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 welltrained 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.
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Mathematical Analysis: A Straightforward Approach, 2nd Edition
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Author: K.G. Binmore
Brand: Cambridge University Press

For the second edition of this very successful text, Professor Binmore has written two chapters on analysis in vector spaces. The discussion extends to the notion of the derivative of a vector function as a matrix and the use of second derivatives in classifying stationary points. Some necessary concepts from linear algebra are included where appropriate. The first edition contained numerous worked examples and an ample collection of exercises for all of which solutions were provided at the end of the book. The second edition retains this feature but in addition offers a set of problems for which no solutions are given. Teachers may find this a helpful innovation.
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The Geocubic Matrix: Flashing in the Universe, and the Cosmos of EnergyMatter Caught in Its TimeFlow
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Author: T. Byron

All of the characteristics of atoms, molecules, and crystals are explained under one unification model, in a revolutionary "Theoryof Everything", which for the first time accounts for the 4 basic forces of the Universe, those being the Strong Atomic Force, Weak Atomic Force, Gravity, and Electromagnitism.


Yet Another Introduction to Analysis
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Author: Victor Bryant
Brand: Brand: Cambridge University Press

Mathematics education in schools has seen a revolution in recent years. Students everywhere expect the subject to be wellmotivated, 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 wellmotivated 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.
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Quasiconformal Mappings and Analysis: A Collection of Papers Honoring F.W. Gehring
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Brand: Brand: Springer

This book comprises a broad selection of expository articles that were written in conjunction with an international conference held to honor F.W. Gehring on the occasion of his 70th birthday. The objective of both the symposium and the present volume was to survey a wide array of topics related to Gehring's fundamental research in the field of quasiconformal mappings, emphasizing the relation of these mappings to other areas of analysis. The book begins with a short biographical sketch and an overview of Gehring's mathematical achievements, including a complete list of his publications. This is followed by Olli Lehto's account of Gehring's careerlong involvement with the Finnish mathematical community and his role in the evolution of the Finnish school of quasiconformal mapping. The remaining articles, written by prominent authorities in diverse branches of analysis, are arranged alphabetically. The principal speakers at the symposium were: Astala, Baernstein Earle, Jones, Kra, Lehto, Martin, Sullivan, and Va"isa"la". Other individuals, some unable to attend the conference, were invited to contribute articles to the volume, which should give readers new insights into numerous aspects of quasiconformal mappings and their applications to other fields of mathematical analysis. Friends and colleagues of Professor Gehring will be especially interested in the personal accounts of his mathematical career and the descriptions of his many important research contributions.
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Analysis: An Introduction
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Author: Richard Beals
Brand: Brand: Cambridge University Press

This selfcontained text, suitable for advanced undergraduates, provides an extensive introduction to mathematical analysis, from the fundamentals to more advanced material. It begins with the properties of the real numbers and continues with a rigorous treatment of sequences, series, metric spaces, and calculus in one variable. Further subjects include Lebesgue measure and integration on the line, Fourier analysis, and differential equations. In addition to this core material, the book includes a number of interesting applications of the subject matter to areas both within and outside the field of mathematics. The aim throughout is to strike a balance between being too austere or too sketchy, and being so detailed as to obscure the essential ideas. A large number of examples and 500 exercises allow the reader to test understanding, practise mathematical exposition and provide a window into further topics.
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Numbers and Functions: Steps to Analysis
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Author: R. P. Burn
Brand: Brand: Cambridge University Press

The transition from studying calculus in schools to studying mathematical analysis at university is notoriously difficult. In this book, Dr Burn follows a route that proved successful with A Pathway to Number Theory and Groups: A Path to Geometry. He invites the student reader to tackle each of the key concepts in turn, progressing from experience (using computers for graph drawing where appropriate) through a structured sequence of several hundred problems to concepts, definitions and proofs of classical real analysis. The sequence of problems, which all have solutions supplied, draws students into constructing definitions and theorems for themselves. This natural development is informed by historical insight and complemented by historical discussion. The sequence also takes into account recent research which has shown how intuitive ideas about numbers, limits, functions and infinity may be at odds with the standard definitions. The novel approach to rigorous analysis offered here is designed to enable students to grow in confidence and skill and thus overcome the traditional difficulties. Teachers in sixth forms will find that questions at the beginning of every chapter provide ways of preparing those at school for university mathematics. Lecturers in universities will be challenged to rethink their conventions about the best way to introduce the central ideas of analysis to undergraduates.
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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.
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Multidimensional Real Analysis I: Differentiation (Cambridge Studies in Advanced Mathematics)
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Author: J. J. Duistermaat
Brand: Brand: Cambridge University Press

Volume 1 provides a comprehensive review of differential analysis in multidimensional Euclidean space.
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A Treatise on the Theory of Bessel Functions (Cambridge Mathematical Library)
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Author: G. N. Watson
Brand: Cambridge University Press

The late Professor G.N. Watson wrote his monumental treatise on the theory of Bessel functions in 1922 with two objects in view. The first was the development of applications of the fundamental processes of the theory of complex variables, and the second was compiling a collection of results of value for mathematicians and physicists who encounter Bessel functions in the course of their researches. The completeness of the theoretical account, combined with the wide scope of the collection of practical examples have resulted in a book that will be indispensable for pure mathematicians, applied mathematicians, and physicists.
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