Bücher der Reihe Undergraduate Texts in Mathematics

Every mathematician agrees that every mathematician must know some set theory; The purpose of the book is to tell the beginning student of advanced mathematics the basic set theoretic facts of life, and to do so with the minimum of philosophical discourse and logical formalism.

This textbook invites the reader to develop a holistic grounding in mathematical finance, where concepts and intuition play as important a role as powerful mathematical tools.

The book also includes current computer algebra material in Appendix C and updated independent projects (Appendix D).The book may serve as a first or second course in undergraduate abstract algebra and with some supplementation perhaps, for beginning graduate level courses in algebraic geometry or computational algebra.

The fourth edition adds material related to mathematical finance as well as expansions on stable laws and martingales.From the reviews: "Almost thirty years after its first edition, this charming book continues to be an excellent text for teaching and for self study."

An introduction to complex analysis for students with some knowledge of complex numbers from high school. Topics studied include Julia sets and the Mandelbrot set, Dirichlet series and the prime number theorem, and the uniformization theorem for Riemann surfaces, with emphasis placed on the three geometries: spherical, euclidean, and hyperbolic.

The unifying approach of functional analysis is to view functions as points in abstract vector space and the differential and integral operators as linear transformations on these spaces.

Deals with modern algebra.

This best-selling textbook for a second course in linear algebra is aimed at undergrad math majors and graduate students. The text focuses on the central goal of linear algebra: understanding the structure of linear operators on finite-dimensional vector spaces.

This book offers a collection of historical essays detailing a large variety of mathematical disciplines and issues; it's accessible to a broad audience. This third edition includes new chapters on simple groups and new sections on alternating groups and the Poincare conjecture. Many more exercises have been added as well as commentary that helps place the exercises in context.

This fifth edition of Lang's book covers all the topics traditionally taught in the first-year calculus sequence. In addition, the rear of the book contains detailed solutions to a large number of the exercises, allowing them to be used as worked-out examples -- one of the main improvements over previous editions.

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 updated and revised second edition is designed to help students advance from basic calculus to higher-level linear and abstract algebra and number theory. It introduces an array of fundamental structures and shows how to balance intuition and rigor.

This much-anticipated textbook illuminates the field of discrete mathematics with examples, theory, and applications of the discrete volume of a polytope. It weaves a unifying thread through basic yet deep ideas in discrete geometry, combinatorics, and number theory.

Unlike other texts in differential geometry, this book develops the architecture necessary to introduce symplectic and contact geometry alongside its Riemannian cousin. Emphasizes the consequences of a definition and the use of examples and constructions.

Payoffs include: concise picture proofs of the Monotone and Dominated Convergence Theorems, a one-line/one-picture proof of Fubini's theorem from Cavalieri's Principle, and, in many cases, the ability to see an integral result from measure theory.

The Subject A little explanation is in order for our choice of the title Linear Opti- 1 mization (and corresponding terminology) for what has traditionally been called Linear Programming.Theword programming in this context can be confusing and/or misleading to students.

This text plugs a gap in the standard curriculum by linking set theory with analysis. It features a distinctive, detailed treatment of the real numbers system, and combines an introduction to set theory with exposition of the essence of analysis.

The first undergraduate text to provide an accessible introduction to real and convex analysis, this book by renowned Princeton University academics covers all the fundamentals as well as the tools of analysis, and features lots of illustrations and exercises.

This self-contained introduction to modern cryptography emphasizes the mathematics behind the theory of public key cryptosystems and digital signature schemes. The book focuses on these key topics. It includes exercises and examples at the end of each section.

This book stresses applications of real analysis, detailing how its principles and theory can be applied in a variety of settings in subjects ranging from Fourier series and polynomial approximation to discrete dynamical systems and nonlinear optimization.

This text presents mathematical biology as a field with a unity of its own, rather than only the intrusion of one science into another. The book focuses on problems of contemporary interest, such as cancer, genetics, and the rapidly growing field of genomics.

Completely rewritten for its second edition, this book concentrates on discrete derivative pricing models, culminating in a thorough derivation of the Black-Scholes option pricing formulas as a limiting case of the Cox-Ross-Rubinstein discrete model.

In this broad introduction to topology, the author searches for topological invariants of spaces, together with techniques for their calculating.

Unlike other texts on differential equations, this one provides an early presentation of the Laplace transform before deploying it in the motivation and development of many of the differential equation concepts for which it is particularly well suited.

This book develops the theory of multivariable analysis, building on the single variable foundations established in the companion volume, Real Analysis: Foundations and Functions of One Variable.

This textbook is designed for a one year course covering the fundamentals of partial differential equations, aimed towards advanced undergraduates and beginning graduate students. It features examples and exercises connected to real world problems.

The authors' novel approach to some interesting mathematical concepts - not normally taught in other courses - places them in a historical and philosophical setting.

The third edition of this concise, popular textbook on elementary differential equations gives instructors an alternative to the many voluminous texts on the market.