Addison-Wesley series in mathematics

The aim of this book is to illustrate by significant special examples three aspects of the theory of Diophantine approximations: the formal relationships that exist between counting processes and the functions entering the theory; the determination of these functions for numbers given as classical numbers; and certain asymptotic estimates holding almost everywhere. Each chapter works out a special case of a much broader general theory, as yet unknown. Indications for this are given throughout the book, together with reference to current publications. The book may be used in a course in number theory, whose students will thus be put in contact with interesting but accessible problems on the ground floor of mathematics.

This book is a short text in linear algebra, intended for a one-term course. In the first chapter, Lang discusses the relation between the geometry and the algebra underlying the subject, and gives concrete examples of the notions which appear later in the book. He then starts with a discussion of linear equations, matrices and Gaussian elimination, and proceeds to discuss vector spaces, linear maps, scalar products, determinants, and eigenvalues. The book contains a large number of exercises, some of the routine computational type, and others are conceptual.

Rate of change of a function - Derivatives - Applications and derivatives - Integration - Transcendental functions - Techniques of integration - Infinite series - Vectors - Conic sections, polar coordinates - Functions of two or more variables - Multiple integrals - Differential equations.

Real Analysis is designed for a basic graduate course in real analysis. This textbook covers the fundamentals of measure and integration theory, and of functional analysis. The author has incorporated the suggestions of users of the first edition to make this an even more useful textbook for beginning graduate students. This second edition contains many more exercises than the first, including concrete applications of the general theory. As well as the pedagogic treatment of basic material, some topics are treated at a more advanced level, including the spectral theory for unbounded operators, the law of large numbers, and Stokes's Theorem on manifolds. This advanced material also makes the book useful as a reference source. --back cover