|The Science of Fractal Images
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The first book to discuss fractals solely from the point of view of computer graphics, this work includes an introduction to the basic axioms of fractals and their applications in the natural sciences, a survey of random fractals together with many pseudocodes for selected algorithms, an introduction into fantastic fractals such as the Mandelbrot set and the Julia sets, together with a detailed discussion of algorithms and fractal modeling of real world objects. 142 illustrations in 277 parts. 39 color plates.
|Handbook of Multivalued Analysis: Volume I: Theory (Mathematics and Its Applications (closed))
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Author: Shouchuan Hu
This is the first of a two-volume exposition on the theory and applications of set-valued maps. Multivalued analysis is a remarkable mixture of many different fields of mathematics, such as topology, measure theory, nonlinear functional analysis and applied mathematics. This two-volume work provides a comprehensive survey of the general theory and applications of set-valued analysis. The existing books on the subject deal with either one particular domain of the subject or present primarily the finite dimensional aspects of the theory. In contrast this volume gives a complete picture of the subject, including important new developments that occurred in recent years and a detailed bibliography. Although the presentation of the subject assumes some knowledge from various areas of mathematical analysis, the authors have made every effort, including the addition of an appendix, to keep the work self-contained.
Audience: The work is an essential reference for graduate students and researchers interested in multivalued analysis.
|A Hilbert Space Problem Book (Graduate Texts in Mathematics)
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Author: P.R. Halmos
From the Preface: "This book was written for the active reader. The first part consists of problems, frequently preceded by definitions and motivation, and sometimes followed by corollaries and historical remarks... The second part, a very short one, consists of hints... The third part, the longest, consists of solutions: proofs, answers, or contructions, depending on the nature of the problem....
This is not an introduction to Hilbert space theory. Some knowledge of that subject is a prerequisite: at the very least, a study of the elements of Hilbert space theory should proceed concurrently with the reading of this book."
|Complex Analysis with MATHEMATICA®
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Author: William T. Shaw
Complex Analysis with Mathematica offers a new way of learning and teaching a subject that lies at the heart of many areas of pure and applied mathematics, physics, engineering and even art. This book offers teachers and students an opportunity to learn about complex numbers in a state-of-the-art computational environment. The innovative approach also offers insights into many areas too often neglected in a student treatment, including complex chaos and mathematical art. Thus readers can also use the book for self-study and for enrichment. The use of Mathematica enables the author to cover several topics that are often absent from a traditional treatment. Students are also led, optionally, into cubic or quartic equations, investigations of symmetric chaos, and advanced conformal mapping. A CD is included which contains a live version of the book, and the Mathematica code enables the user to run computer experiments.
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Author: Kathy Richardson
This valuable teachers resource provides teachers with classroom tested activities that help children develop in-depth understandings about 2-D and 3-D geometry concepts and spatial awareness.
Understanding Geometry is more than a book about geometry activities. Kathy provides the following resources for teachers:
- Background information on what we need to know about geometry
- Assessment and observation moments are highlighted - Geometry Terminology Glossary
- Planning Guide for Grades K-3
- Task Cards
|Excursions in Calculus: An Interplay of the Continuous and the Discrete (Dolciani Mathematical Expositions)
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Author: Robert M. Young
The purpose of this book is to explore the rich and elegant interplay that exists between the two main currents of mathematics, the continuous and the discrete. Such fundamental notions in discrete mathematics as induction, recursion, combinatorics, number theory, discrete probability, and the algorithmic point of view as a unifying principle are continually explored as they interact with traditional calculus. The book is addressed primarily to well-trained calculus students and those who teach them, but it can also serve as a supplement in a traditional calculus course for anyone who wants to see more. The problems, taken for the most part from probability, analysis, and number theory, are an integral part of the text. There are over 400 problems presented in this book.
|Diophantus and Diophantine Equations (Dolciani Mathematical Expositions)
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Author: Isabella G. Bashmakova
Brand: Brand: The Mathematical Association of America
This book tells the story of Diophantine analysis, a subject that, owing to its thematic proximity to algebraic geometry, became fashionable in the last half century and has remained so ever since. This new treatment of the methods of Diophantus - a person whose very existence has long been doubted by most historians of mathematics - will be accessible to readers who have taken some university mathematics. It includes the elementary facts of algebraic geometry indispensable for its understanding. The heart of the book is a fascinating account of the development of Diophantine methods during the Renaissance and in the work of Fermat. This account is continued to our own day and ends with an afterword by Joseph Silverman who notes the most recent developments including the proof of Fermat's Last Theorem.
- Used Book in Good Condition
|Topology via Logic (Cambridge Tracts in Theoretical Computer Science)
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Author: Steven Vickers
This advanced textbook on topology has three unusual features. First, the introduction is from the locale viewpoint, motivated by the logic of finite observations: this provides a more direct approach than the traditional one based on abstracting properties of open sets in the real line. Second, the author freely exploits the methods of locale theory. Third, there is substantial discussion of some computer science applications. As computer scientists become more aware of the mathematical foundations of their discipline, it is appropriate that such topics are presented in a form of direct relevance and applicability. This book goes some way towards bridging the gap for computer scientists.
|Yet Another Introduction to Analysis
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Author: Victor Bryant
Mathematics education in schools has seen a revolution in recent years. Students everywhere expect the subject to be well-motivated, relevant and practical. When such students reach higher education, the traditional development of analysis, often divorced from the calculus they learned at school, seems highly inappropriate. Shouldn't every step in a first course in analysis arise naturally from the student's experience of functions and calculus in school? And shouldn't such a course take every opportunity to endorse and extend the student's basic knowledge of functions? In Yet Another Introduction to Analysis, the author steers a simple and well-motivated path through the central ideas of real analysis. Each concept is introduced only after its need has become clear and after it has already been used informally. Wherever appropriate, new ideas are related to common topics in math curricula and are used to extend the reader's understanding of those topics. In this book the readers are led carefully through every step in such a way that they will soon be predicting the next step for themselves. In this way students will not only understand analysis, but also enjoy it.
|The Seiberg-Witten Equations and Applications to the Topology of Smooth Four-Manifolds (Mathematical Notes, Vol. 44)
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Author: John W. Morgan
The recent introduction of the Seiberg-Witten invariants of smooth four-manifolds has revolutionized the study of those manifolds. The invariants are gauge-theoretic in nature and are close cousins of the much-studied SU(2)-invariants defined over fifteen years ago by Donaldson. On a practical level, the new invariants have proved to be more powerful and have led to a vast generalization of earlier results. This book is an introduction to the Seiberg-Witten invariants.
The work begins with a review of the classical material on Spin c structures and their associated Dirac operators. Next comes a discussion of the Seiberg-Witten equations, which is set in the context of nonlinear elliptic operators on an appropriate infinite dimensional space of configurations. It is demonstrated that the space of solutions to these equations, called the Seiberg-Witten moduli space, is finite dimensional, and its dimension is then computed. In contrast to the SU(2)-case, the Seiberg-Witten moduli spaces are shown to be compact. The Seiberg-Witten invariant is then essentially the homology class in the space of configurations represented by the Seiberg-Witten moduli space. The last chapter gives a flavor for the applications of these new invariants by computing the invariants for most Kahler surfaces and then deriving some basic toological consequences for these surfaces.