Karl Weierstrass's Books

An Introduction to Classical Real Analysis

By: Karl R. Stromberg

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An Introduction to Classical Real Analysis

By: Karl R. Stromberg

This classic book is a text for a standard introductory course in real analysis, covering sequences and series, limits and continuity, differentiation, elementary transcendental functions, integration, infinite series and products, and trigonometric series. The author has scrupulously avoided any presumption at all that the reader has any knowledge of mathematical concepts until they are formally presented in the book. One significant way in which this book differs from other texts at this level is that the integral which is first mentioned is the Lebesgue integral on the real line. There are at least three good reasons for doing this. First, this approach is no more difficult to understand than is the traditional theory of the Riemann integral. Second, the readers will profit from acquiring a thorough understanding of Lebesgue integration on Euclidean spaces before they enter into a study of abstract measure theory. Third, this is the integral that is most useful to current applied mathematicians and theoretical scientists, and is essential for any serious work with trigonometric series. The exercise sets are a particularly attractive feature of this book. A great many of the exercises are projects of many parts which, when completed in the order given, lead the student by easy stages to important and interesting results. Many of the exercises are supplied with copious hints. This new printing contains a large number of corrections and a short author biography as well as a list of selected publications of the author. This classic book is a text for a standard introductory course in real analysis, covering sequences and series, limits and continuity, differentiation, elementary transcendental functions, integration, infinite series and products, and trigonometric series. The author has scrupulously avoided any presumption at all that the reader has any knowledge of mathematical concepts until they are formally presented in the book. - See more at: http://bookstore.ams.org/CHEL-376-H/#sthash.wHQ1vpdk.dpuf This classic book is a text for a standard introductory course in real analysis, covering sequences and series, limits and continuity, differentiation, elementary transcendental functions, integration, infinite series and products, and trigonometric series. The author has scrupulously avoided any presumption at all that the reader has any knowledge of mathematical concepts until they are formally presented in the book. One significant way in which this book differs from other texts at this level is that the integral which is first mentioned is the Lebesgue integral on the real line. There are at least three good reasons for doing this. First, this approach is no more difficult to understand than is the traditional theory of the Riemann integral. Second, the readers will profit from acquiring a thorough understanding of Lebesgue integration on Euclidean spaces before they enter into a study of abstract measure theory. Third, this is the integral that is most useful to current applied mathematicians and theoretical scientists, and is essential for any serious work with trigonometric series. The exercise sets are a particularly attractive feature of this book. A great many of the exercises are projects of many parts which, when completed in the order given, lead the student by easy stages to important and interesting results. Many of the exercises are supplied with copious hints. This new printing contains a large number of corrections and a short author biography as well as a list of selected publications of the author. This classic book is a text for a standard introductory course in real analysis, covering sequences and series, limits and continuity, differentiation, elementary transcendental functions, integration, infinite series and products, and trigonometric series. The author has scrupulously avoided any presumption at all that the reader has any knowledge of mathematical concepts until they are formally presented in the book. - See more at: http://bookstore.ams.org/CHEL-376-H/#sthash.wHQ1vpdk.dpuf

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Page Count

594

Publisher

American Mathematical Soc.

Published Date

ISBN 10

1470425440

ISBN 13

9781470425449

The History of Approximation Theory

From Euler to Bernstein

By: Karl-Georg Steffens

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The History of Approximation Theory

From Euler to Bernstein

By: Karl-Georg Steffens

* Exciting exposition integrates history, philosophy, and mathematics * Combines a mathematical analysis of approximation theory with an engaging discussion of the differing philosophical underpinnings behind its development * Appendices containing biographical data on numerous eminent mathematicians, explanations of Russian nomenclature and academic degrees, and an excellent index round out the presentation

