Real Infinite Series

Author: Daniel D. Bonar,Michael J. Khoury, Jr.,Michael Khoury

Publisher: MAA

ISBN: 9780883857458

Category: Mathematics

Page: 264

View: 381

An introductory treatment of infinite series of real numbers, from basic definitions and tests to advanced results.
Posted in Mathematics

A Primer of Real Functions

Author: Ralph P. Boas,Harold P. Boas

Publisher: Cambridge University Press

ISBN: 9780883850299

Category: Mathematics

Page: 305

View: 5899

Revised edition of a classic Carus monograph with a new chapter on integration and its applications.
Posted in Mathematics

A Radical Approach to Real Analysis

Author: David M. Bressoud

Publisher: MAA

ISBN: 9780883857472

Category: Mathematics

Page: 323

View: 1424

Second edition of this introduction to real analysis, rooted in the historical issues that shaped its development.
Posted in Mathematics

Theory and Application of Infinite Series

Author: Konrad Knopp

Publisher: Courier Corporation

ISBN: 0486318613

Category: Mathematics

Page: 592

View: 6262

Unusually clear and interesting classic covers real numbers and sequences, foundations of the theory of infinite series and development of the theory (series of valuable terms, Euler's summation formula, asymptotic expansions, other topics). Includes exercises.
Posted in Mathematics

Infinite Sequences and Series

Author: Konrad Knopp

Publisher: Courier Corporation

ISBN: 0486152049

Category: Mathematics

Page: 208

View: 1319

Careful presentation of fundamentals of the theory by one of the finest modern expositors of higher mathematics. Covers functions of real and complex variables, arbitrary and null sequences, convergence and divergence, Cauchy's limit theorem, more.
Posted in Mathematics

Real Analysis and Applications

Including Fourier Series and the Calculus of Variations

Author: Frank Morgan

Publisher: American Mathematical Soc.

ISBN: 9780821886113

Category: Mathematics

Page: 197

View: 1148

Real Analysis and Applications starts with a streamlined, but complete, approach to real analysis. It finishes with a wide variety of applications in Fourier series and the calculus of variations, including minimal surfaces, physics, economics, Riemannian geometry, and general relativity. The basic theory includes all the standard topics: limits of sequences, topology, compactness, the Cantor set and fractals, calculus with the Riemann integral, a chapter on the Lebesgue theory, sequences of functions, infinite series, and the exponential and Gamma functions. The applications conclude with a computation of the relativistic precession of Mercury's orbit, which Einstein called "convincing proof of the correctness of the theory [of General Relativity]." The text not only provides clear, logical proofs, but also shows the student how to derive them. The excellent exercises come with select solutions in the back. This is a text that makes it possible to do the full theory and significant applications in one semester. Frank Morgan is the author of six books and over one hundred articles on mathematics. He is an inaugural recipient of the Mathematical Association of America's national Haimo award for excellence in teaching. With this applied version of his Real Analysis text, Morgan brings his famous direct style to the growing numbers of potential mathematics majors who want to see applications along with the theory. The book is suitable for undergraduates interested in real analysis.
Posted in Mathematics

Infinite Series

Author: Isidore Isaac Hirschman

Publisher: Courier Corporation

ISBN: 0486798240

Category: Mathematics

Page: 192

View: 8425

Text for advanced undergraduate and graduate students examines Taylor series, Fourier series, uniform convergence, power series, and real analytic functions. Appendix covers set and sequence operations and continuous functions. 1962 edition.
Posted in Mathematics

Euler

The Master of Us All

Author: William Dunham

Publisher: MAA

ISBN: 9780883853283

Category: Mathematics

Page: 185

View: 3384

Leonhard Euler was one of the most prolific mathematicians that have ever lived. This book examines the huge scope of mathematical areas explored and developed by Euler, which includes number theory, combinatorics, geometry, complex variables and many more. The information known to Euler over 300 years ago is discussed, and many of his advances are reconstructed. Readers will be left in no doubt about the brilliance and pervasive influence of Euler's work.
Posted in Mathematics

Naming Infinity

A True Story of Religious Mysticism and Mathematical Creativity

Author: Loren Graham,Jean-Michel Kantor

Publisher: Harvard University Press

ISBN: 0674032934

Category: History

Page: 239

View: 484

Looks at the competition between French and Russian mathematicians over the nature of infinity during the twentieth century.
Posted in History

