First Course in Calculus (World Student)

Science & Math

Serge Lang

Mathematics

Addison-Wesley Educational Publishers Inc.,U.S.

Analysis I (Addison-Wesley series in mathematics)

Addison-Wesley

The purpose of this book is to give an exposition of the classical and basic algebraic and analytic number theory. In a certain sense the plan of the book is still that used more or less by Hilbert in his Bericht, although, or course, both the algebraic and analytic aspects of number theory have been updated (and the class field theory omitted).  --- from book's dustjacket

Algebraic Numbers

180 page paperback book a Introduction to Linear Algebra.

Introduction to Linear Algebra

Springer, Verlag

This new, revised edition covers all of the basic topics in calculus of several variables, including vectors, curves, functions of several variables, gradient, tangent plane, maxima and minima, potential functions, curve integrals, Green’s theorem, multiple integrals, surface integrals, Stokes’ theorem, and the inverse mapping theorem and its consequences. It includes many completely worked-out problems.

Calculus of Several Variables

Addison-Wesley Educational Publishers, Inc.

This new, revised edition covers all of the basic topics in calculus of several variables, including vectors, curves, functions of several variables, gradient, tangent plane, maxima and minima, potential functions, curve integrals, Greenâ€™s theorem, multiple integrals, surface integrals, Stokesâ€™ theorem, and the inverse mapping theorem and its consequences. It includes many completely worked-out problems.

Calculus of Several Variables (Addison Wesley Series on Managing Human Resources)

Addison-Wesley Educational Pub

This basic text for a one-year course in algebra at the graduate level thoroughly prepares students to handle the algebra they will use in all of mathematics. The author assumes that students have a basic familiarity with the language of mathematics "i.e.: sets and mapping, integers, and rational numbers." The text was thoroughly revised and enhanced in response to reviewers' comments and suggestions. Designed to improve students' retention and comprehension, the text is divided into four parts. The first introduces the basic notions of algebra. The second covers the direction of algebraic equations, including the Galois theory, and the final two parts cover the direction of linear and multilinear algebra.

Algebra

Addison-Wesley Publishing Comp

Analytic number theory and part of the spectral theory of operators (differential, pseudo-differential, elliptic, etc.) are being merged under a more general analytic theory of regularized products of certain sequences satisfying a few basic axioms. The most basic examples consist of the sequence of natural numbers, the sequence of zeros with positive imaginary part of the Riemann zeta function, and the sequence of eigenvalues, say of a positive Laplacian on a compact or certain cases of non-compact manifolds. The resulting theory is applicable to ergodic theory and dynamical systems; to the zeta and L-functions of number theory or representation theory and modular forms; to Selberg-like zeta functions; and to the theory of regularized determinants familiar in physics and other parts of mathematics. Aside from presenting a systematic account of widely scattered results, the theory also provides new results. One part of the theory deals with complex analytic properties, and another part deals with Fourier analysis. Typical examples are given. This LNM provides basic results which are and will be used in further papers, starting with a general formulation of Cram r's theorem and explicit formulas. The exposition is self-contained (except for far-reaching examples), requiring only standard knowledge of analysis.

Basic Analysis of Regularized Series and Products (Lecture Notes in Mathematics)

Jay Jorgenson

This logically self-contained introduction to analysis centers around those properties that have to do with uniform convergence and uniform limits in the context of differentiation and integration. From the reviews: "This material can be gone over quickly by the really well-prepared reader, for it is one of the bookâ€™s pedagogical strengths that the pattern of development later recapitulates this material as it deepens and generalizes it." --AMERICAN MATHEMATICAL SOCIETY

Undergraduate Analysis (Undergraduate Texts in Mathematics)

SL2(R) gives the student an introduction to the infinite dimensional representation theory of semisimple Lie groups by concentrating on one example - SL2(R). This field is of interest not only for its own sake, but for its connections with other areas such as number theory, as brought out, for example, in the work of Langlands. The rapid development of representation theory over the past 40 years has made it increasingly difficult for a student to enter the field. This book makes the theory accessible to a wide audience, its only prerequisites being a knowledge of real analysis, and some differential equations.

SL2(R) (Graduate Texts in Mathematics, 105)

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Books by Serge Lang