A Guide to Functional Analysis

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Author: Steven G. Krantz

Publisher: MAA

ISBN: 0883853574

Category: Mathematics

Page: 150

View: 1643

This book is a quick but precise and careful introduction to the subject of functional analysis. It covers the basic topics that can be found in a basic graduate analysis text. But it also covers more sophisticated topics such as spectral theory, convexity, and fixed-point theorems. A special feature of the book is that it contains a great many examples and even some applications. It concludes with a statement and proof of Lomonosov's dramatic result about invariant subspaces.

A Guide to Advanced Real Analysis

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Author: G. B. Folland

Publisher: MAA

ISBN: 9780883853436

Category: Mathematics

Page: 107

View: 2862

A concise guide to the core material in a graduate level real analysis course.

A Guide to Topology

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Author: Steven G. Krantz

Publisher: MAA

ISBN: 9780883853467

Category: Mathematics

Page: 107

View: 5762

This book is an outline of the core material in the standard graduate-level real analysis course. It is intended as a resource for students in such a course as well as others who wish to learn or review the subject. On the abstract level, it covers the theory of measure and integration and the basics of point set topology, functional analysis, and the most important types of function spaces. On the more concrete level, it also deals with the applications of these general theories to analysis on Euclidean space: the Lebesgue integral, Hausdorff measure, convolutions, Fourier series and transforms, and distributions. The relevant definitions and major theorems are stated in detail. Proofs, however, are generally presented only as sketches, in such a way that the key ideas are explained but the technical details are omitted. In this way a large amount of material is presented in a concise and readable form.

A Guide to Advanced Linear Algebra

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Author: Steven H. Weintraub

Publisher: MAA

ISBN: 0883853515

Category: Mathematics

Page: 251

View: 6516

Linear algebra occupies a central place in modern mathematics. This book provides a rigorous and thorough development of linear algebra at an advanced level, and is directed at graduate students and professional mathematicians. It approaches linear algebra from an algebraic point of view, but its selection of topics is governed not only for their importance in linear algebra itself, but also for their applications throughout mathematics. Students in algebra, analysis, and topology will find much of interest and use to them, and the careful treatment and breadth of subject matter will make this book a valuable reference for mathematicians throughout their professional lives.Topics treated in this book include: vector spaces and linear transformations; dimension counting and applications; representation of linear transformations by matrices; duality; determinants and their uses; rational and especially Jordan canonical form; bilinear forms; inner product spaces; normal linear transformations and the spectral theorem; and an introduction to matrix groups as Lie groups.The book treats vector spaces in full generality, though it concentrates on the finite dimensional case. Also, it treats vector spaces over arbitrary fields, specializing to algebraically closed fields or to the fields of real and complex numbers as necessary.

A Garden of Integrals

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Author: Frank Burk

Publisher: MAA

ISBN: 9780883853375

Category: Mathematics

Page: 281

View: 1016

Burk proves the basic properties of various integrals, draws comparisons and analyses their uses.

A Guide to Complex Variables

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Author: Steven G. Krantz

Publisher: MAA

ISBN: 9780883853382

Category: Mathematics

Page: 182

View: 7568

A quick and easy-to-use introduction to the key topics in complex variables, for mathematicians and non-mathematicians alike.

Essentials of Topology with Applications

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Author: Steven G. Krantz

Publisher: CRC Press

ISBN: 9781420089752

Category: Mathematics

Page: 420

View: 1173

Brings Readers Up to Speed in This Important and Rapidly Growing Area Supported by many examples in mathematics, physics, economics, engineering, and other disciplines, Essentials of Topology with Applications provides a clear, insightful, and thorough introduction to the basics of modern topology. It presents the traditional concepts of topological space, open and closed sets, separation axioms, and more, along with applications of the ideas in Morse, manifold, homotopy, and homology theories. After discussing the key ideas of topology, the author examines the more advanced topics of algebraic topology and manifold theory. He also explores meaningful applications in a number of areas, including the traveling salesman problem, digital imaging, mathematical economics, and dynamical systems. The appendices offer background material on logic, set theory, the properties of real numbers, the axiom of choice, and basic algebraic structures. Taking a fresh and accessible approach to a venerable subject, this text provides excellent representations of topological ideas. It forms the foundation for further mathematical study in real analysis, abstract algebra, and beyond.

