A Course in Convexity

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Author: Alexander Barvinok

Publisher: American Mathematical Soc.

ISBN: 0821829688

Category: Mathematics

Page: 366

View: 499

Convexity is a simple idea that manifests itself in a surprising variety of places. This fertile field has an immensely rich structure and numerous applications. Barvinok demonstrates that simplicity, intuitive appeal, and the universality of applications make teaching (and learning) convexity a gratifying experience. The book will benefit both teacher and student: It is easy to understand, entertaining to the reader, and includes many exercises that vary in degree of difficulty. Overall, the author demonstrates the power of a few simple unifying principles in a variety of pure and applied problems. The prerequisites are minimal amounts of linear algebra, analysis, and elementary topology, plus basic computational skills. Portions of the book could be used by advanced undergraduates. As a whole, it is designed for graduate students interested in mathematical methods, computer science, electrical engineering, and operations research. The book will also be of interest to research mathematicians, who will find some results that are recent, some that are new, and many known results that are discussed from a new perspective.

A Course in Algebra

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Author: Ėrnest Borisovich Vinberg

Publisher: American Mathematical Soc.

ISBN: 9780821834138

Category: Mathematics

Page: 511

View: 946

This is a comprehensive textbook on modern algebra written by an internationally renowned specialist. It covers material traditionally found in advanced undergraduate and basic graduate courses and presents it in a lucid style. The author includes almost no technically difficult proofs, and reflecting his point of view on mathematics, he tries wherever possible to replace calculations and difficult deductions with conceptual proofs and to associate geometric images to algebraic objects. The effort spent on the part of students in absorbing these ideas will pay off when they turn to solving problems outside of this textbook.Another important feature is the presentation of most topics on several levels, allowing students to move smoothly from initial acquaintance with the subject to thorough study and a deeper understanding. Basic topics are included, such as algebraic structures, linear algebra, polynomials, and groups, as well as more advanced topics, such as affine and projective spaces, tensor algebra, Galois theory, Lie groups, and associative algebras and their representations. Some applications of linear algebra and group theory to physics are discussed. The book is written with extreme care and contains over 200 exercises and 70 figures. It is ideal as a textbook and also suitable for independent study for advanced undergraduates and graduate students.

A Course in Robust Control Theory

A Convex Approach

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Author: Geir E. Dullerud,Fernando Paganini

Publisher: Springer Science & Business Media

ISBN: 1475732902

Category: Mathematics

Page: 419

View: 4069

During the 90s robust control theory has seen major advances and achieved a new maturity, centered around the notion of convexity. The goal of this book is to give a graduate-level course on this theory that emphasizes these new developments, but at the same time conveys the main principles and ubiquitous tools at the heart of the subject. Its pedagogical objectives are to introduce a coherent and unified framework for studying the theory, to provide students with the control-theoretic background required to read and contribute to the research literature, and to present the main ideas and demonstrations of the major results. The book will be of value to mathematical researchers and computer scientists, graduate students planning to do research in the area, and engineering practitioners requiring advanced control techniques.

A Course in Multivariable Calculus and Analysis

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Author: Sudhir R. Ghorpade,Balmohan V. Limaye

Publisher: Springer Science & Business Media

ISBN: 1441916210

Category: Mathematics

Page: 475

View: 2616

This self-contained textbook gives a thorough exposition of multivariable calculus. The emphasis is on correlating general concepts and results of multivariable calculus with their counterparts in one-variable calculus. Further, the book includes genuine analogues of basic results in one-variable calculus, such as the mean value theorem and the fundamental theorem of calculus. This book is distinguished from others on the subject: it examines topics not typically covered, such as monotonicity, bimonotonicity, and convexity, together with their relation to partial differentiation, cubature rules for approximate evaluation of double integrals, and conditional as well as unconditional convergence of double series and improper double integrals. Each chapter contains detailed proofs of relevant results, along with numerous examples and a wide collection of exercises of varying degrees of difficulty, making the book useful to undergraduate and graduate students alike.

A Course in Functional Analysis and Measure Theory

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Author: Vladimir Kadets

Publisher: Springer

ISBN: 3319920049

Category: Mathematics

Page: 539

View: 5618

Written by an expert on the topic and experienced lecturer, this textbook provides an elegant, self-contained introduction to functional analysis, including several advanced topics and applications to harmonic analysis. Starting from basic topics before proceeding to more advanced material, the book covers measure and integration theory, classical Banach and Hilbert space theory, spectral theory for bounded operators, fixed point theory, Schauder bases, the Riesz-Thorin interpolation theorem for operators, as well as topics in duality and convexity theory. Aimed at advanced undergraduate and graduate students, this book is suitable for both introductory and more advanced courses in functional analysis. Including over 1500 exercises of varying difficulty and various motivational and historical remarks, the book can be used for self-study and alongside lecture courses.

