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Limits Limits Everywhere

Author: David Applebaum
Publisher: OUP Oxford
ISBN: 0191627879
Size: 51.22 MB
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A quantity can be made smaller and smaller without it ever vanishing. This fact has profound consequences for science, technology, and even the way we think about numbers. In this book, we will explore this idea by moving at an easy pace through an account of elementary real analysis and, in particular, will focus on numbers, sequences, and series. Almost all textbooks on introductory analysis assume some background in calculus. This book doesn't and, instead, the emphasis is on the application of analysis to number theory. The book is split into two parts. Part 1 follows a standard university course on analysis and each chapter closes with a set of exercises. Here, numbers, inequalities, convergence of sequences, and infinite series are all covered. Part 2 contains a selection of more unusual topics that aren't usually found in books of this type. It includes proofs of the irrationality of e and π, continued fractions, an introduction to the Riemann zeta function, Cantor's theory of the infinite, and Dedekind cuts. There is also a survey of what analysis can do for the calculus and a brief history of the subject. A lot of material found in a standard university course on "real analysis" is covered and most of the mathematics is written in standard theorem-proof style. However, more details are given than is usually the case to help readers who find this style daunting. Both set theory and proof by induction are avoided in the interests of making the book accessible to a wider readership, but both of these topics are the subjects of appendices for those who are interested in them. And unlike most university texts at this level, topics that have featured in popular science books, such as the Riemann hypothesis, are introduced here. As a result, this book occupies a unique position between a popular mathematics book and a first year college or university text, and offers a relaxed introduction to a fascinating and important branch of mathematics.

A Sequential Introduction To Real Analysis

Author: J M Speight
Publisher: World Scientific Publishing Company
ISBN: 1783267852
Size: 55.38 MB
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Real analysis provides the fundamental underpinnings for calculus, arguably the most useful and influential mathematical idea ever invented. It is a core subject in any mathematics degree, and also one which many students find challenging. A Sequential Introduction to Real Analysis gives a fresh take on real analysis by formulating all the underlying concepts in terms of convergence of sequences. The result is a coherent, mathematically rigorous, but conceptually simple development of the standard theory of differential and integral calculus ideally suited to undergraduate students learning real analysis for the first time. This book can be used as the basis of an undergraduate real analysis course, or used as further reading material to give an alternative perspective within a conventional real analysis course. Request Inspection Copy

Introduction To Analysis

Author: Corey M. Dunn
Publisher: CRC Press
ISBN: 149873202X
Size: 19.43 MB
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Introduction to Analysis is an ideal text for a one semester course on analysis. The book covers standard material on the real numbers, sequences, continuity, differentiation, and series, and includes an introduction to proof. The author has endeavored to write this book entirely from the student’s perspective: there is enough rigor to challenge even the best students in the class, but also enough explanation and detail to meet the needs of a struggling student. From the Author to the student: "I vividly recall sitting in an Analysis class and asking myself, ‘What is all of this for?’ or ‘I don’t have any idea what’s going on.’ This book is designed to help the student who finds themselves asking the same sorts of questions, but will also challenge the brightest students."

Mathematical Analysis Wavelets And Signal Processing

Author: Mourad Ismail
Publisher: American Mathematical Soc.
ISBN: 0821803840
Size: 65.66 MB
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This book contains the proceedings of an international conference held in Cairo, Egypt (January 1994). Mathematics and engineering discoveries, such as wavelets, multiresolution analysis, and subband coding schemes, caused rapid advancements in signal processing, necessitating an interdisciplinary approach. Contributors to this conference demonstrated that some traditional areas of mathematical analysis - sampling theory, approximation theory, and orthogonal polynomials - have proven extremely useful in solving various signal processing problems.

Fundamentals Of Mathematical Analysis

Author: Paul J. Sally, Jr.
Publisher: American Mathematical Soc.
ISBN: 0821891413
Size: 17.52 MB
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This is a textbook for a course in Honors Analysis (for freshman/sophomore undergraduates) or Real Analysis (for junior/senior undergraduates) or Analysis-I (beginning graduates). It is intended for students who completed a course in ``AP Calculus'', possibly followed by a routine course in multivariable calculus and a computational course in linear algebra. There are three features that distinguish this book from many other books of a similar nature and which are important for the use of this book as a text. The first, and most important, feature is the collection of exercises. These are spread throughout the chapters and should be regarded as an essential component of the student's learning. Some of these exercises comprise a routine follow-up to the material, while others challenge the student's understanding more deeply. The second feature is the set of independent projects presented at the end of each chapter. These projects supplement the content studied in their respective chapters. They can be used to expand the student's knowledge and understanding or as an opportunity to conduct a seminar in Inquiry Based Learning in which the students present the material to their class. The third really important feature is a series of challenge problems that increase in impossibility as the chapters progress.

Mathematical Analysis

Author: Tom M. Apostol
Publisher: Addison Wesley
ISBN: 9780201002881
Size: 16.13 MB
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It provides a transition from elementary calculus to advanced courses in real and complex function theory and introduces the reader to some of the abstract thinking that pervades modern analysis.

Neuroeconomics

Author: Paul W. Glimcher
Publisher: Academic Press
ISBN: 9780080921068
Size: 10.38 MB
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Neuroeconomics is a new highly promising approach to understanding the neurobiology of decision making and how it affects cognitive social interactions between humans and societies/economies. This book is the first edited reference to examine the science behind neuroeconomics, including how it influences human behavior and societal decision making from a behavioral economics point of view. Presenting a truly interdisciplinary approach, Neuroeconomics presents research from neuroscience, psychology, and behavioral economics, and includes chapters by all the major figures in the field, including two Economics Nobel laureates. * An authoritative reference written and edited by acknowledged experts and founders of the field * Presents an interdisciplinary view of the approaches, concepts, and results of the emerging field of neuroeconomics relevant for anyone interested in this area of research * Full-color presentation throughout with carefully selected illustrations to highlight key concepts

Supersymmetry In Disorder And Chaos

Author: Konstantin Efetov
Publisher: Cambridge University Press
ISBN: 9780521663823
Size: 21.75 MB
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This book provides a comprehensive treatment of the ideas and applications of supersymmetry.