A Friendly Approach to Functional Analysis

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Author: Amol Sasane

Publisher: World Scientific Publishing Company

ISBN: 1786343363

Category:

Page: 396

View: 6367

This book constitutes a concise introductory course on Functional Analysis for students who have studied calculus and linear algebra. The topics covered are Banach spaces, continuous linear transformations, Frechet derivative, geometry of Hilbert spaces, compact operators, and distributions. In addition, the book includes selected applications of functional analysis to differential equations, optimization, physics (classical and quantum mechanics), and numerical analysis. The book contains 197 problems, meant to reinforce the fundamental concepts. The inclusion of detailed solutions to all the exercises makes the book ideal also for self-study. A Friendly Approach to Functional Analysis is written specifically for undergraduate students of pure mathematics and engineering, and those studying joint programmes with mathematics. Request Inspection Copy

Math Made Visual

Creating Images for Understanding Mathematics

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Author: Claudi Alsina,Roger B. Nelsen

Publisher: MAA

ISBN: 9780883857465

Category: Mathematics

Page: 173

View: 7776

A book describing how visualization techniques can be used in the teaching of mathematics.

A Course in Abstract Harmonic Analysis, Second Edition

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Author: Gerald B. Folland

Publisher: CRC Press

ISBN: 1498727158

Category: Mathematics

Page: 305

View: 9041

A Course in Abstract Harmonic Analysis is an introduction to that part of analysis on locally compact groups that can be done with minimal assumptions on the nature of the group. As a generalization of classical Fourier analysis, this abstract theory creates a foundation for a great deal of modern analysis, and it contains a number of elegant results and techniques that are of interest in their own right. This book develops the abstract theory along with a well-chosen selection of concrete examples that exemplify the results and show the breadth of their applicability. After a preliminary chapter containing the necessary background material on Banach algebras and spectral theory, the text sets out the general theory of locally compact groups and their unitary representations, followed by a development of the more specific theory of analysis on Abelian groups and compact groups. There is an extensive chapter on the theory of induced representations and its applications, and the book concludes with a more informal exposition on the theory of representations of non-Abelian, non-compact groups. Featuring extensive updates and new examples, the Second Edition: Adds a short section on von Neumann algebras Includes Mark Kac’s simple proof of a restricted form of Wiener’s theorem Explains the relation between SU(2) and SO(3) in terms of quaternions, an elegant method that brings SO(4) into the picture with little effort Discusses representations of the discrete Heisenberg group and its central quotients, illustrating the Mackey machine for regular semi-direct products and the pathological phenomena for nonregular ones A Course in Abstract Harmonic Analysis, Second Edition serves as an entrée to advanced mathematics, presenting the essentials of harmonic analysis on locally compact groups in a concise and accessible form.

A TeXas Style Introduction to Proof

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Author: Ron Taylor,Patrick X. Rault

Publisher: The Mathematical Association of America

ISBN: 1939512131

Category: Mathematics

Page: 176

View: 8144

A TeXas Style Introduction to Proof is an IBL textbook designed for a one-semester course on proofs (the "bridge course") that also introduces TeX as a tool students can use to communicate their work. As befitting "textless" text, the book is, as one reviewer characterized it, "minimal." Written in an easy-going style, the exposition is just enough to support the activities, and it is clear, concise, and effective. The book is well organized and contains ample carefully selected exercises that are varied, interesting, and probing, without being discouragingly difficult.

Linear Algebra Problem Book

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Author: Paul R. Halmos

Publisher: MAA

ISBN: 9780883853221

Category: Mathematics

Page: 336

View: 4791

Takes the student step by step from basic axioms to advanced concepts. 164 problems, each with hints and full solutions.

Functional Analysis

A Terse Introduction

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Author: Gerardo Chacón,Humberto Rafeiro,Juan Camilo Vallejo

Publisher: Walter de Gruyter GmbH & Co KG

ISBN: 3110441926

Category: Mathematics

Page: 245

View: 3197

This textbook on functional analysis offers a short and concise introduction to the subject. The book is designed in such a way as to provide a smooth transition between elementary and advanced topics and its modular structure allows for an easy assimilation of the content. Starting from a dedicated chapter on the axiom of choice, subsequent chapters cover Hilbert spaces, linear operators, functionals and duality, Fourier series, Fourier transform, the fixed point theorem, Baire categories, the uniform bounded principle, the open mapping theorem, the closed graph theorem, the Hahn–Banach theorem, adjoint operators, weak topologies and reflexivity, operators in Hilbert spaces, spectral theory of operators in Hilbert spaces, and compactness. Each chapter ends with workable problems. The book is suitable for graduate students, but also for advanced undergraduates, in mathematics and physics. Contents: List of Figures Basic Notation Choice Principles Hilbert Spaces Completeness, Completion and Dimension Linear Operators Functionals and Dual Spaces Fourier Series Fourier Transform Fixed Point Theorem Baire Category Theorem Uniform Boundedness Principle Open Mapping Theorem Closed Graph Theorem Hahn–Banach Theorem The Adjoint Operator Weak Topologies and Reflexivity Operators in Hilbert Spaces Spectral Theory of Operators on Hilbert Spaces Compactness Bibliography Index

