Bøger i Undergraduate Texts in Mathematics serien

Intended as a rigorous first course, the book introduces and develops the various axioms slowly, and then, in a departure from other texts, continually illustrates the major definitions and axioms with two or three models, enabling the reader to picture the idea more clearly.

Presenting mathematics as forming a natural bridge between the humanities and the sciences, this book makes calculus accessible to those in the liberal arts.

Concentrates on how to make predictions about the numbers of each kind of basic state of a quantum system from only two ingredients: the symmetry and linear model of quantum mechanics.

The theory of elliptic curves involves a blend of algebra, geometry, analysis, and number theory. This book stresses this interplay as it develops the basic theory, providing an opportunity for readers to appreciate the unity of modern mathematics.

this section gained proofs of the Schroeder-Bernstein theorem and the Trichotomy Law for Sets, and lost most of the material about finite and countable sets, which has now been moved to a new section devoted to those two types of sets.

This book, which is based on Polya's method of problem solving, aids students in their transition from calculus (or precalculus) to higher-level mathematics.

Written by an expert in the field, this undergraduate textbook will prepare the next generation of pure and applied mathematicians. Key topics include walks on graphs, cubes and the Radon transform, the Matrix-Tree Theorem, and the Sperner property.

Conics and Cubics offers an accessible and well illustrated introduction to algebraic curves. By classifying irreducible cubics over the real numbers and proving that their points form Abelian groups, the book gives readers easy access to the study of elliptic curves.

Intended as a first course in probability at post-calculus level, this book is of special interest to students majoring in computer science as well as in mathematics.

yet it provides coverage of the main topics usually studied in the standard course, as well as an introduction to using computer algebra packages to solve and understand partial differential equations.For the 3rd edition the section on numerical methods has been considerably expanded to reflect their central role in PDE's.

Presenting historical perspective and notes on important figures in mathematics, covering current activity in the mathematical community, and raising famous and lesser-known questions, this book shows that abstract mathematics is a vibrant, dynamic enterprise.

The calculus of variations, whose origins can be traced to the works of Aristotle and Zenodoros, is now Ii vast repository supplying fundamental tools of exploration not only to the mathematician, but-as evidenced by current literature-also to those in most branches of science in which mathematics is applied.

This book explains the basic methods of modern cryptography. It is written for readers with only basic mathematical knowledge who are interested in modern cryptographic algorithms and their mathematical foundation.

This concise, up-to-date textbook is designed for the standard sophomore course in differential equations. The basic ideas, models, and solution methods are presented in a user friendly format that is accessible to engineers, scientists, economists, and mathematics majors.

Accessible to junior and senior undergraduate students, this survey contains many examples, solved exercises, sets of problems, and parts of abstract algebra of use in many other areas of discrete mathematics.

mathematicians, turning away from the roots of mathematics in intuition, have concentrated on refinement and emphasized the postulational side of mathematics, anel at times have overlooked the unity of their science with physics and other fields.

There is no one best way for an undergraduate student to learn elementary algebra. This text presents elementary algebra organized accord ing to some principles of universal algebra. This means abandoning terms peculiar to one branch of algebra when there is available a more general term applicable to all of algebra.

Designed for an undergraduate course or for independent study, this textbook presents sophisticated mathematical ideas in an elementary and friendly fashion. It features techniques to solve proofs as well as exercises of varying difficulty.

Students with a background in single variable calculus are guided through a variety of problem solving techniques and practice problems. Examples from the physical sciences are utilized to highlight the essential relationship between calculus and modern science.

This book provides a self-contained and rigorous introduction to calculus of functions of one variable, in a presentation which emphasizes the structural development of calculus.

This new book offers a fresh approach to matrix and linear algebra by providing a balanced blend of applications, theory, and computation, while highlighting their interdependence.

This textbook develops the essential tools of linear algebra, with the goal of imparting technique alongside contextual understanding. Applications go hand-in-hand with theory, each reinforcing and explaining the other. This approach encourages students to develop not only the technical proficiency needed to go on to further study, but an appreciation for when, why, and how the tools of linear algebra can be used across modern applied mathematics.Providing an extensive treatment of essential topics such as Gaussian elimination, inner products and norms, and eigenvalues and singular values, this text can be used for an in-depth first course, or an application-driven second course in linear algebra. In this second edition, applications have been updated and expanded to include numerical methods, dynamical systems, data analysis, and signal processing, while the pedagogical flow of the core material has been improved. Throughout, the text emphasizes the conceptual connections between each application and the underlying linear algebraic techniques, thereby enabling students not only to learn how to apply the mathematical tools in routine contexts, but also to understand what is required to adapt to unusual or emerging problems.No previous knowledge of linear algebra is needed to approach this text, with single-variable calculus as the only formal prerequisite. However, the reader will need to draw upon some mathematical maturity to engage in the increasing abstraction inherent to the subject. Once equipped with the main tools and concepts from this book, students will be prepared for further study in differential equations, numerical analysis, data science and statistics, and a broad range of applications. The first author¿s text, Introduction to Partial Differential Equations, is an ideal companion volume, forming a natural extension of the linear mathematical methods developed here.

This textbook provides a unified and concise exploration of undergraduate mathematics by approaching the subject through its history. however, biographical sketches have been omitted. Mathematics and Its History: A Concise Edition is an essential resource for courses or reading programs on the history of mathematics.

" Our goals, like those of the other books in the series, are to explain connections and common viewpoints between various mathematical areas, to emphasize the motivation for studying certain prob lem areas, and to present the historical development of our subject.

Throughout, the theory unfolds via over 150 carefully selected problems for students to solve, many of which connect to state-of-the-art research. Inquiry-Based Enumerative Combinatorics is ideal for lower-division undergraduate students majoring in math or computer science, as there are no formal mathematics prerequisites.

This introduction to first-order logic clearly works out the role of first-order logic in the foundations of mathematics, particularly the two basic questions of the range of the axiomatic method and of theorem-proving by machines.