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219

Publisher

Springer Science & Business Media

Published Date

ISBN 10

081764475X

ISBN 13

9780817644758

Calculus

A Modern Approach

By: Karl Menger

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Calculus

A Modern Approach

By: Karl Menger

One of the twentieth century's most original mathematicians and thinkers, Karl Menger taught students of many backgrounds. In this, his radical revision of the traditional calculus text, he presents pure and applied calculus in a unified conceptual frame, offering a thorough understanding of theory as well as of the methodology underlying the use of calculus as a tool. The most outstanding feature of this text is the care with which it explains basic ideas, a feature that makes it equally suitable for beginners and experienced readers. The text begins with a "mini-calculus" which brings out the fundamental results without recourse to the notions of limit and continuity. The standard subject matter is then presented as a pure and unambiguous calculus of functions. The issues surrounding the applications of pure calculus to problems in the sciences are faced in a forthright manner by carefully analyzing the meaning of "variable quantity" and clarified by resuscitating Newton's concept of fluents. The accompanying exercises are original, insightful and an integral part of the text. This Dover edition features a new Preface and Guide to Further Reading by Bert Schweizer and Abe Sklar.

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387

Publisher

Courier Corporation

Published Date

ISBN 10

0486151603

ISBN 13

9780486151601

Probability For Analysts

By: Karl Stromberg

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Probability For Analysts

By: Karl Stromberg

This book will enable researchers and students of analysis to more easily understand research papers in which probabilistic methods are used to prove theorems of analysis, many of which have no other known proofs. The book assumes a course in measure and integration theory but requires little or no background in probability theory. It emplhasizes topics of interest to analysts, including random series, martingales and Brownian motion.

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330

Publisher

Routledge

Published Date

ISBN 10

1351421611

ISBN 13

9781351421614

Nonstandard Analysis

In Higher Education, Logic and Philosophy

By: Karl Kuhlemann

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Nonstandard Analysis

In Higher Education, Logic and Philosophy

By: Karl Kuhlemann

Currently, nonstandard analysis is barely considered in university teaching. The author argues that nonstandard analysis is valuable not only for teaching, but also for understanding standard analysis and mathematics itself. An axiomatic approach wich pays attention to different language levels (for example, in the distinction between sums of ones and the natural numbers of the theory) leads naturally to a nonstandard theory. For motivation historical ideas of Leibniz can be taken up. The book contains an elaborated concept that follows this approach and is suitable, for example, as a basis for a lecture-supplementary course. The monograph part presents all major approaches to nonstandard analysis and discusses logical, model-theoretic, and set-theoretic investigations to reveal possible mathematical reasons that may lead to reservations about nonstandard analysis. Also various foundational positions as well as ontological, epistemological, and application-related issues are addressed. It turns out that the one-sided preference for standard analysis is justified neither from a didactic, mathematical nor philosophical point of view. Thus, the book is especially valuable for students and instructors of analysis who are also interested in the foundations of their subject.

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293

Publisher

Walter de Gruyter GmbH & Co KG

Published Date

ISBN 10

3111430537

ISBN 13

9783111430539

Mathematical Methods Of Theoretical Physics

By: Karl Svozil

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Mathematical Methods Of Theoretical Physics

By: Karl Svozil

This book could serve either as a good reference to remind students about what they have seen in their completed courses or as a starting point to show what needs more investigation. Svozil (Vienna Univ. of Technology) offers a very thorough text that leaves no mathematical area out, but it is best described as giving a synopsis of each application and how it relates to other areas … The text is organized well and provides a good reference list. Summing Up: Recommended. Upper-division undergraduates and graduate students.'CHOICEThis book contains very explicit proofs and demonstrations through examples for a comprehensive introduction to the mathematical methods of theoretical physics. It also combines and unifies many expositions of this subject, suitable for readers with interest in experimental and applied physics.

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331

Publisher

World Scientific

Published Date

ISBN 10

9811208425

ISBN 13

9789811208423

General investigations of curved surfaces

By: Karl Friedrich Gauss

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General investigations of curved surfaces

