Bücher der Reihe Undergraduate Texts in Mathematics

The third of a three-volume work, this book is the outgrowth of the authors' experience teaching calculus at Berkeley. It covers multivariable calculus and begins with the necessary material from analytical geometry. The authors motivate the study of calculus using its applications.

- Fundamental Concepts. -Topological Vector Spaces.- The Quotient Topology. -Completion of Metric Spaces. - Homotopy. - The TwoCountability Axioms. - CW-Complexes. - Construction ofContinuous Functions on Topological Spaces. - CoveringSpaces. - The Theorem of Tychonoff. - Set Theory (by T. - References. - Table of Symbols.

Algebra is abstract mathematics - let us make no bones about it - yet it is also applied mathematics in its best and purest form. Algebra emerged from the struggle to solve concrete, physical problems in geometry, and succeeded after 2000 years of failure by other forms of mathematics.

This text on advanced calculus discusses such topics as number systems, the extreme value problem, continuous functions, differentiation, integration and infinite series. The book is intended both for a terminal course and as preparation for more advanced studies in mathematics, science, engineering and computation.

From the author of the highly-acclaimed "A First Course in Real Analysis" comes a volume designed specifically for a short one-semester course in real analysis. The author meets this need with such elementary topics as the real number system, the theory at the basis of elementary calculus, the topology of metric spaces and infinite series.

This new edition, like the first, presents a thorough introduction to differential and integral calculus, including the integration of differential forms on manifolds.

This text covers the parts of contemporary set theory relevant to other areas of pure mathematics. After a review of "naive" set theory, it develops the Zermelo-Fraenkel axioms of the theory before discussing the ordinal and cardinal numbers.

Finally, the book illustrates the many connections between topology and other subjects, such as analysis and set theory, via the inclusion of "Extras" at the end of each chapter presenting a brief foray outside topology.

Covers the topics traditionally taught in the first-year calculus sequence in a brief and elementary fashion. This title is suitable for those taking the first calculus course, in high school or college.

Translated from the German by Buhler, W.K.; Cornell, G.

Calculus and linear algebra are two dominant themes in contemporary mathematics and its applications. The aim of this book is to introduce linear algebra in an intuitive geometric setting as the study of linear maps and to use these simpler linear functions to study more complicated nonlinear functions.

The next course the average stu dent would take would be a graduate course in algebraic topology, and such courses are commonly very homological in nature, providing quick access to current research, but not developing any intuition or geometric sense.

This book is a text for junior, senior, or first-year graduate courses traditionally titled Foundations of Geometry and/or Non Euclidean Geometry.

For instance, when we apply the Laplace trans form method to a linear ordinary differential equation with constant coefficients, any(n) + an-lY(n-l) + * * * + aoy = f(t), why is it justified to take the Laplace transform of both sides of the equation (Theorem A.

Chapter 4 presents plane projective geometry both synthetically and analytically, and the new Chapter 5 uses a descriptive and exploratory approach to introduce chaos theory and fractal geometry, stressing the self-similarity of fractals and their generation by transformations from Chapter 3.

This book is unique in that it looks at geometry from 4 different viewpoints - Euclid-style axioms, linear algebra, projective geometry, and groups and their invariantsApproach makes the subject accessible to readers of all mathematical tastes, from the visual to the algebraicAbundantly supplemented with figures and exercises

The goal of this text is to help students learn to use calculus intelligently for solving a wide variety of mathematical and physical problems. Examples and Exercises The exercise sets have been carefully constructed to be of maximum use to the students.

This book has a nonstandard choice of topics, including material on differential galois groups and proofs of the transcendence of e and pi. The author uses a conversational tone and has included a selection of stamps to accompany the text.

Monte Carlo methods are among the most used and useful computational tools available, providing efficient and practical algorithms to solve a wide range of scientific and engineering problems. This book provides a hands-on approach to learning this subject.

The honors course (at the University of Wisconsin) which inspired this book was, I think, more fun than the book itself. Yet, I hope enough of the spontaneity, enough of the spirit of that course, is left to enable those using the book to create exciting courses of their own.

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.

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.