Convexity

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Author: Roger Webster

Publisher: Oxford University Press

ISBN: 9780198531470

Category: Mathematics

Page: 444

View: 6924

A wide-ranging introduction to convex sets and functions, suitable for final-year undergraduates and also graduate students.

A Course in Analysis

Vol. II: Differentiation and Integration of Functions of Several Variables, Vector Calculus

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Author: Niels Jacob,Kristian P Evans

Publisher: World Scientific Publishing Company

ISBN: 9813140984

Category: Mathematics

Page: 788

View: 8458

This is the second volume of "A Course in Analysis" and it is devoted to the study of mappings between subsets of Euclidean spaces. The metric, hence the topological structure is discussed as well as the continuity of mappings. This is followed by introducing partial derivatives of real-valued functions and the differential of mappings. Many chapters deal with applications, in particular to geometry (parametric curves and surfaces, convexity), but topics such as extreme values and Lagrange multipliers, or curvilinear coordinates are considered too. On the more abstract side results such as the Stone–Weierstrass theorem or the Arzela–Ascoli theorem are proved in detail. The first part ends with a rigorous treatment of line integrals. The second part handles iterated and volume integrals for real-valued functions. Here we develop the Riemann (–Darboux–Jordan) theory. A whole chapter is devoted to boundaries and Jordan measurability of domains. We also handle in detail improper integrals and give some of their applications. The final part of this volume takes up a first discussion of vector calculus. Here we present a working mathematician's version of Green's, Gauss' and Stokes' theorem. Again some emphasis is given to applications, for example to the study of partial differential equations. At the same time we prepare the student to understand why these theorems and related objects such as surface integrals demand a much more advanced theory which we will develop in later volumes. This volume offers more than 260 problems solved in complete detail which should be of great benefit to every serious student.

A Course in Calculus and Real Analysis

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Author: Sudhir R. Ghorpade,Balmohan V. Limaye

Publisher: Springer Science & Business Media

ISBN: 0387364250

Category: Mathematics

Page: 432

View: 640

This book provides a self-contained and rigorous introduction to calculus of functions of one variable, in a presentation which emphasizes the structural development of calculus. Throughout, the authors highlight the fact that calculus provides a firm foundation to concepts and results that are generally encountered in high school and accepted on faith; for example, the classical result that the ratio of circumference to diameter is the same for all circles. A number of topics are treated here in considerable detail that may be inadequately covered in calculus courses and glossed over in real analysis courses.

A First Course in Optimization Theory

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Author: Rangarajan K. Sundaram

Publisher: Cambridge University Press

ISBN: 9780521497701

Category: Business & Economics

Page: 357

View: 4822

Divided into three separate parts, this book introduces students to optimization theory and its use in economics and allied disciplines. A preliminary chapter and three appendices are designed to keep the book mathematically self-contained.

Fourier Analysis and Convexity

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Author: Luca Brandolini,Leonardo Colzani,Alex Iosevich,Giancarlo Travaglini

Publisher: Springer Science & Business Media

ISBN: 0817681728

Category: Mathematics

Page: 268

View: 4181

Explores relationship between Fourier Analysis, convex geometry, and related areas; in the past, study of this relationship has led to important mathematical advances Presents new results and applications to diverse fields such as geometry, number theory, and analysis Contributors are leading experts in their respective fields Will be of interest to both pure and applied mathematicians

A Course in Metric Geometry

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Author: Dmitri Burago,I͡Uriĭ Dmitrievich Burago,Sergeĭ Ivanov

Publisher: American Mathematical Soc.

ISBN: 0821821296

Category: Mathematics

Page: 415

View: 3911

``Metric geometry'' is an approach to geometry based on the notion of length on a topological space. This approach experienced a very fast development in the last few decades and penetrated into many other mathematical disciplines, such as group theory, dynamical systems, and partial differential equations. The objective of this graduate textbook is twofold: to give a detailed exposition of basic notions and techniques used in the theory of length spaces, and, more generally, to offer an elementary introduction into a broad variety of geometrical topics related to the notion of distance, including Riemannian and Carnot-Caratheodory metrics, the hyperbolic plane, distance-volume inequalities, asymptotic geometry (large scale, coarse), Gromov hyperbolic spaces, convergence of metric spaces, and Alexandrov spaces (non-positively and non-negatively curved spaces). The authors tend to work with ``easy-to-touch'' mathematical objects using ``easy-to-visualize'' methods. The authors set a challenging goal of making the core parts of the book accessible to first-year graduate students. Most new concepts and methods are introduced and illustrated using simplest cases and avoiding technicalities. The book contains many exercises, which form a vital part of the exposition.