A Guide to Plane Algebraic Curves

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Author: Keith Kendig

Publisher: MAA

ISBN: 0883853531

Category: Mathematics

Page: 193

View: 6564

This Guide is a friendly introduction to plane algebraic curves. It emphasizes geometry and intuition, and the presentation is kept concrete. You'll find an abundance of pictures and examples to help develop your intuition about the subject, which is so basic to understanding and asking fruitful questions. Highlights of the elementary theory are covered, which for some could be an end in itself, and for others an invitation to investigate further. Proofs, when given, are mostly sketched, some in more detail, but typically with less. References to texts that provide further discussion are often included. Computer algebra software has made getting around in algebraic geometry much easier. Algebraic curves and geometry are now being applied to areas such as cryptography, complexity and coding theory, robotics, biological networks, and coupled dynamical systems. Algebraic curves were used in Andrew Wiles' proof of Fermat's Last Theorem, and to understand string theory, you need to know some algebraic geometry. There are other areas on the horizon for which the concepts and tools of algebraic curves and geometry hold tantalizing promise. This introduction to algebraic curves will be appropriate for a wide segment of scientists and engineers wanting an entrance to this burgeoning subject.

A Guide to Advanced Real Analysis

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Author: G. B. Folland

Publisher: MAA

ISBN: 9780883853436

Category: Mathematics

Page: 107

View: 4297

A concise guide to the core material in a graduate level real analysis course.

A Guide to Groups, Rings, and Fields

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Author: Fernando Q. Gouvêa

Publisher: MAA

ISBN: 0883853558

Category: Mathematics

Page: 309

View: 4003

This Guide offers a concise overview of the theory of groups, rings, and fields at the graduate level, emphasizing those aspects that are useful in other parts of mathematics. It focuses on the main ideas and how they hang together. It will be useful to both students and professionals.In addition to the standard material on groups, rings, modules, fields, and Galois theory, the book includes discussions of other important topics that are often omitted in the standard graduate course, including linear groups, group representations, the structure of Artinian rings, projective, injective and flat modules, Dedekind domains, and central simple algebras. All of the important theorems are discussed, without proofs but often with a discussion of the intuitive ideas behind those proofs.Those looking for a way to review and refresh their basic algebra will benefit from reading this Guide, and it will also serve as a ready reference for mathematicians who make use of algebra in their work.

From Vector Spaces to Function Spaces

Introduction to Functional Analysis with Applications

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Author: Yutaka Yamamoto

Publisher: SIAM

ISBN: 1611972302

Category: Mathematics

Page: 260

View: 6332

A guide to analytic methods in applied mathematics from the perspective of functional analysis, suitable for scientists, engineers and students.

A Guide to Elementary Number Theory

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Author: Underwood Dudley

Publisher: MAA

ISBN: 9780883853474

Category: Mathematics

Page: 141

View: 1411

"A Guide to Elementary Number Theory is a 140-page exposition of the topics considered in a first course in number theory. It is intended for those who may have seen the material before but have half-forgotten it, and also for those who may have misspent their youth by not having a course in number theory and who want to see what it is about without having to wade through traditional texts, some of which approach 500 pages in length. It will be especially useful to graduate students preparing for qualifying exams. Though Plato did not quite say, "He is unworthy of the name of man who does not know which integers are the sums of two squares," he came close. This guide can make everyone more worthy."--P. [4] of cover.

The Survival of a Mathematician

From Tenure-track to Emeritus

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Author: Steven George Krantz

Publisher: American Mathematical Soc.

ISBN: 0821846299

Category: Mathematics

Page: 310

View: 8374

"One of the themes of the book is how to have a fulfilling professional life. In order to achieve this goal, Krantz discusses keeping a vigorous scholarly program going and finding new challenges, as well as dealing with the everyday tasks of research, teaching, and administration." "In short, this is a survival manual for the professional mathematician - both in academics and in industry and government agencies. It is a sequel to the author's A Mathematician's Survival Guide."--BOOK JACKET.

Real Analysis

Foundations and Functions of One Variable

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Author: Miklós Laczkovich,Vera T. Sós

Publisher: Springer

ISBN: 1493927663

Category: Mathematics

Page: 483

View: 3874

Based on courses given at Eötvös Loránd University (Hungary) over the past 30 years, this introductory textbook develops the central concepts of the analysis of functions of one variable — systematically, with many examples and illustrations, and in a manner that builds upon, and sharpens, the student’s mathematical intuition. The book provides a solid grounding in the basics of logic and proofs, sets, and real numbers, in preparation for a study of the main topics: limits, continuity, rational functions and transcendental functions, differentiation, and integration. Numerous applications to other areas of mathematics, and to physics, are given, thereby demonstrating the practical scope and power of the theoretical concepts treated. In the spirit of learning-by-doing, Real Analysis includes more than 500 engaging exercises for the student keen on mastering the basics of analysis. The wealth of material, and modular organization, of the book make it adaptable as a textbook for courses of various levels; the hints and solutions provided for the more challenging exercises make it ideal for independent study.