Perfect Rigour

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Perfect Rigour

Author : Masha Gessen
Publisher : Icon Books Ltd
ISBN 13 : 1848313098
Total Pages : 119 pages
Book Rating : 4.8/5 (483 download)

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Book Synopsis Perfect Rigour by : Masha Gessen

Download or read book Perfect Rigour written by Masha Gessen and published by Icon Books Ltd. This book was released on 2011-03-03 with total page 119 pages. Available in PDF, EPUB and Kindle. Book excerpt: In 2006, an eccentric Russian mathematician named Grigori Perelman solved one of the world's greatest intellectual puzzles. The Poincare conjecture is an extremely complex topological problem that had eluded the best minds for over a century. In 2000, the Clay Institute in Boston named it one of seven great unsolved mathematical problems, and promised a million dollars to anyone who could find a solution. Perelman was awarded the prize this year - and declined the money. Journalist Masha Gessen was determined to find out why. Drawing on interviews with Perelman's teachers, classmates, coaches, teammates, and colleagues in Russia and the US - and informed by her own background as a math whiz raised in Russia - she set out to uncover the nature of Perelman's astonishing abilities. In telling his story, Masha Gessen has constructed a gripping and tragic tale that sheds rare light on the unique burden of genius.

Reason & Rigor

Author : Sharon M. Ravitch
Publisher : SAGE Publications
ISBN 13 : 148334696X
Total Pages : 265 pages
Book Rating : 4.4/5 (833 download)

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Book Synopsis Reason & Rigor by : Sharon M. Ravitch

Download or read book Reason & Rigor written by Sharon M. Ravitch and published by SAGE Publications. This book was released on 2016-01-04 with total page 265 pages. Available in PDF, EPUB and Kindle. Book excerpt: Designed for novice as well as more experienced researchers, Reason & Rigor by Sharon M. Ravitch and Matthew Riggan presents conceptual frameworks as a mechanism for aligning literature review, research design, and methodology. The book explores the conceptual framework—defined as both a process and a product—that helps to direct and ground researchers as they work through common research challenges. Focusing on published studies on a range of topics and employing both quantitative and qualitative methods, the updated Second Edition features two new chapters and clearly communicates the processes of developing and defining conceptual frameworks.

Perfect Rigor

Author : Masha Gessen
Publisher : HarperCollins
ISBN 13 : 0547427565
Total Pages : 259 pages
Book Rating : 4.5/5 (474 download)

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Book Synopsis Perfect Rigor by : Masha Gessen

Download or read book Perfect Rigor written by Masha Gessen and published by HarperCollins. This book was released on 2009-11-11 with total page 259 pages. Available in PDF, EPUB and Kindle. Book excerpt: A gripping and tragic tale that sheds rare light on the unique burden of genius In 2006, an eccentric Russian mathematician named Grigori Perelman solved the Poincare Conjecture, an extremely complex topological problem that had eluded the best minds for over a century. A prize of one million dollars was offered to anyone who could unravel it, but Perelman declined the winnings, and in doing so inspired journalist Masha Gessen to tell his story. Drawing on interviews with Perelman’s teachers, classmates, coaches, teammates, and colleagues in Russia and the United States—and informed by her own background as a math whiz raised in Russia—Gessen uncovered a mind of unrivaled computational power, one that enabled Perelman to pursue mathematical concepts to their logical (sometimes distant) end. But she also discovered that this very strength turned out to be Perelman's undoing and the reason for his withdrawal, first from the world of mathematics and then, increasingly, from the world in general.

Mathematical Rigour and Informal Proof

Author : Fenner Stanley Tanswell
Publisher : Cambridge University Press
ISBN 13 : 1009325132
Total Pages : 158 pages
Book Rating : 4.0/5 (93 download)

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Book Synopsis Mathematical Rigour and Informal Proof by : Fenner Stanley Tanswell

Download or read book Mathematical Rigour and Informal Proof written by Fenner Stanley Tanswell and published by Cambridge University Press. This book was released on 2024-03-28 with total page 158 pages. Available in PDF, EPUB and Kindle. Book excerpt: This Element looks at the contemporary debate on the nature of mathematical rigour and informal proofs as found in mathematical practice. The central argument is for rigour pluralism: that multiple different models of informal proof are good at accounting for different features and functions of the concept of rigour. To illustrate this pluralism, the Element surveys some of the main options in the literature: the 'standard view' that rigour is just formal, logical rigour; the models of proofs as arguments and dialogues; the recipe model of proofs as guiding actions and activities; and the idea of mathematical rigour as an intellectual virtue. The strengths and weaknesses of each are assessed, thereby providing an accessible and empirically-informed introduction to the key issues and ideas found in the current discussion.