By: Karl Friedrich Gauss

INTRODUCTION In 1827 Gauss presented to the Royal Society of Göttingen his important paper on the theory of surfaces, which seventy-three years afterward the eminent French geometer, who has done more than any one else to propagate these principles, characterizes as one of Gauss’s chief titles to fame, and as still the most finished andusefulintroductiontothestudyofinfinitesimalgeometry.∗ Thismemoirmay be called: General Investigations of Curved Surfaces, or the Paper of 1827, to distinguish it from the original draft written out in 1825, but not published until 1900. A list of the editions and translations of the Paper of 1827 follows. There are three editions in Latin, two translations into French, and two into German. The paper was originally published in Latin under the title: Ia. Disquisitiones generales circa superficies curvas auctore Carolo Friderico Gauss. Societati regiæ oblatæ D. 8. Octob. 1827, and was printed in: Commentationes societatis regiæ scientiarum Gottingensis recentiores, Commentationes classis mathematicæ. Tom. VI. (ad a. 1823–1827). Gottingæ, 1828, pages 99–146. This sixth volume is rare; so much so, indeed, that the British Museum Catalogue indicates that it is missing in that collection. With the signatures changed, and the paging changed to pages 1–50, Ia also appears with the title page added: Ib. Disquisitiones generales circa superficies curvas auctore Carolo Friderico Gauss. Gottingæ. Typis Dieterichianis. 1828. II. In Monge’s Application de l’analyse à la géométrie, fifth edition, edited by Liouville, Paris, 1850, on pages 505–546, is a reprint, added by the Editor, in Latin under the title: Recherches sur la théorie générale des surfaces courbes; Par M. C.-F. Gauss. IIIa. A third Latin edition of this paper stands in: Gauss, Werke, Her- ausgegeben von der Königlichen Gesellschaft der Wissenschaften zu Göttingen, Vol. 4, Göttingen, 1873, pages 217–258, without change of the title of the original paper (Ia). IIIb. The same, without change, in Vol. 4 of Gauss, Werke, Zweiter Abdruck, Göttingen, 1880. IV. A French translation was made from Liouville’s edition, II, by Captain Tiburce Abadie, ancien élève de l’École Polytechnique, and appears in Nouvelles Annales de Mathématique, Vol. 11, Paris, 1852, pages 195–252, under the title: Recherches générales sur les surfaces courbes; Par M. Gauss. This latter also appears under its own title. Va. Another French translation is: Recherches Générales sur les Surfaces Courbes. Par M. C.-F. Gauss, traduites en français, suivies de notes et d’études sur divers points de la Théorie des Surfaces et sur certaines classes de Courbes, par M. E. Roger, Paris, 1855.

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145

Publisher

BoD - Books on Demand

Published Date

ISBN 13

9791041941087

Physical (A)Causality

Determinism, Randomness and Uncaused Events

By: Karl Svozil

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Physical (A)Causality

Determinism, Randomness and Uncaused Events

By: Karl Svozil

This book is open access under a CC BY 4.0 license. This book addresses the physical phenomenon of events that seem to occur spontaneously and without any known cause. These are to be contrasted with events that happen in a (pre-)determined, predictable, lawful, and causal way. All our knowledge is based on self-reflexive theorizing, as well as on operational means of empirical perception. Some of the questions that arise are the following: are these limitations reflected by our models? Under what circumstances does chance kick in? Is chance in physics merely epistemic? In other words, do we simply not know enough, or use too crude levels of description for our predictions? Or are certain events "truly", that is, irreducibly, random? The book tries to answer some of these questions by introducing intrinsic, embedded observers and provable unknowns; that is, observables and procedures which are certified (relative to the assumptions) to be unknowable or undoable. A (somewhat iconoclastic) review of quantum mechanics is presented which is inspired by quantum logic. Postulated quantum (un-)knowables are reviewed. More exotic unknowns originate in the assumption of classical continua, and in finite automata and generalized urn models, which mimic complementarity and yet maintain value definiteness. Traditional conceptions of free will, miracles and dualistic interfaces are based on gaps in an otherwise deterministic universe.

