Books in the Textbooks in Mathematics series

"The Shape of Space, Third Edition maintains the standard of excellence set by the previous editions. This lighthearted textbook covers the basic geometry and topology of two- and three-dimensional spaces-stretching students' minds as they learn to visualize new possibilities for the shape of our universe"--

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.

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.

This popular text provides students with hands-on modeling skills for a wide variety of problems involving differential equations that describe rates of change. This edition includes updated Maple¿ and MATLAB® code as well as new case studies and exercises. The text focuses on growth and decay processes

This book is designed to prepare students for higher mathematics by focusing on the development of theorems and proofs. Beginning with logic, the text discusses deductive mathematical systems and the systems of natural numbers, integers, rational numbers, and real numbers. It covers elementary topics in set theory, explores various properties of relations and functions, and proves several theorems using induction. The final chapters introduce the concept of cardinalities of sets and the concepts and proofs of real analysis and group theory.

Some of the most famous questions in mathematical history have involved equations with coefficients in Z, the set of integers. This book deals with their solutions, which are achieved with an economy of effort through the process of abstraction. It presents both results and their underlying ideas.

This is the second of a two-part set of books for the undergraduate linear algebra sequence. The text is for more advanced courses taught in mathematics departments. This course is based around matrix theory and focused on the theory of linear algebra. Along with the chapters found in Elementary Linear Algebra, he offers seven additional chapters .

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.

The textbook for Funcational Analysis provides not only solid mathematical foundations for the subject but, with many examples drawing from mechanics and science, motivates an engineering or science student to study the subject, and provides the necessary connections with applications.

Strikingly different from typical presentations, Principles of Fourier Analysis provides an introduction to and comprehensive overview of the mathematical theory of Fourier analysis as it is used in applications in engineering, science, and mathematics.

This textbook is for a first undergraduate course in abstract algebra. It differs from the first edition in that it offers optional technology and less focus on interactivity. It has a more traditional approach where additional topics to the primary syllabus are placed after primary topics are covered, creating a more common table of contents. Where technology was the primary motivation of the first edition, this edition is transformed by historical notes and better explanations of why topics are covered.

Introduction to Abstract Algebra, Second Edition presents abstract algebra as the main tool underlying discrete mathematics. This edition offers numerous updates based on feedback from first edition adopters, as well as improved and simplified proofs of a number of important theorems. Many new exercises have been added throughout, while new study projects examine skewfields, quaternions, and octonions. Each chapter includes exercises of varying levels of difficulty, chapter notes that point out variations in notation and approach, and study projects that cover an array of applications.

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.

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.