Bøger i Textbooks in Mathematics serien

This book presents the essentials of harmonic analysis on locally compact groups in a concise and accessible form. The text provides necessary background on Banach algebras and spectral theory, develops the theory of analysis on Abelian groups and compact groups, examines the theory of induced representations, and explores the theory of representations of non-Abelian, non-compact groups. This second edition adds material on representations of the discrete Heisenberg group, coverage of von Neumann algebras and Wiener¿s theorem, and discussion of SU(2), SO(3), and SO(4) using quaternions.

This second edition is a valuable, up-to-date tool for instructors teaching courses about differential equations. It serves as an excellent introductory textbook for undergraduate students. Tthe textbook will aide them greatly in their professional careers because of its instructions on how to use computers to solve equations.

Previous edition: Mathematical groups / Tony Barnard and Hugh Neill (London: Teach Yourself Books, 1996).

The study of nonlinear optimization is both fundamental and a key course for applied mathematics, operations research, management science, industrial engineering, and economics at most colleges and universities.

This book provides the traditional role of exercises in a course to provide more-or-less routine applications of the main results, for the student's edification and also as possible material for examinations. It discusses Noetherian rings and prime ideals for algebraic geometry.

Complex Variables: A Physical Approach with Applications, Second Edition offers a notable revision. The emphasis remains on theory and practice. The first part of the text focuses on the fundamental concepts. The author then moves on to a detailed look at how complex variables are used in the real world.

Designed for an introductory course on differential equations, this book uses explicit explanation to ensure students fully comprehend the subject matter. Emphasizing modeling and applications, the third edition of this classic text presents a substantial new section on Gauss¿s bell curve and improves coverage of Fourier analysis, numerical methods, and linear algebra. Relating the development of mathematics to human activity, the text includes unique examples and exercises, as well as the author¿s distinctive historical notes, throughout.

This text provides students with a solid geometric grasp of linear transformations. It stresses the linear case of the inverse function and rank theorems and gives a careful geometric treatment of the spectral theorem. The text starts with basic questions about images and pre-images of mappings, injectivity, surjectivity, and distortion. In the process of answering these questions in the linear setting, the book covers all the standard topics for a first course on linear algebra.

This book focuses on mathematical thinking and problem solving, demonstrating how discrete probability, statistics, and elementary discrete mathematics can be applied in games, sports, and gambling situations. The text draws on numerous examples, questions, and problems to explain the application of mathematical theory to various real-life games.

This book demonstrates the power of numerical methods in the context of solving complex engineering and scientific problems. With a wealth of exercises, it emphasizes the practical aspects of numerical methods and addresses their advantages and disadvantages. Each chapter contains many computational examples, as well as a section on applications that contains additional engineering examples.

This book provides a detailed examination of the central assertions of measure theory in n-dimensional Euclidean space. It emphasizes the roles of Hausdorff measure and the capacity in characterizing the fine properties of sets and functions. The book covers theorems and differentiation in Rn , Hausdorff measures, area and coarea formulas for Lipschitz mappings and related change-of-variable formulas, and Sobolev functions and functions of bounded variation. This second edition includes countless improvements in notation, format, and clarity of exposition. Also new are several sections describing the ¿-¿ theorem, weak compactness criteria in L1, and Young measure methods for weak convergence. In addition, the bibliography has been updated.

This classroom-tested, student-friendly text covers a diverse array of number theory topics, from the ancient Euclidean algorithm for finding the greatest common divisor of two integers to recent developments such as cryptography, the theory of elliptic curves, and the negative solution of Hilbert¿s tenth problem. Ideal for a one- or two-semester undergraduate-level course, the second edition features a more flexible structure, adds several new sections, expands exercise sets to encompass a wider variety of problems, and provides calculations, tutorials, and code via an author-maintained website.

This supplement for linear algebra courses provides a hands-on lab manual that includes exercises, theorems, and problems. The exercises section integrates problems, technology, Mathematica® visualization, and Mathematica CDFs, enabling students to discover the theory and applications of linear algebra in a meaningful way. The theorems and problems section presents the theoretical aspects of linear algebra. Each chapter also contains application-driven projects that students can use as the basis for further undergraduate research.