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215

Publisher

Springer

Published Date

ISBN 10

3319708155

ISBN 13

9783319708157

Linear Chaos

By: Karl-G. Grosse-Erdmann,Alfred Peris Manguillot

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Linear Chaos

By: Karl-G. Grosse-Erdmann,Alfred Peris Manguillot

It is commonly believed that chaos is linked to non-linearity, however many (even quite natural) linear dynamical systems exhibit chaotic behavior. The study of these systems is a young and remarkably active field of research, which has seen many landmark results over the past two decades. Linear dynamics lies at the crossroads of several areas of mathematics including operator theory, complex analysis, ergodic theory and partial differential equations. At the same time its basic ideas can be easily understood by a wide audience. Written by two renowned specialists, Linear Chaos provides a welcome introduction to this theory. Split into two parts, part I presents a self-contained introduction to the dynamics of linear operators, while part II covers selected, largely independent topics from linear dynamics. More than 350 exercises and many illustrations are included, and each chapter contains a further ‘Sources and Comments’ section. The only prerequisites are a familiarity with metric spaces, the basic theory of Hilbert and Banach spaces and fundamentals of complex analysis. More advanced tools, only needed occasionally, are provided in two appendices. A self-contained exposition, this book will be suitable for self-study and will appeal to advanced undergraduate or beginning graduate students. It will also be of use to researchers in other areas of mathematics such as partial differential equations, dynamical systems and ergodic theory.

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391

Publisher

Springer Science & Business Media

Published Date

ISBN 10

1447121708

ISBN 13

9781447121701

Selected Papers in Logic and Foundations, Didactics, Economics

By: Karl Menger

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Selected Papers in Logic and Foundations, Didactics, Economics

By: Karl Menger

This volume brings together those papers of mine which may be of interest not only to various specialists but also to philosophers. Many of my writings in mathematics were motivated by epistemological considerations; some papers originated in the critique of certain views that at one time dominated the discussions of the Vienna Cirele; others grew out of problems in teaching fundamental ideas of mathematics; sti II others were occasioned by personal relations with economists. Hence a wide range of subjects will be discussed: epistemology, logic, basic concepts of pure and applied mathematics, philosophical ideas resulting from geometric studies, mathematical didactics and, finally, economics. The papers also span a period of more than fifty years. What unifies the various parts of the book is the spirit of searching for the elarification of basic concepts and methods and of articulating hidden ideas and tacit procedures. Part 1 ineludes papers published about 1930 which expound an idea that Carnap, after a short period of opposition in the Cirele, fully adopted ; and, under the name "Princip/e of To/erance", he eloquently formulated it in great generality in his book, Logica/ Syntax of Language (1934), through which it was widely disseminated. "The New Logic" in Chapter 1 furthermore ineludes the first report (I932) to a larger public of Godel's epochal discovery presented among the great logic results of ali time. Chapter 2 is a translation of an often quoted 1930 paper presenting a detailed exposition and critique of intuitionism.

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343

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Springer Science & Business Media

Published Date

ISBN 10

9400993471

ISBN 13

9789400993471

Numerical Mathematics

By: Günther Hämmerlin,Karl-Heinz Hoffmann

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Numerical Mathematics

By: Günther Hämmerlin,Karl-Heinz Hoffmann

In truth, it is not knowledge, but learning, not possessing, but production, not being there, but travelling there, which provides the greatest pleasure. When I have completely understood something, then I turn away and move on into the dark; indeed, so curious is the insatiable man, that when he has completed one house, rather than living in it peacefully, he starts to build another. " Letter from C. F. Gauss to W. Bolyai on Sept. 2, 1808 This textbook adds a book devoted to applied mathematics to the series "Grundwissen Mathematik. " Our goals, like those of the other books in the series, are to explain connections and common viewpoints between various mathematical areas, to emphasize the motivation for studying certain prob lem areas, and to present the historical development of our subject. Our aim in this book is to discuss some of the central problems which arise in applications of mathematics, to develop constructive methods for the numerical solution of these problems, and to study the associated questions of accuracy. In doing so, we also present some theoretical results needed for our development, especially when they involve material which is beyond the scope of the usual beginning courses in calculus and linear algebra. This book is based on lectures given over many years at the Universities of Freiburg, Munich, Berlin and Augsburg.

