Analysis with Ultrasmall Numbers 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. Students 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 is suitable for a calculus course at the undergraduate or high school level or for...

Convexity is an ancient idea going back to Archimedes. Used sporadically in the mathematical literature over the centuries, today it is a flourishing area of research and a mathematical subject in its own right. Convexity is used in optimization theory, functional analysis, complex analysis, and other parts of mathematics.

Convex Analysis introduces analytic tools for studying convexity and provides analytical applications of the concept. The book includes a general background on classical geometric theory which allows readers to obtain a glimpse of how modern...

Numerical Analysis for Engineers: Methods and Applications demonstrates the power of numerical methods in the context of solving complex engineering and scientific problems. The book helps to prepare future engineers and assists practicing engineers in understanding the fundamentals of numerical methods, especially their applications, limitations, and potentials.

Each chapter contains many computational examples, as well as a section on applications that contain additional engineering examples. Each chapter also includes a set of exercise problems.

Advanced Linear Algebra, Second Edition takes a gentle approach that starts with familiar concepts and then gradually builds to deeper results. Each section begins with an outline of previously introduced concepts and results necessary for mastering the new material. By reviewing what students need to know before moving forward, the text builds a solid foundation upon which to progress.

The new edition of this successful text focuses on vector spaces and the maps between them that preserve their structure (linear transformations). Designed for advanced...

Mathematics in Games, Sports, and Gambling: The Games People Play, Second Edition demonstrates how discrete probability, statistics, and elementary discrete mathematics are used in games, sports, and gambling situations. With emphasis on mathematical thinking and problem solving, the text draws on numerous examples, questions, and problems to explain the application of mathematical theory to various real-life games.
This updated edition of a widely adopted textbook considers a number of popular games and diversions that are mathematically based or can be studied from a...

Introduction to Abstract Algebra, Second Edition presents abstract algebra as the main tool underlying discrete mathematics and the digital world. It avoids the usual groups first/rings first dilemma by introducing semigroups and monoids, the multiplicative structures of rings, along with groups.
This new edition of a widely adopted textbook covers applications from biology, science, and engineering. It 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...

Differential Equations: Theory, Technique, and Practice with Boundary Value Problems presents classical ideas and cutting-edge techniques for a contemporary, undergraduate-level, one- or two-semester course on ordinary differential equations. Authored by a widely respected researcher and teacher, the text covers standard topics such as partial differential equations (PDEs), boundary value problems, numerical methods, and dynamical systems. Lively historical notes and mathematical nuggets of information enrich the reading experience by offering perspective on the lives of...

ABET, the accrediting board for engineering programs, makes it clear that engineering graduates must be skilled in the art of programming in a language such as MATLAB(r). Supplying students with a bridge between the functions of complex variable theory and MATLAB, this supplemental text enables instructors to easily add a MATLAB component to their complex variables courses.
A MATLAB(r) Companion to Complex Variables provides readers with a clear understanding of the utility of MATLAB in complex variable calculus. An ideal adjunct to standard texts on the functions of complex variables,...

Advanced Linear Algebra features a student-friendly approach to the theory of linear algebra. The author s emphasis on vector spaces over general fields, with corresponding current applications, sets the book apart. He focuses on finite fields and complex numbers, and discusses matrix algebra over these fields. The text then proceeds to cover vector spaces in depth. Also discussed are standard topics in linear algebra including linear transformations, Jordan canonical form, inner product spaces, spectral theory, and, as supplementary topics, dual spaces, quotient spaces, and tensor...

Introduction to Number Theory is a classroom-tested, student-friendly text that 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. The authors illustrate the connections between number theory and other areas of mathematics, including algebra, analysis, and combinatorics. They also describe applications of number theory to real-world problems, such as...