Limits

A New Approach to Real Analysis

Author: Alan F. Beardon

Publisher: Springer Science & Business Media

ISBN: 1461206979

Category: Mathematics

Page: 190

View: 691

Intended as an undergraduate text on real analysis, this book includes all the standard material such as sequences, infinite series, continuity, differentiation, and integration, together with worked examples and exercises. By unifying and simplifying all the various notions of limit, the author has successfully presented a novel approach to the subject matter, which has not previously appeared in book form. The author defines the term limit once only, and all of the subsequent limiting processes are seen to be special cases of this one definition. Accordingly, the subject matter attains a unity and coherence that is not to be found in the traditional approach. Students will be able to fully appreciate and understand the common source of the topics they are studying while also realising that they are "variations on a theme", rather than essentially different topics, and therefore, will gain a better understanding of the subject.
Posted in Mathematics

Roads to Infinity

The Mathematics of Truth and Proof

Author: John C. Stillwell

Publisher: CRC Press

ISBN: 1439865507

Category: Mathematics

Page: 250

View: 7725

Winner of a CHOICE Outstanding Academic Title Award for 2011! This book offers an introduction to modern ideas about infinity and their implications for mathematics. It unifies ideas from set theory and mathematical logic, and traces their effects on mainstream mathematical topics of today, such as number theory and combinatorics. The treatment is historical and partly informal, but with due attention to the subtleties of the subject. Ideas are shown to evolve from natural mathematical questions about the nature of infinity and the nature of proof, set against a background of broader questions and developments in mathematics. A particular aim of the book is to acknowledge some important but neglected figures in the history of infinity, such as Post and Gentzen, alongside the recognized giants Cantor and Gödel.
Posted in Mathematics

Calculus Gems

Brief Lives and Memorable Mathematics

Author: George F. Simmons

Publisher: MAA

ISBN: 9780883855614

Category: Mathematics

Page: 355

View: 3845

Calculus Gems, a collection of essays written about mathematicians and mathematics, is a spin-off of two appendices (""Biographical Notes"" and ""Variety of Additional Topics"") found in Simmons' 1985 calculus book. With many additions and some minor adjustments, the material will now be available in a separate softcover volume. The text is suitable as a supplement for a calculus course and/or a history of mathematics course, The overall aim is bound up in the question, ""What is mathematics for?"" and in Simmons' answer, ""To delight the mind and help us understand the world"". The essays are independent of one another, allowing the instructor to pick and choose among them. Part A, ""Brief Lives"", is a biographical history of mathematics from earliest times (Thales, 625-547 BC) through the late 19th century (Weierstrass, 1815-1897) that serves to connect mathematics to the broader intellectual and social history of Western civilization. Part B, ""Memorable Mathematics"", is a collection of interesting topics from number theory, geometry, and science arranged in an order roughly corresponding to the order of most calculus courses. Some of these sections have a few problems for the student to solve. Students can gain perspective on the mathematical experience and learn some mathematics not contained in the usual courses, and instructors can assign student papers and projects based on the essays. The book teaches by example that mathematics is more than computation. Original illustrations of influential mathematicians in history and their inventions accompany the brief biographies and mathematical discussions.
Posted in Mathematics

What is Mathematics, Really?

Author: Reuben Hersh

Publisher: Oxford University Press, USA

ISBN: 9780195130874

Category: Medical

Page: 343

View: 9045

Most philosophers of mathematics treat it as isolated, timeless, ahistorical, inhuman. Reuben Hersh argues the contrary, that mathematics must be understood as a human activity, a social phenomenon, part of human culture, historically evolved, and intelligible only in a social context. Hersh pulls the screen back to reveal mathematics as seen by professionals, debunking many mathematical myths, and demonstrating how the "humanist" idea of the nature of mathematics more closely resembles how mathematicians actually work. At the heart of his book is a fascinating historical account of the mainstream of philosophy--ranging from Pythagoras, Descartes, and Spinoza, to Bertrand Russell, David Hilbert, and Rudolph Carnap--followed by the mavericks who saw mathematics as a human artifact, including Aristotle, Locke, Hume, Mill, and Lakatos. What is Mathematics, Really? reflects an insider's view of mathematical life, and will be hotly debated by anyone with an interest in mathematics or the philosophy of science.
Posted in Medical

A Radical Approach to Lebesgue's Theory of Integration

Author: David M. Bressoud

Publisher: Cambridge University Press

ISBN: 0521884748

Category: Mathematics

Page: 329

View: 4936

Meant for advanced undergraduate and graduate students in mathematics, this introduction to measure theory and Lebesgue integration is motivated by the historical questions that led to its development. The author tells the story of the mathematicians who wrestled with the difficulties inherent in the Riemann integral, leading to the work of Jordan, Borel, and Lebesgue.
Posted in Mathematics

Tools of the Trade

Introduction to Advanced Mathematics

Author: Paul Sally

Publisher: American Mathematical Soc.