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437

Publisher

Springer Science & Business Media

Published Date

ISBN 10

1461244420

ISBN 13

9781461244424

Realism and the Aim of Science

From the Postscript to The Logic of Scientific Discovery

By: Karl Popper

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Realism and the Aim of Science

From the Postscript to The Logic of Scientific Discovery

By: Karl Popper

Realism and the Aim of Science is one of the three volumes of Karl Popper’s Postscript to the Logic of scientific Discovery. The Postscript is the culmination of Popper’s work in the philosophy of physics and a new famous attack on subjectivist approaches to philosophy of science. Realism and the Aim of Science is the first volume of the Postcript. Popper here formulates and explains his non-justificationist theory of knowledge: science aims at true explanatory theories, yet it can never prove, or justify, any theory to be true, not even if is a true theory. Science must continue to question and criticise all its theories, even those that happen to be true. Realism and the Aim of Science presents Popper’s mature statement on scientific knowledge and offers important insights into his thinking on problems of method within science.

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465

Publisher

Routledge

Published Date

ISBN 10

1135858888

ISBN 13

9781135858889

The Logic of Scientific Discovery

By: Karl Raimund Popper

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The Logic of Scientific Discovery

By: Karl Raimund Popper

When first published in 1959, this book revolutionized contemporary thinking about science and knowledge. It remains one of the most widely read books about science to come out of the 20th century.

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548

Publisher

Psychology Press

Published Date

ISBN 10

0415278449

ISBN 13

9780415278447

Introduction to Partial Differential Equations and Hilbert Space Methods

By: Karl E. Gustafson

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Introduction to Partial Differential Equations and Hilbert Space Methods

By: Karl E. Gustafson

Easy-to-use text examines principal method of solving partial differential equations, 1st-order systems, computation methods, and much more. Over 600 exercises, with answers for many. Ideal for a 1-semester or full-year course.

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500

Publisher

Courier Corporation

Published Date

ISBN 10

0486140873

ISBN 13

9780486140872

Concentration Compactness

Functional-analytic Grounds and Applications

By: Kyril Tintarev,Karl-Heinz Fieseler

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Concentration Compactness

Functional-analytic Grounds and Applications

By: Kyril Tintarev,Karl-Heinz Fieseler

Concentration compactness is an important method in mathematical analysis which has been widely used in mathematical research for two decades. This unique volume fulfills the need for a source book that usefully combines a concise formulation of the method, a range of important applications to variational problems, and background material concerning manifolds, non-compact transformation groups and functional spaces.Highlighting the role in functional analysis of invariance and, in particular, of non-compact transformation groups, the book uses the same building blocks, such as partitions of domain and partitions of range, relative to transformation groups, in the proofs of energy inequalities and in the weak convergence lemmas.

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279

Publisher

World Scientific

Published Date

ISBN 10

1860946666

ISBN 13

9781860946660

The Logic of Scientific Discovery

By: Karl Popper

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The Logic of Scientific Discovery

By: Karl Popper

Described by the philosopher A.J. Ayer as a work of 'great originality and power', this book revolutionized contemporary thinking on science and knowledge. Ideas such as the now legendary doctrine of 'falsificationism' electrified the scientific community, influencing even working scientists, as well as post-war philosophy. This astonishing work ranks alongside The Open Society and Its Enemies as one of Popper's most enduring books and contains insights and arguments that demand to be read to this day.

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552

Publisher

Routledge

Published Date

ISBN 10

1134470010

ISBN 13

9781134470013

Periodic Differential Operators

By: B. Malcolm Brown,Michael S.P. Eastham,Karl Michael Schmidt

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Periodic Differential Operators

By: B. Malcolm Brown,Michael S.P. Eastham,Karl Michael Schmidt

Periodic differential operators have a rich mathematical theory as well as important physical applications. They have been the subject of intensive development for over a century and remain a fertile research area. This book lays out the theoretical foundations and then moves on to give a coherent account of more recent results, relating in particular to the eigenvalue and spectral theory of the Hill and Dirac equations. The book will be valuable to advanced students and academics both for general reference and as an introduction to active research topics.

