The Real and the Complex: A History of Analysis in the 19th Century

Author: Jeremy Gray

Publisher: Springer

ISBN: 3319237152

Category: Mathematics

Page: 350

View: 2337

This book contains a history of real and complex analysis in the nineteenth century, from the work of Lagrange and Fourier to the origins of set theory and the modern foundations of analysis. It studies the works of many contributors including Gauss, Cauchy, Riemann, and Weierstrass. This book is unique owing to the treatment of real and complex analysis as overlapping, inter-related subjects, in keeping with how they were seen at the time. It is suitable as a course in the history of mathematics for students who have studied an introductory course in analysis, and will enrich any course in undergraduate real or complex analysis.
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Geschichte der Analysis

Author: Hans Niels Jahnke

Publisher: Spektrum Akademischer Verlag

ISBN: 9783827403926

Category: Mathematics

Page: 564

View: 8762

"Geschichte der Analysis" ist von einem internationalen Expertenteam geschrieben und stellt die gegenwärtig umfassendste Darstellung der Herausbildung und Entwicklung dieser mathematischen Kerndisziplin dar. Der tiefgreifende begriffliche Wandel, den die Analysis im Laufe der Zeit durchgemacht hat, wird ebenso dargestellt, wie auch der Einfluß, den vor allem physikalische Probleme gehabt haben. Biographische und philosophische Hintergründe werden ausgeleuchtet und ihre Relevanz für die Theorieentwicklung gezeigt. Neben der eigentlichen Geschichte der Analysis bis ungefähr 1900 enthält das Buch Spezialkapitel über die Entwicklung der analytischen Mechanik im 18. Jahrhundert, Randwertprobleme der mathematischen Physik im 19. Jahrhundert, die Theorie der komplexen Funktionen, die Grundlagenkrise sowie historische Überblicke über die Variationsrechnung, Differentialgleichungen und Funktionalanalysis.
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A History of Abstract Algebra

From Algebraic Equations to Modern Algebra

Author: Jeremy Gray

Publisher: Springer

ISBN: 3319947737

Category: Mathematics

Page: 415

View: 5581

This textbook provides an accessible account of the history of abstract algebra, tracing a range of topics in modern algebra and number theory back to their modest presence in the seventeenth and eighteenth centuries, and exploring the impact of ideas on the development of the subject. Beginning with Gauss’s theory of numbers and Galois’s ideas, the book progresses to Dedekind and Kronecker, Jordan and Klein, Steinitz, Hilbert, and Emmy Noether. Approaching mathematical topics from a historical perspective, the author explores quadratic forms, quadratic reciprocity, Fermat’s Last Theorem, cyclotomy, quintic equations, Galois theory, commutative rings, abstract fields, ideal theory, invariant theory, and group theory. Readers will learn what Galois accomplished, how difficult the proofs of his theorems were, and how important Camille Jordan and Felix Klein were in the eventual acceptance of Galois’s approach to the solution of equations. The book also describes the relationship between Kummer’s ideal numbers and Dedekind’s ideals, and discusses why Dedekind felt his solution to the divisor problem was better than Kummer’s. Designed for a course in the history of modern algebra, this book is aimed at undergraduate students with an introductory background in algebra but will also appeal to researchers with a general interest in the topic. With exercises at the end of each chapter and appendices providing material difficult to find elsewhere, this book is self-contained and therefore suitable for self-study.
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Real Analysis

Author: John M. Howie

Publisher: Springer Science & Business Media

ISBN: 9781852333140

Category: Mathematics

Page: 276

View: 5857

Real Analysis is a comprehensive introduction to this core subject and is ideal for self-study or as a course textbook for first and second-year undergraduates. Combining an informal style with precision mathematics, the book covers all the key topics with fully worked examples and exercises with solutions. All the concepts and techniques are deployed in examples in the final chapter to provide the student with a thorough understanding of this challenging subject. This book offers a fresh approach to a core subject and manages to provide a gentle and clear introduction without sacrificing rigour or accuracy.
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Mathematics and Its History

Author: John Stillwell

Publisher: Springer Science & Business Media

ISBN: 144196052X

Category: Mathematics

Page: 662

View: 7520

From a review of the second edition: "This book covers many interesting topics not usually covered in a present day undergraduate course, as well as certain basic topics such as the development of the calculus and the solution of polynomial equations. The fact that the topics are introduced in their historical contexts will enable students to better appreciate and understand the mathematical ideas involved...If one constructs a list of topics central to a history course, then they would closely resemble those chosen here." (David Parrott, Australian Mathematical Society) This book offers a collection of historical essays detailing a large variety of mathematical disciplines and issues; it’s accessible to a broad audience. This third edition includes new chapters on simple groups and new sections on alternating groups and the Poincare conjecture. Many more exercises have been added as well as commentary that helps place the exercises in context.
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Elements of the History of Mathematics

Author: N. Bourbaki

Publisher: Springer Science & Business Media

ISBN: 9783540647676

Category: Mathematics

Page: 301

View: 4296

Each volume of Nicolas Bourbakis well-known work, The Elements of Mathematics, contains a section or chapter devoted to the history of the subject. This book collects together those historical segments with an emphasis on the emergence, development, and interaction of the leading ideas of the mathematical theories presented in the Elements. In particular, the book provides a highly readable account of the evolution of algebra, geometry, infinitesimal calculus, and of the concepts of number and structure, from the Babylonian era through to the 20th century.
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Funktionentheorie

