The Way of Analysis gives a thorough account of real analysis in one or several variables, from the construction of the real number system to an introduction of the Lebesgue integral. The text provides proofs of all main results, as well as motivations, examples, applications, exercises, and formal chapter summaries. Additionally, there are three chapters on application of analysis, ordinary differential equations, Fourier series, and curves and surfaces to show how the techniques of analysis are used in concrete settings.

This elementary presentation exposes readers to both the process of rigor and the rewards inherent in taking an axiomatic approach to the study of functions of a real variable. The aim is to challenge and improve mathematical intuition rather than to verify it. The philosophy of this book is to focus attention on questions which give analysis its inherent fascination. Each chapter begins with the discussion of some motivating examples and concludes with a series of questions.

In The Way to Win, two of the country’s most accomplished political reporters explain what separates the victors from the victims in the unforgiving environment of modern presidential campaigns. Mark Halperin, political director of ABC News, and John F. Harris, the national politics editor of The Washington Post, tell the story of how two families–the Bushes and the Clintons–have held the White House for nearly a generation and examine Hillary Clinton’s prospects for extending this record in 2008. Based on years of research, including private campaign memos and White House communications, The Way to Win reveals the surprising details of how the Bushes and Clintons have closely studied each the other’s successes and failures and used these lessons to shape their own strategies for winning elections and wielding power. In the case of George W. Bush, the strategic genius is Karl C. Rove, arguably the most influential White House aide in history. For the first time, Halperin and Harris cut through the myths and controversies surrounding Rove to illuminate in brilliant, behind-the-scenes detail what he actually does–his Trade Secrets for winning elections. In the case of the Clintons, the chief strategist is Bill Clinton himself. Drawing on their fifteen years reporting on and interviewing him, Halperin and Harris deconstruct and decipher the Clinton style, identifying the methods that all candidates can use in their pursuit of the White House. The Way to Win takes a lively and irreverent approach, but Halperin and Harris also show the disturbing ways that American politics has become a Freak Show–their name for a political culture that provides incentives for candidates, activists, interest groups, and the news media to emphasize ideological extremism and personal attack. For the first time, Halperin and Harris describe how Freak Show campaigns orchestrated by the likes of Internet pioneer Matt Drudge forced Al Gore and John Kerry to lose control of their public images (with considerable help from the candidates’ own ineptitude) and lose the White House. On the brink of what will be one of the most intense, most exciting presidential elections in American history, The Way to Win is the book that armchair political junkies have been waiting for. Filled with peerless analysis and eye-opening revelations from the trenches, it is a must read for everyone who follows American politics.

Natural numbers, zero, negative integers, rational numbers, irrational numbers, real numbers, complex numbers, . . ., and, what are numbers? The most accurate mathematical answer to the question is given in this book.

This work by Zorich on Mathematical Analysis constitutes a thorough first course in real analysis, leading from the most elementary facts about real numbers to such advanced topics as differential forms on manifolds, asymptotic methods, Fourier, Laplace, and Legendre transforms, and elliptic functions.

This is part one of a two-volume book on real analysis and is intended for senior undergraduate students of mathematics who have already been exposed to calculus. The emphasis is on rigour and foundations of analysis. Beginning with the construction of the number systems and set theory, the book discusses the basics of analysis (limits, series, continuity, differentiation, Riemann integration), through to power series, several variable calculus and Fourier analysis, and then finally the Lebesgue integral. These are almost entirely set in the concrete setting of the real line and Euclidean spaces, although there is some material on abstract metric and topological spaces. The book also has appendices on mathematical logic and the decimal system. The entire text (omitting some less central topics) can be taught in two quarters of 25–30 lectures each. The course material is deeply intertwined with the exercises, as it is intended that the student actively learn the material (and practice thinking and writing rigorously) by proving several of the key results in the theory.

Subjects of Analysis is a work of incomparable significance for the field of psychoanalysis. Ogden reworks and recombines the basic contributions of Freud, Klein, and Winnicott to create a vision of the analytic process that has never existed beforeDstartling in its freshness, moving in its depth and integrity.

Foundations of Analysis has two main goals. The first is to develop in students the mathematical maturity and sophistication they will need as they move through the upper division curriculum. The second is to present a rigorous development of both single and several variable calculus, beginning with a study of the properties of the real number system. The presentation is both thorough and concise, with simple, straightforward explanations. The exercises differ widely in level of abstraction and level of difficulty. They vary from the simple to the quite difficult and from the computational to the theoretical. Each section contains a number of examples designed to illustrate the material in the section and to teach students how to approach the exercises for that section. --Book cover.

Mathematics is the music of science, and real analysis is the Bach of mathematics. There are many other foolish things I could say about the subject of this book, but the foregoing will give the reader an idea of where my heart lies. The present book was written to support a first course in real analysis, normally taken after a year of elementary calculus. Real analysis is, roughly speaking, the modern setting for Calculus, "real" alluding to the field of real numbers that underlies it all. At center stage are functions, defined and taking values in sets of real numbers or in sets (the plane, 3-space, etc.) readily derived from the real numbers; a first course in real analysis traditionally places the emphasis on real-valued functions defined on sets of real numbers. The agenda for the course: (1) start with the axioms for the field ofreal numbers, (2) build, in one semester and with appropriate rigor, the foun dations of calculus (including the "Fundamental Theorem"), and, along the way, (3) develop those skills and attitudes that enable us to continue learning mathematics on our own. Three decades of experience with the exercise have not diminished my astonishment that it can be done.