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220

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Springer Science & Business Media

Published Date

ISBN 10

3034805284

ISBN 13

9783034805285

The Waltz of Reason

The Entanglement of Mathematics and Philosophy

By: Karl Sigmund

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The Waltz of Reason

The Entanglement of Mathematics and Philosophy

By: Karl Sigmund

A mind-bending jaunt ... that makes clear in fascinating detail how math is more than a sum of its parts" (Publishers Weekly) “Let no one ignorant of geometry enter here,” Plato warned would-be philosophers. Mathematician Karl Sigmund agrees. In The Waltz of Reason, he shows how mathematics and philosophy together have shaped our understanding of space, chance, logic, cooperation, voting, and the social contract. Sigmund shows how game theory is integral to moral philosophy, how statistics shaped the meaning of reason, and how the search for a logical basis for math leads to deep questions about the nature of truth itself. But this is no dry tome: Sigmund’s wit and humor shine as brightly as his erudition. The Waltz of Reason is an engrossing history of ideas as vibrant as a ballroom full of dancers, one that empowers as it entertains, following the complex and occasionally dizzying steps of the thinkers who have molded our thought and founded our world.

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346

Publisher

Basic Books

Published Date

ISBN 10

1541602706

ISBN 13

9781541602700

Finding Ellipses: What Blaschke Products, Poncelet’s Theorem, and the Numerical Range Know about Each Other

By: Ulrich Daepp,Pamela Gorkin,Andrew Shaffer,Karl Voss

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Finding Ellipses: What Blaschke Products, Poncelet’s Theorem, and the Numerical Range Know about Each Other

By: Ulrich Daepp,Pamela Gorkin,Andrew Shaffer,Karl Voss

Mathematicians delight in finding surprising connections between seemingly disparate areas of mathematics. Finding Ellipses is a delight-filled romp across a three-way unexpected connection between complex analysis, linear algebra, and projective geometry.

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282

Publisher

American Mathematical Soc.

Published Date

ISBN 10

147044383X

ISBN 13

9781470443832

Reminiscences of the Vienna Circle and the Mathematical Colloquium

By: Karl Menger

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Reminiscences of the Vienna Circle and the Mathematical Colloquium

By: Karl Menger

Karl Menger was born in Vienna on January 13, 1902, the only child of two gifted parents. His mother Hermione, nee Andermann (1870-1922), in addition to her musical abilities, wrote and published short stories and novelettes, while his father Carl (1840-1921) was the noted Austrian economist, one of the founders of marginal utility theory. A highly cultured man, and a liberal rationalist in the nine teenth century sense, the elder Menger had witnessed the defeat and humiliation of the old Austrian empire by Bismarck's Prussia, and the subsequent establishment under Prussian leadership of a militaristic, mystically nationalistic, state-capitalist German empire - in effect, the first modern "military-industrial complex. " These events helped frame in him a set of attitudes that he later transmitted to his son, and which included an appreciation of cultural attainments and tolerance and respect for cultural differences, com bined with a deep suspicion of rabid nationalism, particularly the German variety. Also a fascination with structure, whether artistic, scientific, philosophical, or theological, but a rejection of any aura of mysticism or mumbo-jumbo accompanying such structure. Thus the son remarked at least once that the archangels' chant that begins the Prolog im Himmel in Goethe's Faust was perhaps the most viii INTRODUCTION beautiful thing in the German language "but of course it doesn't mean anything.

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271

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Springer Science & Business Media

Published Date

ISBN 10

9401111022

ISBN 13

9789401111027

Conjectures and Refutations

The Growth of Scientific Knowledge

By: Karl Popper

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Conjectures and Refutations

The Growth of Scientific Knowledge

By: Karl Popper

Conjectures and Refutations is one of Karl Popper's most wide-ranging and popular works, notable not only for its acute insight into the way scientific knowledge grows, but also for applying those insights to politics and to history. It provides one of the clearest and most accessible statements of the fundamental idea that guided his work: not only our knowledge, but our aims and our standards, grow through an unending process of trial and error.

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607

Publisher

Routledge

Published Date

ISBN 10

1135971307

ISBN 13

9781135971304

Splines And Compartment Models: An Introduction

By: Karl-ernst Erich Biebler,Michael Wodny

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Splines And Compartment Models: An Introduction

By: Karl-ernst Erich Biebler,Michael Wodny

This book presents methods of mathematical modeling from two points of view. Splines provide a general approach while compartment models serve as examples for context related to modeling. The preconditions and characteristics of the developed mathematical models as well as the conditions surrounding data collection and model fit are taken into account. The substantial statements of this book are mathematically proven. The results are ready for application with examples and related program codes given.In this book, splines are algebraically developed such that the reader or user can easily understand and vary the numerical construction of the different kinds of spline functions. The classical compartment models of the pharmacokinetics are systematically analyzed and connected with lifetime distributions. As such, parameter estimation and model fit can be treated statistically with a varied minimum chi-square method. This method is applicable for single kinetics and also allows the calculation of average kinetics.

