions of Chapters 1-5, and revise the definition of a key concept in Chapter 6 (measurable equivalence relations).
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General Topology

Chapters 1–4

Author: N. Bourbaki

Publisher: Springer Science & Business Media

ISBN: 3642617018

Category: Mathematics

Page: 437

View: 1818

This is the softcover reprint of the 1971 English translation of the first four chapters of Bourbaki’s Topologie Generale. It gives all basics of the subject, starting from definitions. Important classes of topological spaces are studied, and uniform structures are introduced and applied to topological groups. In addition, real numbers are constructed and their properties established.
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Algebra I

Chapters 1-3

Author: N. Bourbaki

Publisher: Springer Science & Business Media

ISBN: 9783540642435

Category: Mathematics

Page: 710

View: 3416

This is the softcover reprint of the English translation of 1974 (available from Springer since 1989) of the first 3 chapters of Bourbaki's 'Algebre'. It gives a thorough exposition of the fundamentals of general, linear and multilinear algebra. The first chapter introduces the basic objects; groups, actions, rings, fields. The second chapter studies the properties of modules and linear maps, especially with respect to the tensor product and duality constructions. The third chapter investigates algebras, in particular tensor algebras. Determinants, norms, traces and derivations are also studied.
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Literatur der Mathematik, Natur- und Gewerbs-Kunde

mit Inbegriff der Kriegskunst und anderer Künste, ausser den Schönen, seit der Mitte des achtzehnten Jahrhunderts bis auf die neueste Zeit

Author: Johann Samuel Ersch

Publisher: N.A

ISBN: N.A

Category: Industrial arts

Page: 1

View: 8986

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Algebra II

Chapters 4 - 7

Author: N. Bourbaki

Publisher: Springer

ISBN: 9783540193753

Category: Mathematics

Page: 453

View: 5779

This is a softcover reprint of chapters four through seven of the 1990 English translation of the revised and expanded version of Bourbaki’s Algebre. Much material was added or revised for this edition, which thoroughly establishes the theories of commutative fields and modules over a principal ideal domain.
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UML 2 Semantics and Applications

Author: Kevin Lano

Publisher: John Wiley & Sons

ISBN: 0470522615

Category: Computers

Page: 400

View: 7368

A coherent and integrated account of the leading UML 2 semantics work and the practical applications of UML semantics development With contributions from leading experts in the field, the book begins with an introduction to UML and goes on to offer in-depth and up-to-date coverage of: The role of semantics Considerations and rationale for a UML system model Definition of the UML system model UML descriptive semantics Axiomatic semantics of UML class diagrams The object constraint language Axiomatic semantics of state machines A coalgebraic semantic framework for reasoning about interaction designs Semantics of activity diagrams Verification of UML models State invariants Model transformation specification and verification Additionally, readers are provided with expert guidance on how to resolve semantic problems and a section on applications of UML semantics with model analysis. UML 2 Semantics and Applications is an ideal resource for researchers and tool-builders working in UML, among others. It is also an excellent textbook for postgraduate teaching and research.
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Hopf Algebras and Congruence Subgroups

Author: Yorck Sommerhäuser,Yongchang Zhu

Publisher: American Mathematical Soc.

ISBN: 0821869132

Category: Mathematics

Page: 134

View: 3374

The authors prove that the kernel of the action of the modular group on the center of a semisimple factorizable Hopf algebra is a congruence subgroup whenever this action is linear. If the action is only projective, they show that the projective kernel is a congruence subgroup. To do this, they introduce a class of generalized Frobenius-Schur indicators and endow it with an action of the modular group that is compatible with the original one.
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Foundations of Discrete Mathematics

