Bøger i Textbooks in Mathematics serien

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.