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349

Publisher

World Scientific

Published Date

ISBN 10

9814522244

ISBN 13

9789814522243

Working Knowledge

STEM Essentials for the 21st Century

By: Karl Hess

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Working Knowledge

STEM Essentials for the 21st Century

By: Karl Hess

Working Knowledge: STEM Essentials for the 21st Century is designed to inspire a wide range of readers from high school and undergraduate students with an interest in Science, Technology, Engineering, and Mathematics (STEM) to STEM teachers and those who wish to become teachers. Written by renowned scientist and teacher Dr. Karl Hess of the University of Illinois at Urbana, a member of both the National Academy of Sciences and the National Academy of Engineering, the book presents a critical collection of timeless STEM concepts and connects them with contemporary research advances in addition to the needs of our daily lives. With an engaging and accessible style not requiring a formal background in STEM, Dr. Hess takes the reader on a journey from Euclidean Geometry and Cartesian Coordinates up through 21st Century scientific topics like the global positioning system, nanotechnology, and super-efficient alternative energy systems. Working Knowledge: STEM Essentials for the 21st Century at once serves as an almanac on the fascinating physical, chemical, quantitative features of the natural world and built environment, as well as a need-to-know list of topics for students, teachers, and parents interested in STEM education.

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330

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Springer Science & Business Media

Published Date

ISBN 10

146143274X

ISBN 13

9781461432746

The Riemann Hypothesis

The Greatest Unsolved Problem in Mathematics

By: Karl Sabbagh

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The Riemann Hypothesis

The Greatest Unsolved Problem in Mathematics

By: Karl Sabbagh

An engaging, informative, and wryly humorous exploration of one of the great conundrums of all time In 1859 Bernhard Riemann, a shy German mathematician, wrote an eight-page article giving an answer to a problem that had long puzzled mathematicians. But he didn’t provide a proof. In fact, he said he couldn’t prove it but he thought that his answer was “very probably” true. From the publication of that paper to the present day, the world’s mathematicians have been fascinated, infuriated, and obsessed with proving the Riemann Hypothesis, and so great is the interest in its solution that in 2001 an American foundation put up prize money of $1 million for the first person to demonstrate that the hypothesis is correct. The hypothesis refers to prime numbers, which are in some sense the atoms from which all other numbers are constructed, and seeks to explain where every single prime to infinity will occur. Riemann’s idea—if true—would illuminate how these numbers are distributed, and if false will throw pure mathematics into confusion. Karl Sabbagh meets some of the world’s mathematicians who spend their lives thinking about the Riemann Hypothesis, focusing attention in particular on “Riemann’s zeros,” a series of points that are believed to lie in a straight line, though no one can prove it. Accessible and vivid, The Riemann Hypothesis is a brilliant explanation of numbers and a profound meditation on the ultimate meaning of mathematics.

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364

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Macmillan

Published Date

ISBN 10

0374250073

ISBN 13

9780374250072

Mathematische Werke

Herausgegeben Unter Mitwirkung Einer Von Der Königlich Preussischen Akademie Der Wissenschaften Eingesetzten Commission

By: Karl Weierstrass

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Mathematische Werke

Herausgegeben Unter Mitwirkung Einer Von Der Königlich Preussischen Akademie Der Wissenschaften Eingesetzten Commission

By: Karl Weierstrass

Published 1894-1927, the seven-volume collected works in German of the father of modern mathematical analysis, Karl Weierstrass (1815-97).

