Education is an admirable thing, but it is well to remember from time to time that nothing worth knowing can be taught. Oscar Wilde, "The Critic as Artist," 1890. Analysis is a profound subject; it is neither easy to understand nor summarize. However, Real Analysis can be discovered by solving problems. This book aims to give independent students the opportunity to discover Real Analysis by themselves through problem solving. ThedepthandcomplexityofthetheoryofAnalysiscanbeappreciatedbytakingaglimpseatits developmental history. Although Analysis was conceived in the 17th century during the...
Education is an admirable thing, but it is well to remember from time to time that nothing worth knowing can be taught. Oscar Wilde, "The Critic as Ar...
The theory of function spaces endowed with the topology of point wise convergence, or Cp-theory, exists at the intersection of three important areas of mathematics: topological algebra, functional analysis, and general topology. Cp-theory has an important role in the classification and unification of heterogeneous results from each of these areas of research. Through over 500 carefully selected problems and exercises, this volume provides a self-contained introduction to Cp-theory and general topology. By systematically introducing each of the major topics in Cp-theory, this volume is...
The theory of function spaces endowed with the topology of point wise convergence, or Cp-theory, exists at the intersection of three important areas o...
Pell's equation is an important topic of algebraic number theory that involves quadratic forms and the structure of rings of integers in algebraic number fields. The history of this equation is long and circuitous, and involved a number of different approaches before a definitive theory was found. There were partial patterns and quite effective methods of finding solutions, but a complete theory did not emerge until the end of the eighteenth century. The topic is motivated and developed through sections of exercises which allow the student to recreate known theory and provide a focus for...
Pell's equation is an important topic of algebraic number theory that involves quadratic forms and the structure of rings of integers in algebraic num...
The idea of writing this book came roughly at the time of publication of my graduate text Lectures on Modules and Rings, Springer GTM Vol. 189, 1999. Since that time, teaching obligations and intermittent intervention of other projects caused prolonged delays in the work on this volume. Only a lucky break in my schedule in 2006 enabled me to put the finishing touches on the completion of this long overdue book. This book is intended to serve a dual purpose. First, it is designed as a "problem book" for Lectures. As such, it contains the statements and full solutions of the many exercises that...
The idea of writing this book came roughly at the time of publication of my graduate text Lectures on Modules and Rings, Springer GTM Vol. 189, 1999. ...
This useful book, which grew out of the author's lectures at Berkeley, presents some 400 exercises of varying degrees of difficulty in classical ring theory, together with complete solutions, background information, historical commentary, bibliographic details, and indications of possible improvements or generalizations. The book should be especially helpful to graduate students as a model of the problem-solving process and an illustration of the applications of different theorems in ring theory. The author also discusses "the folklore of the subject: the tricks of the trade' in ring theory,...
This useful book, which grew out of the author's lectures at Berkeley, presents some 400 exercises of varying degrees of difficulty in classical ring ...
The book that follows is an experiment in the teaching of population theory and analysis. A sequence of problems where each is a self-contained puzzle, and the successful solution of each which puts the student in a position to tackle the next, is a means of securing the active participation of the learner and so the mastery of a technical subject. How far our questions are the exciting puzzles at which we aimed, and how far the sequence constitutes a rounded course in demography, must be left to the user to judge. One test of a good problem is whether a solution, that may take hours of...
The book that follows is an experiment in the teaching of population theory and analysis. A sequence of problems where each is a self-contained puzzle...
The textbook Geometry, published in French by CEDICjFernand Nathan and in English by Springer-Verlag (scheduled for 1985) was very favorably re ceived. Nevertheless, many readers found the text too concise and the exercises at the end of each chapter too difficult, and regretted the absence of any hints for the solution of the exercises. This book is intended to respond, at least in part, to these needs. The length of the textbook (which will be referred to as B] throughout this book) and the volume of the material covered in it preclude any thought of publishing an expanded version, but we...
The textbook Geometry, published in French by CEDICjFernand Nathan and in English by Springer-Verlag (scheduled for 1985) was very favorably re ceived...
This book mainly discusses the representation theory of the special linear group 8L(2, 1R), and some applications of this theory. In fact the emphasis is on the applications; the working title of the book while it was being writ- ten was "Some Things You Can Do with 8L(2). " Some of the applications are outside representation theory, and some are to representation theory it- self. The topics outside representation theory are mostly ones of substantial classical importance (Fourier analysis, Laplace equation, Huyghens' prin- ciple, Ergodic theory), while the ones inside representation theory...
This book mainly discusses the representation theory of the special linear group 8L(2, 1R), and some applications of this theory. In fact the emphasis...