Author: K. D. Joshi

Publisher: New Age International

ISBN: 9788122401202

Category: Combinatorial analysis

Page: 748

View: 5714

This Book Is Meant To Be More Than Just A Text In Discrete Mathematics. It Is A Forerunner Of Another Book Applied Discrete Structures By The Same Author. The Ultimate Goal Of The Two Books Are To Make A Strong Case For The Inclusion Of Discrete Mathematics In The Undergraduate Curricula Of Mathematics By Creating A Sequence Of Courses In Discrete Mathematics Parallel To The Traditional Sequence Of Calculus-Based Courses.The Present Book Covers The Foundations Of Discrete Mathematics In Seven Chapters. It Lays A Heavy Emphasis On Motivation And Attempts Clarity Without Sacrificing Rigour. A List Of Typical Problems Is Given In The First Chapter. These Problems Are Used Throughout The Book To Motivate Various Concepts. A Review Of Logic Is Included To Gear The Reader Into A Proper Frame Of Mind. The Basic Counting Techniques Are Covered In Chapters 2 And 7. Those In Chapter 2 Are Elementary. But They Are Intentionally Covered In A Formal Manner So As To Acquaint The Reader With The Traditional Definition-Theorem-Proof Pattern Of Mathematics. Chapters 3 Introduces Abstraction And Shows How The Focal Point Of Todays Mathematics Is Not Numbers But Sets Carrying Suitable Structures. Chapter 4 Deals With Boolean Algebras And Their Applications. Chapters 5 And 6 Deal With More Traditional Topics In Algebra, Viz., Groups, Rings, Fields, Vector Spaces And Matrices.The Presentation Is Elementary And Presupposes No Mathematical Maturity On The Part Of The Reader. Instead, Comments Are Inserted Liberally To Increase His Maturity. Each Chapter Has Four Sections. Each Section Is Followed By Exercises (Of Various Degrees Of Difficulty) And By Notes And Guide To Literature. Answers To The Exercises Are Provided At The End Of The Book.
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Algorithmic Cryptanalysis

Author: Antoine Joux

Publisher: CRC Press

ISBN: 9781420070033

Category: Computers

Page: 520

View: 2285

Illustrating the power of algorithms, Algorithmic Cryptanalysis describes algorithmic methods with cryptographically relevant examples. Focusing on both private- and public-key cryptographic algorithms, it presents each algorithm either as a textual description, in pseudo-code, or in a C code program. Divided into three parts, the book begins with a short introduction to cryptography and a background chapter on elementary number theory and algebra. It then moves on to algorithms, with each chapter in this section dedicated to a single topic and often illustrated with simple cryptographic applications. The final part addresses more sophisticated cryptographic applications, including LFSR-based stream ciphers and index calculus methods. Accounting for the impact of current computer architectures, this book explores the algorithmic and implementation aspects of cryptanalysis methods. It can serve as a handbook of algorithmic methods for cryptographers as well as a textbook for undergraduate and graduate courses on cryptanalysis and cryptography.
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Lie Groups and Lie Algebras

Chapters 1-3

Author: Nicolas Bourbaki

Publisher: Springer Science & Business Media

ISBN: 9783540642428

Category: Mathematics

Page: 450

View: 2213

This is the softcover reprint of the 1975 English translation of the first three chapters of Bourbaki’s Groupes et algebres de Lie. The first chapter describes the theory of Lie algebras, their deviations, representations, and enveloping algebras. Chapter two introduces free Lie algebras in order to discuss the exponential, logarithmic and the Hausdorff series. Chapter three deals with the theory of Lie groups over R and C ultrametric fields.
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Russell's Unknown Logicism

A Study in the History and Philosophy of Mathematics

Author: S. Gandon

Publisher: Springer

ISBN: 1137024658

Category: Mathematics

Page: 263

View: 7267

In this excellent book Sebastien Gandon focuses mainly on Russell's two major texts, Principa Mathematica and Principle of Mathematics , meticulously unpicking the details of these texts and bringing a new interpretation of both the mathematical and the philosophical content. Winner of The Bertrand Russell Society Book Award 2013.
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Mathematical Analysis

Approximation and Discrete Processes

Author: Mariano Giaquinta,Giuseppe Modica

Publisher: Springer Science & Business Media

ISBN: 0817644148

Category: Mathematics

Page: 388

View: 694

* Embraces a broad range of topics in analysis requiring only a sound knowledge of calculus and the functions of one variable. * Filled with beautiful illustrations, examples, exercises at the end of each chapter, and a comprehensive index.
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