Pierre Duhem

Author : R. Niall D. Martin
Publisher : Open Court Publishing
ISBN 13 : 9780812691603
Total Pages : 292 pages
Book Rating : 4.6/5 (916 download)

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Book Synopsis Pierre Duhem by : R. Niall D. Martin

Download or read book Pierre Duhem written by R. Niall D. Martin and published by Open Court Publishing. This book was released on 1991 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: More than any other major twentieth-century writer, Pierre Duhem has been the victim of ill-informed guesswork. For instance, many references to Duhem stress the importance of his Catholic faith, but nearly all of them draw the obvious-and entirely erroneous-conclusions about the role of Catholicism in Duhem's thinking. This book pays particular attention to the political and intellectual context of French Catholicism, wracked as it was by the tensions of Dreyfus affair and the so-called modernist crisis. Duhem took his inspiration, not from the papally-sponsored revival of the thought of St. Thomas Aquinas, but from Pascal, a fact that aroused suspicions of skepticism in the minds of conservative Catholics. The tensions between Duhem's work and authoritarian Catholic positions became more explicit as his historical work unfolded. Most famous for his denial of the possibility of a crucial experiment which could unambiguously decide between contending scientific theories, Duhem has often been interpreted as a mere instrumentalist or conventionalist, denying the meaningfulness of a reality behind the theory. Dr. Martin shows that Duhem was a Pascalian who argued for both logic and intuition as indispensable in approaching the truth. Duhem argues that physics could not legitimately be used to attack Christianity, but he held that physics was equally useless for the defense of Christianity, a position which made him unpopular with many Catholics.

Ideas, Evidence, and Method

Author : Graciela De Pierris
Publisher : OUP Oxford
ISBN 13 : 0191057665
Total Pages : 336 pages
Book Rating : 4.1/5 (91 download)

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Book Synopsis Ideas, Evidence, and Method by : Graciela De Pierris

Download or read book Ideas, Evidence, and Method written by Graciela De Pierris and published by OUP Oxford. This book was released on 2015-04-30 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: Graciela De Pierris presents a novel interpretation of the relationship between skepticism and naturalism in Hume's epistemology, and a new appraisal of Hume's place within early modern thought. Whereas a dominant trend in recent Hume scholarship maintains that there are no skeptical arguments concerning causation and induction in Book I, Part III of the Treatise, Graciela De Pierris presents a detailed reading of the skeptical argument she finds there and how this argument initiates a train of skeptical reasoning that begins in Part III and culminates in Part IV. This reasoning is framed by Hume's version of the modern theory of ideas developed by Descartes and Locke. The skeptical implications of this theory, however, do not arise, as in traditional interpretations of Hume's skepticism, from the 'veil of perception.' They arise from Hume's elaboration of a presentational-phenomenological model of ultimate evidence, according to which there is always a justificatory gap between what is or has been immediately presented to the mind and any ideas that go beyond it. This happens, paradigmatically, in the causal-inductive inference, and, as De Pierris argues, in demonstrative inference as well. Yet, in spite of his firm commitment to radical skepticism, Hume also accepts the naturalistic standpoint of science and common life, and he does so, on the novel interpretation presented here, because of an equally firm commitment to Newtonian science in general and the Newtonian inductive method in particular. Hume defends the Newtonian method (against the mechanical philosophy) while simultaneously rejecting all attempts (including those of the Newtonians) to find a place for the supernatural within our understanding of nature.

Philosophy of Logic and Mathematics

Author : Gabriele M. Mras
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110654547
Total Pages : 565 pages
Book Rating : 4.1/5 (16 download)

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Book Synopsis Philosophy of Logic and Mathematics by : Gabriele M. Mras

Download or read book Philosophy of Logic and Mathematics written by Gabriele M. Mras and published by Walter de Gruyter GmbH & Co KG. This book was released on 2019-11-18 with total page 565 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents different conceptions of logic and mathematics and discuss their philosophical foundations and consequences. This concerns first of all topics of Wittgenstein's ideas on logic and mathematics; questions about the structural complexity of propositions; the more recent debate about Neo-Logicism and Neo-Fregeanism; the comparison and translatability of different logics; the foundations of mathematics: intuitionism, mathematical realism, and formalism. The contributing authors are Matthias Baaz, Francesco Berto, Jean-Yves Beziau, Elena Dragalina-Chernya, Günther Eder, Susan Edwards-McKie, Oliver Feldmann, Juliet Floyd, Norbert Gratzl, Richard Heinrich, Janusz Kaczmarek, Wolfgang Kienzler, Timm Lampert, Itala Maria Loffredo D'Ottaviano, Paolo Mancosu, Matthieu Marion, Felix Mühlhölzer, Charles Parsons, Edi Pavlovic, Christoph Pfisterer, Michael Potter, Richard Raatzsch, Esther Ramharter, Stefan Riegelnik, Gabriel Sandu, Georg Schiemer, Gerhard Schurz, Dana Scott, Stewart Shapiro, Karl Sigmund, William W. Tait, Mark van Atten, Maria van der Schaar, Vladimir Vasyukov, Jan von Plato, Jan Woleński and Richard Zach.