Convexity and Optimization in Rn

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Author: Leonard D. Berkovitz

Publisher: John Wiley & Sons

ISBN: 0471461660

Category: Mathematics

Page: 280

View: 1999

A comprehensive introduction to convexity and optimization inRn This book presents the mathematics of finite dimensionalconstrained optimization problems. It provides a basis for thefurther mathematical study of convexity, of more generaloptimization problems, and of numerical algorithms for the solutionof finite dimensional optimization problems. For readers who do nothave the requisite background in real analysis, the author providesa chapter covering this material. The text features abundantexercises and problems designed to lead the reader to a fundamentalunderstanding of the material. Convexity and Optimization in Rn provides detailed discussionof: * Requisite topics in real analysis * Convex sets * Convex functions * Optimization problems * Convex programming and duality * The simplex method A detailed bibliography is included for further study and an indexoffers quick reference. Suitable as a text for both graduate andundergraduate students in mathematics and engineering, thisaccessible text is written from extensively class-tested notes.

Combinatorial Convexity and Algebraic Geometry

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Author: Günter Ewald

Publisher: Springer Science & Business Media

ISBN: 1461240441

Category: Mathematics

Page: 374

View: 2158

The book is an introduction to the theory of convex polytopes and polyhedral sets, to algebraic geometry, and to the connections between these fields, known as the theory of toric varieties. The first part of the book covers the theory of polytopes and provides large parts of the mathematical background of linear optimization and of the geometrical aspects in computer science. The second part introduces toric varieties in an elementary way.

A Short Course in Automorphic Functions

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Author: Joseph Lehner

Publisher: Courier Corporation

ISBN: 0486789748

Category: Mathematics

Page: 160

View: 8073

Concise treatment covers basics of Fuchsian groups, development of Poincaré series and automorphic forms, and the connection between theory of Riemann surfaces with theories of automorphic forms and discontinuous groups. 1966 edition.

A Course in Fuzzy Systems and Control

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Author: Li-Xin Wang

Publisher: Prentice Hall

ISBN: 9780135408827

Category: Computers

Page: 424

View: 7366

Providing a self-tutorial course in fuzzy logic and its increasing role in control theory, this work answers questions about fuzzy systems and fuzzy control. The book introduces concepts such as fuzzy sets, fuzzy union, fuzzy intersection, fuzzy complement, fuzzy relations and fuzzy

Combinatorics and Complexity of Partition Functions

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Author: Alexander Barvinok

Publisher: Springer

ISBN: 3319518291

Category: Mathematics

Page: 303

View: 8208

Partition functions arise in combinatorics and related problems of statistical physics as they encode in a succinct way the combinatorial structure of complicated systems. The main focus of the book is on efficient ways to compute (approximate) various partition functions, such as permanents, hafnians and their higher-dimensional versions, graph and hypergraph matching polynomials, the independence polynomial of a graph and partition functions enumerating 0-1 and integer points in polyhedra, which allows one to make algorithmic advances in otherwise intractable problems. The book unifies various, often quite recent, results scattered in the literature, concentrating on the three main approaches: scaling, interpolation and correlation decay. The prerequisites include moderate amounts of real and complex analysis and linear algebra, making the book accessible to advanced math and physics undergraduates.

Lectures on Discrete Geometry

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Author: Ji?í Matoušek

Publisher: Springer Science & Business Media

ISBN: 9780387953731

Category: Mathematics

Page: 486

View: 6786

The main topics in this introductory text to discrete geometry include basics on convex sets, convex polytopes and hyperplane arrangements, combinatorial complexity of geometric configurations, intersection patterns and transversals of convex sets, geometric Ramsey-type results, and embeddings of finite metric spaces into normed spaces. In each area, the text explains several key results and methods.

Dense Sphere Packings

A Blueprint for Formal Proofs

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Author: Thomas Hales

Publisher: Cambridge University Press

ISBN: 113957647X

Category: Mathematics

Page: N.A

View: 5226

The 400-year-old Kepler conjecture asserts that no packing of congruent balls in three dimensions can have a density exceeding the familiar pyramid-shaped cannonball arrangement. In this book, a new proof of the conjecture is presented that makes it accessible for the first time to a broad mathematical audience. The book also presents solutions to other previously unresolved conjectures in discrete geometry, including the strong dodecahedral conjecture on the smallest surface area of a Voronoi cell in a sphere packing. This book is also currently being used as a blueprint for a large-scale formal proof project, which aims to check every logical inference of the proof of the Kepler conjecture by computer. This is an indispensable resource for those who want to be brought up to date with research on the Kepler conjecture.

Convex Analysis and Optimization

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Author: Dimitri P. Bertsekas,Angelia Nedić,Asuman E. Ozdaglar

Publisher: N.A

ISBN: 9781886529458

Category: Mathematics

Page: 534

View: 8308