This book is an introductory text in functional analysis, aimed at the graduate student with a firm background in integration and measure theory. Unlike many modern treatments, this book begins with the particular and works its way to the more general, helping the student to develop an intuitive feel for the subject. For example, the author introduces the concept of a Banach space only after having introduced Hilbert spaces, and discussing their properties. The student will also appreciate the large number of examples and exercises which have been included.

This is an abstract book written in a modern, up to date style at about the second year graduate level, which seeks to bring the unifying principles of functional analysis to bear on diverse problems in applied mathematics. It is addressed to students and researchers in applied mathematics and the theoretical sciences.

This book is from the Springer-Verlag "Problem Books in Mathematics" Series edited by P. R. Halmos. Contains problem sets with complete solutions in measurable sets, sigma-algebras and positive measures, fundamental theorems in the integration of measurable functions, Fubini's theorem, Lp spaces, the L2 space, convolution products, Fourier transforms, functions of bounded variation, summation processes: trignometric polynomials and trignometric series.

Miller and Childers have focused on creating a clear presentation of foundational concepts with specific applications to signal processing and communications, clearly the two areas of most interest to students and instructors in this course. It is aimed at graduate students as well as practicing engineers, and includes unique chapters on narrowband random processes and simulation techniques. The appendices provide a refresher in such areas as linear algebra, set theory, random variables, and more. Probability and Random Processes also includes applications in digital communications, information theory, coding theory, image processing, speech analysis, synthesis and recognition, and other fields.

Assuming only modest knowledge of undergraduate level math, Invitation to the Mathematics of Fermat-Wiles presents diverse concepts required to comprehend Wiles' extraordinary proof. Furthermore, it places these concepts in their historical context.

Geometric measure theory has become increasingly essential to geometry as well as numerous and varied physical applications. The third edition of this leading text/reference introduces the theory, the framework for the study of crystal growth, clusters of soap bubbles, and similar structures involving minimization of energy.
Over the past thirty years, this theory has contributed to major advances in geometry and analysis including, for example, the original proof of the positive mass conjecture in cosmology.
This third edition of Geometric Measure Theory: A Beginner's Guide presents, for the first time in print, the proofs of the double bubble and the hexagonal honeycomb conjectures. Four new chapters lead the reader through treatments of the Weaire-Phelan counterexample of Kelvin's conjecture, Almgren's optimal isoperimetric inequality, and immiscible fluids and crystals. The abundant illustrations, examples, exercises, and solutions in this book will enhance its reputation as the most accessible introduction to the subject.

The Lebesgue integral is now standard for both applications and advanced mathematics. This books starts with a review of the familiar calculus integral and then constructs the Lebesgue integral from the ground up using the same ideas. A Primer of Lebesgue Integration has been used successfully both in the classroom and for individual study. Bear presents a clear and simple introduction for those intent on further study in higher mathematics. Additionally, this book serves as a refresher providing new insight for those in the field. The author writes with an engaging, commonsense style that appeals to readers at all levels.

This collection includes more than 100 of the best (and some of the toughest)mathematical puzzles ever to appear in one volume. You'll need a love for mathematical reasoning and a streak of determination. You won't need a professional acquaintance with mathematics; a motivated high school student has what it takes! If you're up to the challenge, there's even a chapter on Unsolved Puzzles.

Proceedings of lectures given at the Second Session of the Centro Internazionale Matematico Estivo (C.I.M.E.) held in Cetraro, Italy, June 15-22, 1996. The international summer school on Calculus of Variations and Geometric Evolution Problems was held at Cetraro, Italy, 1996. The contributions to this volume reflect quite closely the lectures given at Cetraro which have provided an image of a fairly broad field in analysis where in recent years we have seen many important contributions. Among the topics treated in the courses were variational methods for Ginzburg-Landau equations, variational models for microstructure and phase transitions, a variational treatment of the Plateau problem for surfaces of prescribed mean curvature in Riemannian manifolds - both from the classical point of view and in the setting of geometric measure theory.

One of the themes of this book is the recognition that many students will at first feel uncomfortable or at least unfamiliar with the theoretical nature inherent in many of the topics of linear algebra.
There are numerous discussions of the logical structure of proofs, the need to translate terminology into notations, and suggestions about efficient ways to discover a proof.
This book combines the many simple and beautiful results of elementary linear algebra with some powerful computational techniques to demonstrate that theoreetical mathematics need not be difficult, mysterious, or useless.

Embedded Image Processing on the TMS320C6000™ DSP: Examples in Code Composer Studio™ and MATLAB focuses on efficient implementations of advanced image processing algorithms for resource-constrained embedded DSP systems. Featuring the popular Texas Instruments TMS320C6000TM line of Digital Signal Processors, it utilizes a proven methodology of beginning with a high-level algorithmic point-of-view, proceeding to develop prototype code in MATLAB and Visual Studio, and concluding with an efficient implementation suitable for deployment on an embedded DSP system.

Continuous-Time Signals is an extended description of continuous-time signals related to the course of Signals and Systems. As a time-varying process of any physical state of any object, which serves for representation, detection, and transmission of messages, a modern electrical signal possesses, in applications, many specific properties. To make possible for readers to deal with signals free, the book systematically covers major principle foundations of the signals theory. The representation of signals in the frequency domain (by Fourier transform) is considered with strong emphasis on how the spectral density of a single waveform becomes that of its burst and then the spectrum of its train. Different kinds of amplitude and angular modulations are analyzed noticing a consistency between the spectra of modulating and modulated signals. The energy and power presentation of signals is given along with their correlation properties. Finally, presenting the bandlimited and analytic signals, the book elucidates the methods of their description, transformation (by Hilbert transform), and sampling.

The theory of measure and of the Lebesgue integal set forth in this book is based on lectures by A. N. Kolmogorov delivered at the Mechanics-Mathematics Faculty at Moscow State University. The final preparation of the text for publication was carried out by S. V. Fomin

The book is an introductory textbook mainly for students of computer science and mathematics. Our guiding phrase is "what every theoretical computer scientist should know about linear programming". A major focus is on applications of linear programming, both in practice and in theory. The book is concise, but at the same time, the main results are covered with complete proofs and in sufficient detail, ready for presentation in class. The book does not require more prerequisites than basic linear algebra, which is summarized in an appendix. One of its main goals is to help the reader to see linear programming "behind the scenes".