Brownian Motion Calculus

Author : Ubbo F. Wiersema
Publisher : John Wiley & Sons
ISBN 13 : 0470021705
Total Pages : 342 pages
Book Rating : 4.4/5 (7 download)

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Book Synopsis Brownian Motion Calculus by : Ubbo F. Wiersema

Download or read book Brownian Motion Calculus written by Ubbo F. Wiersema and published by John Wiley & Sons. This book was released on 2008-12-08 with total page 342 pages. Available in PDF, EPUB and Kindle. Book excerpt: BROWNIAN MOTION CALCULUS Brownian Motion Calculus presents the basics of Stochastic Calculus with a focus on the valuation of financial derivatives. It is intended as an accessible introduction to the technical literature. The sequence of chapters starts with a description of Brownian motion, the random process which serves as the basic driver of the irregular behaviour of financial quantities. That exposition is based on the easily understood discrete random walk. Thereafter the gains from trading in a random environment are formulated in a discrete-time setting. The continuous-time equivalent requires a new concept, the Itō stochastic integral. Its construction is explained step by step, using the so-called norm of a random process (its magnitude), of which a motivated exposition is given in an Annex. The next topic is Itō’s formula for evaluating stochastic integrals; it is the random process counter part of the well known Taylor formula for functions in ordinary calculus. Many examples are given. These ingredients are then used to formulate some well established models for the evolution of stock prices and interest rates, so-called stochastic differential equations, together with their solution methods. Once all that is in place, two methodologies for option valuation are presented. One uses the concept of a change of probability and the Girsanov transformation, which is at the core of financial mathematics. As this technique is often perceived as a magic trick, particular care has been taken to make the explanation elementary and to show numerous applications. The final chapter discusses how computations can be made more convenient by a suitable choice of the so-called numeraire. A clear distinction has been made between the mathematics that is convenient for a first introduction, and the more rigorous underpinnings which are best studied from the selected technical references. The inclusion of fully worked out exercises makes the book attractive for self study. Standard probability theory and ordinary calculus are the prerequisites. Summary slides for revision and teaching can be found on the book website www.wiley.com/go/brownianmotioncalculus.

Proofs and Refutations

Author : Imre Lakatos
Publisher : Cambridge University Press
ISBN 13 : 1107268109
Total Pages : 190 pages
Book Rating : 4.1/5 (72 download)

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Book Synopsis Proofs and Refutations by : Imre Lakatos

Download or read book Proofs and Refutations written by Imre Lakatos and published by Cambridge University Press. This book was released on 1976-01-01 with total page 190 pages. Available in PDF, EPUB and Kindle. Book excerpt: Proofs and Refutations is essential reading for all those interested in the methodology, the philosophy and the history of mathematics. Much of the book takes the form of a discussion between a teacher and his students. They propose various solutions to some mathematical problems and investigate the strengths and weaknesses of these solutions. Their discussion (which mirrors certain real developments in the history of mathematics) raises some philosophical problems and some problems about the nature of mathematical discovery or creativity. Imre Lakatos is concerned throughout to combat the classical picture of mathematical development as a steady accumulation of established truths. He shows that mathematics grows instead through a richer, more dramatic process of the successive improvement of creative hypotheses by attempts to 'prove' them and by criticism of these attempts: the logic of proofs and refutations.

From Kant to Hilbert Volume 2

Author : William Bragg Ewald
Publisher : Oxford University Press
ISBN 13 : 0198505361
Total Pages : 709 pages
Book Rating : 4.1/5 (985 download)

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Book Synopsis From Kant to Hilbert Volume 2 by : William Bragg Ewald

Download or read book From Kant to Hilbert Volume 2 written by William Bragg Ewald and published by Oxford University Press. This book was released on 1999 with total page 709 pages. Available in PDF, EPUB and Kindle. Book excerpt: This two-volume work brings together a comprehensive selection of mathematical works from the period 1707-1930. During this time the foundations of modern mathematics were laid, and From Kant to Hilbert provides an overview of the foundational work in each of the main branches of mathmeatics with narratives showing how they were linked. Now available as a separate volume.