ISBN: 0821846345

Category: Mathematics

Page: 193

View: 1683

This book provides a transition from the formula-full aspects of the beginning study of college level mathematics to the rich and creative world of more advanced topics. It is designed to assist the student in mastering the techniques of analysis and proof that are required to do mathematics. Along with the standard material such as linear algebra, construction of the real numbers via Cauchy sequences, metric spaces and complete metric spaces, there are three projects at the end of each chapter that form an integral part of the text. These projects include a detailed discussion of topics such as group theory, convergence of infinite series, decimal expansions of real numbers, point set topology and topological groups. They are carefully designed to guide the student through the subject matter. Together with numerous exercises included in the book, these projects may be used as part of the regular classroom presentation, as self-study projects for students, or for Inquiry Based Learning activities presented by the students.
Posted in Mathematics

A History in Sum

Author: Steve Nadis

Publisher: Harvard University Press

ISBN: 0674727894

Category: Mathematics

Page: N.A

View: 4773

In the twentieth century, American mathematicians began to make critical advances in a field previously dominated by Europeans. Harvard's mathematics department was at the center of these developments. A History in Sum is an inviting account of the pioneers who trailblazed a distinctly American tradition of mathematics--in algebraic geometry, complex analysis, and other esoteric subdisciplines that are rarely written about outside of journal articles or advanced textbooks. The heady mathematical concepts that emerged, and the men and women who shaped them, are described here in lively, accessible prose. The story begins in 1825, when a precocious sixteen-year-old freshman, Benjamin Peirce, arrived at the College. He would become the first American to produce original mathematics--an ambition frowned upon in an era when professors largely limited themselves to teaching. Peirce's successors transformed the math department into a world-class research center, attracting to the faculty such luminaries as George David Birkhoff. Influential figures soon flocked to Harvard, some overcoming great challenges to pursue their elected calling. A History in Sum elucidates the contributions of these extraordinary minds and makes clear why the history of the Harvard mathematics department is an essential part of the history of mathematics in America and beyond.
Posted in Mathematics

A Basic Course in Real Analysis

Author: Ajit Kumar,S. Kumaresan

Publisher: CRC Press

ISBN: 1482216388

Category: Mathematics

Page: 322

View: 4409

Based on the authors’ combined 35 years of experience in teaching, A Basic Course in Real Analysis introduces students to the aspects of real analysis in a friendly way. The authors offer insights into the way a typical mathematician works observing patterns, conducting experiments by means of looking at or creating examples, trying to understand the underlying principles, and coming up with guesses or conjectures and then proving them rigorously based on his or her explorations. With more than 100 pictures, the book creates interest in real analysis by encouraging students to think geometrically. Each difficult proof is prefaced by a strategy and explanation of how the strategy is translated into rigorous and precise proofs. The authors then explain the mystery and role of inequalities in analysis to train students to arrive at estimates that will be useful for proofs. They highlight the role of the least upper bound property of real numbers, which underlies all crucial results in real analysis. In addition, the book demonstrates analysis as a qualitative as well as quantitative study of functions, exposing students to arguments that fall under hard analysis. Although there are many books available on this subject, students often find it difficult to learn the essence of analysis on their own or after going through a course on real analysis. Written in a conversational tone, this book explains the hows and whys of real analysis and provides guidance that makes readers think at every stage.
Posted in Mathematics

Beyond Infinity

An expedition to the outer limits of the mathematical universe

Author: Eugenia Cheng

Publisher: Profile Books

ISBN: 1782830812

Category: Mathematics

Page: 204

View: 7857

SHORTLISTED FOR THE 2017 ROYAL SOCIETY SCIENCE BOOK PRIZE Even small children know there are infinitely many whole numbers - start counting and you'll never reach the end. But there are also infinitely many decimal numbers between zero and one. Are these two types of infinity the same? Are they larger or smaller than each other? Can we even talk about 'larger' and 'smaller' when we talk about infinity? In Beyond Infinity, international maths sensation Eugenia Cheng reveals the inner workings of infinity. What happens when a new guest arrives at your infinite hotel - but you already have an infinite number of guests? How does infinity give Zeno's tortoise the edge in a paradoxical foot-race with Achilles? And can we really make an infinite number of cookies from a finite amount of cookie dough? Wielding an armoury of inventive, intuitive metaphor, Cheng draws beginners and enthusiasts alike into the heart of this mysterious, powerful concept to reveal fundamental truths about mathematics, all the way from the infinitely large down to the infinitely small.
Posted in Mathematics