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373

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Cambridge University Press

Published Date

ISBN 10

110805918X

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9781108059183

Conjectures and Refutations

The Growth of Scientific Knowledge

By: Karl Raimund Popper

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Conjectures and Refutations

The Growth of Scientific Knowledge

By: Karl Raimund Popper

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614

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Psychology Press

Published Date

ISBN 10

0415285941

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9780415285940

Quantum Chaos Y2K

Proceedings of Nobel Symposium 116, Bäckaskog Castle, Sweden, June 13-17, 2000

By: Karl-Fredrik Berggren

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Quantum Chaos Y2K

Proceedings of Nobel Symposium 116, Bäckaskog Castle, Sweden, June 13-17, 2000

By: Karl-Fredrik Berggren

Spectral twinkling: A new example of singularity-dominated strong fluctuations (summary) / M. Berry -- Quantum chaos in GaAs/AlxGa1-x As microstructures / A. M. Chang -- Ground state spin and Coulomb blockade peak motion in chaotic quantum dots / J. A. Folk ... [et al.] -- Quantum chaos and transport phenomena in quantum dots / A. S. Sachrajda -- Conductance of a ballistic electron billiard in a magnetic field: Does the semiclassical approach apply? / T. Blomquist and I. Zozoulenko -- Semiconductor billiards - a controlled environment to study fractals / R. P. Taylor ... [et al.] -- Experimental signatures of wavefunction scarring in open semiconductor billiards / J. P. Bird, R. Akis, and D. K. Ferry -- Chaos in quantum ratchets / H. Linke ... [et al.] -- Statistics of resonances in open billiards / H. Ishio -- The exterior and interior edge states of magnetic billiards: Spectral statistics and correlations / K. Hornberger and U. Smilansky -- Non-universality of chaotic classical dynamics: implications for quantum chaos / M. Wilkinson -- Chaos and interactions in quantum dots / Y. Alhassid -- Stochastic aspects of many-body systems: The embedded Gaussian ensembles / H. A. Weidenmuller -- Quantum-classical correspondence for isolated systems of interacting particles: Localization and ergodicity energy space / F. M. Izrailev -- Effect of symmetry breaking on statistical distributions / G. E. Mitchell and J. F. Shriner, Jr. -- Quantum chaos and quantum computers / D. L. Shepelyansky -- Disorder and quantum chronodynamics - non-linear [symbol] models / T. Guhr and T. Wilke -- Correlations between periodic orbits and their role in spectral statistics / M. Sieber and K. Richeter -- Quantum spectra and wave functions in terms of periodic orbits for weakly chaotic systems / R. E. Prange, R. Narevich and O. Zaitsev -- Bifurcation of periodic orbit as semiclassical origin of superdeformed shell structure / K. Matsuyanagi -- Wavefunction localization and its semiclassical description in a 3-dimensional system with mixed classical dynamics / M. Brack, M. Sieber and S. M. Reimann -- Neutron stars and quantum billiards / A. Bulgac and P. Magierski -- Scars and other weak localization effects in classically chaotic systems / E. J. Heller -- Tunneling and chaos / S. Tomsovic -- Relaxation and fluctuations in quantum chaos / G. Casati -- Rydberg electrons in crossed fields: A paradigm for nonlinear dynamics beyond two degrees of freedom / T. Uzer -- Classical analysis of correlated multiple ionization in strong fields / B. Eckhardt and K. Sacha -- Classically forbidden processes in photoabsorption spectra / J. B. Delos ... [et al.] -- Quantum Hall effect breakdown steps due to an instability of laminar flow against electron-hole pair formation / L. Eaves -- Dynamical and wave chaos in the Bose-Einstein condensate / W. P. Reinhardt and S. B. McKinney -- Wave dynamical chaos: An experimental approach in billiards / A. Richter -- Acoustic chaos / C. Ellegaard, K. Schaadt and P. Bertelsen -- Ultrasound resonances in a rectangular plate described by random matrices / K. Schaadt, G. Simon and C. Ellegaard -- Quantum correlations and classical resonances in an open chaotic system / W. T. Lu ... [et al.] -- Why do an experiment, if theory is exact, and any experiment can at best approximate theory? / H.-J. Stockmann -- Wave-Chaotic optical resonators and lasers / A. D. Stone -- Angular momentum localization in oval billiards / J. U. Nockel -- Chaos and time-reversed acoustics / M. Fink -- Single-mode delay time statistics for scattering by a chaotic cavity / K. J. H. van Bemmel, H. Schomerus and C. W. J. Beenakker.

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