This book provides a one-semester undergraduate introduction to counterexamples in calculus and analysis. It helps engineering, natural sciences, and mathematics students tackle commonly made erroneous conjectures. The book encourages students to think critically and analytically, and helps to reveal common errors in many examples. It is intended for students who are interested in developing a deeper understanding of the topics of calculus. The gathered counterexamples may also be used by calculus instructors in their classes.

Designed for a second theoretical course in linear algebra, this text explores a variety of advanced topics in linear algebra that highlight the rich interconnections of the subject to geometry, algebra, analysis, combinatorics, numerical computation, and many other areas of mathematics. The author covers algebraic structures, matrices, structured matrices, geometric aspects of linear algebra, modules, and multilinear algebra. He gives complete proofs of all results and supplements the general theory with many specific examples and concrete computations.

Designed for an undergraduate course on mathematical modeling or differential equations, this text provides students with an understanding of the practical and theoretical aspects of mathematical models involving ODEs and PDEs. It develops students¿ intuition by building the theory from the ground up and illustrates the analysis of more than 20 distinct models through concrete applications in physics, engineering, finance, and many other areas. The book also uses MATLAB® GUIs that enable students to discover patterns and make conjectures.

Tested and refined through years of the authors¿ teaching experiences, this text provides a unified, self-contained account of the main theory and application of methods behind modern-day financial mathematics. With an abundance of examples, problems, and fully worked out solutions, the text introduces the financial theory and relevant mathematical methods in a mathematically rigorous yet engaging way. Unlike similar texts in the field, this one presents multiple problem-solving approaches, linking related comprehensive techniques for pricing different types of financial derivatives.

This text presents an intuitive treatment of mathematics using ultrasmall numbers. With this modern approach to infinitesimals, proofs become simpler and more focused on the combinatorial heart of arguments, unlike traditional treatments that use epsilon¿delta methods. Readers can fully prove fundamental results, such as the Extreme Value Theorem, from the axioms immediately, without needing to master notions of supremum or compactness. The book includes numerous exercises throughout and at the end of each chapter.

Covers how to define and compute standard geometric functions using Mathematica for constructing various curves and surfaces from existing ones. This book addresses important topics, such as quaternions. It presents techniques that help reader to understand concepts geometrically, plotting curves and surfaces on a monitor and printing them.

This text presents a unified treatment of the three classical geometries: Euclidean, hyperbolic, and spherical (elliptic). This unique approach of combining all three geometries simultaneously using twelve concise axioms has never appeared in book form before at this level. The text introduces each axiom, including its reasons for use and implications, and then explains it in detail. In addition to numerous figures, examples, and exercises, the book includes Geometera (TM)s Sketchpad to help students build and investigate math models, objects, figures, and graphs. The author provides programs for students to use on a supporting website. A solutions manual is available for qualifying instructors.

Exploring what mathematics can reveal about applications, this book focuses on the design of appropriate experiments to validate the development of mathematical models. It guides students through the modeling process, from empirical observations and formalization of properties to model analysis and interpretation of results.

Explores the fundamental ideas of linear algebra as well as a variety of applications. This book discusses proofs to show how to correctly create and write them. It offers the option of using Maple, MATLAB[registered], and TI-83 Plus to help solve problems and reinforce the learning of standard procedures. It includes examples of applications.

This is an introductory game theory book that quickly moves readers through the fundamental ideas of game theory to enable them to engage in creative modeling projects based on game theoretic concepts.

This book delivers a stimulating exposition of modeling and computing, preparing students for higher-level mathematical and analytical thinking. Designed for an undergraduate-level course on ordinary differential equations, the text presents classical ideas and cutting-edge techniques in dynamical systems and other areas, highlighting applications from engineering, physics, and applied science. This version adds coverage of Sturm-Liouville theory and problems, streamlines content for the interests of engineers, enhances examples, and augments the substantial and valuable exercise sets. A solutions manual is available with qualifying course adoption.

Emphasizing active learning, this text not only teaches abstract algebra but also provides a deeper understanding of what mathematics is, how it is done, and how mathematicians think. The book can be used in both rings-first and groups-first abstract algebra courses. Numerous activities, examples, and exercises illustrate the definitions, theorems, and concepts. Each chapter also discusses the connections among topics in ring theory and group theory, helping students see the relationships between the two main types of algebraic objects studied throughout the text.

Provides an introduction to the basics of modern topology. This work 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.

This version of the author's DE text will include a new chapter on Linear Boundary Value Problems for instructors who want to add this coverage to their DE course.