Books in the Textbooks in Mathematics series

Written in clear and concise language, this book covers the standard topics in a second linear algebra course. The book first introduces general fields and emphasizes matrix algebra over finite fields and complex numbers. It then proceeds to cover vector spaces in depth, addressing vector spaces over general fields. Also discussed are standard topics in linear algebra including linear transformations, Jordan canonical form, inner product spaces, and spectral theory. Additional material covers dual spaces, quotient spaces, and tensor products. It includes well-designed exercises and full solutions to almost all exercises.

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 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.

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.

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.

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.

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.

This book discusses structure theory of an operator, topics on inner product spaces, and trace and determinant functions of a linear operator. It addresses bilinear forms with a full treatment of symplectic spaces and orthogonal spaces, as well as explains construction of tensor, symmetric, and exterior algebras. Featuring several new exercises, the second edition adds coverage of sesquilinear forms, linear groups, matrices, normed vector spaces, orthogonal spaces over perfect fields of characteristic two, and Clifford algebras. A solutions manual is available upon qualifying course adoption.

Designed for a one- or two-semester undergraduate course, this text educates a new generation of mathematical scientists and engineers on differential equations. This edition continues to emphasize examples and mathematical modeling as well as promote analytical thinking to help students in future studies. It improves the exercise sets and examples, reorganizes the material on numerical techniques, and enriches the presentation of predator-prey problems. It also updates the material on nonlinear differential equations and dynamical systems and includes a new appendix that reviews linear algebra.