The Laplace transform is a wonderful tool for solving ordinary and partial differential equations and has enjoyed much success in this realm. With its success, however, a certain casualness has been bred concerning its application, without much regard for hypotheses and when they are valid. Even proofs of theorems often lack rigor, and dubious mathematical practices are not uncommon in the literature for students. In the present text, I have tried to bring to the subject a certain amount of mathematical correctness and make it accessible to un- dergraduates. Th this end, this text addresses a...
The Laplace transform is a wonderful tool for solving ordinary and partial differential equations and has enjoyed much success in this realm. With its...
The approach taken by this book is based on two beliefs. The first is that almost nobody understands calculus fully the first time around: multiple exposures are required. The second belief is that graphing calculators can be used to make the introduction of the theory of limits much easier for the students. This book presents the theoretical pieces of introductory calculus, using appropriate technology, in a style suitable to accompany almost any first calculus text. It offers a large range of increasingly sophisticated examples and problems to build understanding of the notion of limit and...
The approach taken by this book is based on two beliefs. The first is that almost nobody understands calculus fully the first time around: multiple ex...
"In the world of mathematics, the 1980's might well be described as the "decade of the fractal." Starting with Benoit Mandelbrot's remarkable text The Fractal Geometry of Nature, there has been a deluge of books, articles and television programmes about the beautiful mathematical objects, drawn by computers using recursive or iterative algorithms, which Mandelbrot christened fractals. Gerald Edgar's book is a significant addition to this deluge. Based on a course given to talented high- school students at Ohio University in 1988, it is, in fact,...
From reviews of the first edition:
"In the world of mathematics, the 1980's might well be described as the "decade of the fractal." Startin...
This volume contains the proceedings of the 1988 SEI Conference on Software Engineering Education. The Software Engineering Institute (SEI) is a United States government-funded research and development center operated by Carnegie Mellon University. Its principal responsibility is to accelerate the reduction to practice of modern software engineering techniques and methods. An annual activity of the SEI is the SEI Conference on Software Engineering Education. The purpose of the conference is to promote enhanced software engineering education in the academic, industrial, and government...
This volume contains the proceedings of the 1988 SEI Conference on Software Engineering Education. The Software Engineering Institute (SEI) is a Unite...
Cryptography is a key technology in electronic key systems. It is used to keep data secret, digitally sign documents, access control, and so forth. Users therefore should not only know how its techniques work, but they must also be able to estimate their efficiency and security. Based on courses taught by the author, this book explains the basic methods of modern cryptography. It is written for readers with only basic mathematical knowledge who are interested in modern cryptographic algorithms and their mathematical foundation. Several exercises are included following each chapter. This...
Cryptography is a key technology in electronic key systems. It is used to keep data secret, digitally sign documents, access control, and so forth....
Discrete mathematics is quickly becoming one of the most important areas of mathematical research, with applications to cryptography, linear programming, coding theory and the theory of computing. This book is aimed at undergraduate mathematics and computer science students interested in developing a feeling for what mathematics is all about, where mathematics can be helpful, and what kinds of questions mathematicians work on. The authors discuss a number of selected results and methods of discrete mathematics, mostly from the areas of combinatorics and graph theory, with a little number...
Discrete mathematics is quickly becoming one of the most important areas of mathematical research, with applications to cryptography, linear progra...
This is a logically self-contained introduction to analysis, suitable for students who have had two years of calculus. The book centers around those properties that have to do with uniform convergence and uniform limits in the context of differentiation and integration. Topics discussed include the classical test for convergence of series, Fourier series, polynomial approximation, the Poisson kernel, the construction of harmonic functions on the disc, ordinary differential equation, curve integrals, derivatives in vector spaces, multiple integrals, and others. One of the author's main...
This is a logically self-contained introduction to analysis, suitable for students who have had two years of calculus. The book centers around those p...
The book deals with a powerful and convenient approach to a great variety of types of problems of the recursive monte-carlo or stochastic approximation type. Such recu- sive algorithms occur frequently in stochastic and adaptive control and optimization theory and in statistical esti- tion theory. Typically, a sequence {X } of estimates of a n parameter is obtained by means of some recursive statistical th st procedure. The n estimate is some function of the n_l estimate and of some new observational data, and the aim is to study the convergence, rate of convergence, and the pa- metric...
The book deals with a powerful and convenient approach to a great variety of types of problems of the recursive monte-carlo or stochastic approximatio...
This is a book about prime numbers, congruences, secret messages, and elliptic curves that you can read cover to cover. It grew out of undergr- uate courses that the author taught at Harvard, UC San Diego, and the University of Washington. The systematic study of number theory was initiated around 300B. C. when Euclid proved that there are in?nitely many prime numbers, and also cleverly deduced the fundamental theorem of arithmetic, which asserts that every positive integer factors uniquely as a product of primes. Over a thousand years later (around 972A. D. ) Arab mathematicians formulated...
This is a book about prime numbers, congruences, secret messages, and elliptic curves that you can read cover to cover. It grew out of undergr- uate c...
This book began life as a set of notes that I developed for a course at the University of Washington entitled Introduction to Modern Algebra for Tea- ers. Originally conceived as a text for future secondary-school mathematics teachers, it has developed into a book that could serve well as a text in an - dergraduatecourseinabstractalgebraoracoursedesignedasanintroduction to higher mathematics. This book di?ers from many undergraduate algebra texts in fundamental ways; the reasons lie in the book s origin and the goals I set for the course. The course is a two-quarter sequence required of...
This book began life as a set of notes that I developed for a course at the University of Washington entitled Introduction to Modern Algebra for Tea- ...