Author: Reinhold Remmert

Publisher: N.A

ISBN: 9783540553847

Category: Functions of complex variables

Page: 299

View: 6761

Diese dritte Auflage wurde zusammen mit dem zweitgenannten Autor kritisch durchgesehen, ergnzt und verbessert. Ein weiteres Kapitel ber geometrische Funktionentheorie und schlichte Funktionen enthlt einen Beweis der Bieberbachschen Vermutung. Der ... vorliegende zweite Band der Funktionentheorie erfllt voll die Erwartungen, die der erste Band geweckt hat. Wieder beeindrucken vor allem die hochinteressanten historischen Bemerkungen zu den einzelnen Themenkreisen, als besonderer Leckerbissen wird das Gutachten von Gau ber Riemanns Dissertation vorgestellt... Jedes einzelne Kapitel enthlt ausfhrliche Literaturangaben. Ferner werden oft sehr aufschlussreiche Hinweise auf die Funktionentheorie mehrerer Vernderlicher gegeben. Die vielen Beispiele und bungsaufgaben bilden eine wertvolle Ergnzung der brillant dargelegten Theorie. Der Rezensent bedauert, dass ihm nicht schon als Student ein derartig umfassendes, qualitativ hochstehendes Lehrbuch zur Verfgung stand." Monatshefte fr Mathematik
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Special Relativity

Author: Nicholas M.J. Woodhouse

Publisher: Springer-Verlag

ISBN: 3540466762

Category: Science

Page: 88

View: 9483

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The American Mathematical Monthly

The Official Journal of the Mathematical Association of America

Author: N.A

Publisher: N.A

ISBN: N.A

Category: Mathematicians

Page: N.A

View: 5919

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Mathematical Physics

A Modern Introduction to Its Foundations

Author: Sadri Hassani

Publisher: Springer Science & Business Media

ISBN: 9780387985794

Category: Science

Page: 1026

View: 4203

For physics students interested in the mathematics they use, and for math students interested in seeing how some of the ideas of their discipline find realization in an applied setting. The presentation strikes a balance between formalism and application, between abstract and concrete. The interconnections among the various topics are clarified both by the use of vector spaces as a central unifying theme, recurring throughout the book, and by putting ideas into their historical context. Enough of the essential formalism is included to make the presentation self-contained.
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Books in Series

Author: N.A

Publisher: N.A

ISBN: N.A

Category: Monographic series

Page: N.A

View: 4047

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Mathematische Modellierung

Author: Christof Eck,Harald Garcke,Peter Knabner

Publisher: Springer-Verlag

ISBN: 3662543354

Category: Mathematics

Page: 515

View: 1347

Das Lehrbuch bietet eine lebendige und anschauliche Einführung in die mathematische Modellierung von Phänomenen aus den Natur- und Ingenieurwissenschaften. Leser lernen, mathematische Modelle zu verstehen und selbst herzuleiten und finden eine Fülle von Beispielen, u. a. aus den Bereichen chemische Reaktionskinetik, Populationsdynamik, Strömungsdynamik, Elastizitätstheorie und Kristallwachstum. Die Methoden der Linearen Algebra, der Analysis und der Theorie der gewöhnlichen und partiellen Differentialgleichungen werden sorgfältig eingeführt.
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Relational Frame Theory

A Post-Skinnerian Account of Human Language and Cognition

Author: Steven C. Hayes,Dermot Barnes-Holmes,Bryan Roche

Publisher: Springer Science & Business Media

ISBN: 9780306466007

Category: Computers

Page: 285

View: 6532

In August 1859 Bernhard Riemann, a little-known 32-year old mathematician, presented a paper to the Berlin Academy titled: "On the Number of Prime Numbers Less Than a Given Quantity." In the middle of that paper, Riemann made an incidental remark a " a guess, a hypothesis. What he tossed out to the assembled mathematicians that day has proven to be almost cruelly compelling to countless scholars in the ensuing years. Today, after 150 years of careful research and exhaustive study, the question remains. Is the hypothesis true or false? Riemann's basic inquiry, the primary topic of his paper, concerned a straightforward but nevertheless important matter of arithmetic a " defining a precise formula to track and identify the occurrence of prime numbers. But it is that incidental remark a " the Riemann Hypothesis a " that is the truly astonishing legacy of his 1859 paper. Because Riemann was able to see beyond the pattern of the primes to discern traces of something mysterious and mathematically elegant shrouded in the shadows a " subtle variations in the distribution of those prime numbers. Brilliant for its clarity, astounding for its potential consequences, the Hypothesis took on enormous importance in mathematics. Indeed, the successful solution to this puzzle would herald a revolution in prime number theory. Proving or disproving it became the greatest challenge of the age. It has become clear that the Riemann Hypothesis, whose resolution seems to hang tantalizingly just beyond our grasp, holds the key to a variety of scientific and mathematical investigations. The making and breaking of modern codes, which depend on the properties of the prime numbers, have roots in the Hypothesis. In a series of extraordinary developments during the 1970s, it emerged that even the physics of the atomic nucleus is connected in ways not yet fully understood to this strange conundrum. Hunting down the solution to the Riemann Hypothesis has become an obsession for many a " the veritable "great white whale" of mathematical research. Yet despite determined efforts by generations of mathematicians, the Riemann Hypothesis defies resolution. Alternating passages of extraordinarily lucid mathematical exposition with chapters of elegantly composed biography and history, Prime Obsession is a fascinating and fluent account of an epic mathematical mystery that continues to challenge and excite the world. Posited a century and a half ago, the Riemann Hypothesis is an intellectual feast for the cognoscenti and the curious alike. Not just a story of numbers and calculations, Prime Obsession is the engrossing tale of a relentless hunt for an elusive proof a " and those who have been consumed by it. "
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Choice

Publication of the Association of College and Research Libraries, a Division of the American Library Association

Author: N.A

Publisher: N.A

ISBN: N.A

Category: Academic libraries

Page: N.A

View: 372

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