The Mathematical Theory of Black Holes

Author : Subrahmanyan Chandrasekhar
Publisher : Oxford University Press
ISBN 13 : 9780198503705
Total Pages : 676 pages
Book Rating : 4.5/5 (37 download)

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Book Synopsis The Mathematical Theory of Black Holes by : Subrahmanyan Chandrasekhar

Download or read book The Mathematical Theory of Black Holes written by Subrahmanyan Chandrasekhar and published by Oxford University Press. This book was released on 1998 with total page 676 pages. Available in PDF, EPUB and Kindle. Book excerpt: Part of the reissued Oxford Classic Texts in the Physical Sciences series, this book was first published in 1983, and has swiftly become one of the great modern classics of relativity theory. It represents a personal testament to the work of the author, who spent several years writing and working-out the entire subject matter. The theory of black holes is the most simple and beautiful consequence of Einstein's relativity theory. At the time of writing there was no physical evidence for the existence of these objects, therefore all that Professor Chandrasekhar used for their construction were modern mathematical concepts of space and time. Since that time a growing body of evidence has pointed to the truth of Professor Chandrasekhar's findings, and the wisdom contained in this book has become fully evident.

Introduction to Mathematical Philosophy

Author : Bertrand Russell
Publisher : Read Books Ltd
ISBN 13 : 1447486870
Total Pages : 216 pages
Book Rating : 4.4/5 (474 download)

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Book Synopsis Introduction to Mathematical Philosophy by : Bertrand Russell

Download or read book Introduction to Mathematical Philosophy written by Bertrand Russell and published by Read Books Ltd. This book was released on 2013-01-21 with total page 216 pages. Available in PDF, EPUB and Kindle. Book excerpt: Originally published in 1919, this work on the philosophy of mathematics is both expensive and hard to find in its first edition. It contains Bertrand Russell's ideas on number definition, cardinal numbers, propositional functions and much more. This is a fascinating work and thoroughly recommended for anyone interested in the philosophy of mathematics. Many of the earliest books, particularly those dating back to the 1900s and before, are now extremely scarce. We are republishing these classic works in affordable, high quality, modern editions, using the original text and artwork.

Leadership Rigor!

Author : Erica Peitler
Publisher : Circle Takes the Square
ISBN 13 : 9780981512426
Total Pages : 0 pages
Book Rating : 4.5/5 (124 download)

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Book Synopsis Leadership Rigor! by : Erica Peitler

Download or read book Leadership Rigor! written by Erica Peitler and published by Circle Takes the Square. This book was released on 2014-07-15 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Transform the Way You Lead! Leadership Rigor offers innovation in leadership through its breakthrough approaches for transforming the way you lead. The simple truth is that "how" you lead is the precursor to "what" you can achieve as a leader, yet it is often underestimated, dismissed, or not given a conscious consideration. In March 2014, Bersin by Deloitte published their latest Global Human Capital Trend Survey stating: Building leadership capability is by far the most urgent need for companies today... and companies see the need for leadership at all levels, in all geographies, and across all functional areas. In addition, this continuous need for new and better leaders has accelerated. Leadership Rigor views your development as a journey with a road map rather than a black-box mystery! It is both a practice and a philosophy designed to accelerate your leadership performance and productivity across the life cycle of your career. Already becoming a movement, Leadership Rigor prepares you to lead yourself, teams, and organizations. The essence of Leadership Rigor is creating "change-ready" leaders who can embrace challenges because they have the tools, models, and language to assess, structure, and facilitate aligned actions. They also have the mindset and emotional skills to lean into the change process despite its uncomfortable nature. By innovating on their preparedness first, these "change-ready" leaders are equipped to realize the growth in themselves and in their teams or organizations. Are you ready to take on your personal journey of Leadership Rigor?

A Commentary on the Gospel According to John

Author : Johann Peter Lange
Publisher :
ISBN 13 :
Total Pages : 456 pages
Book Rating : 4.V/5 ( download)

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Book Synopsis A Commentary on the Gospel According to John by : Johann Peter Lange

Download or read book A Commentary on the Gospel According to John written by Johann Peter Lange and published by . This book was released on 1872 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Intimations of Christianity Among the Ancient Greeks

Author : Simone Weil
Publisher : Taylor & Francis
ISBN 13 : 1000964957
Total Pages : 171 pages
Book Rating : 4.0/5 (9 download)

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Book Synopsis Intimations of Christianity Among the Ancient Greeks by : Simone Weil

Download or read book Intimations of Christianity Among the Ancient Greeks written by Simone Weil and published by Taylor & Francis. This book was released on 2023-09-28 with total page 171 pages. Available in PDF, EPUB and Kindle. Book excerpt: Simone Weil (1909–1943) is one of the most brilliant and unorthodox religious and philosophical minds of the twentieth century. She was also a political activist, worked in the Renault car factory in France in the 1930s and fought briefly as an anarchist in the Spanish Civil War, before her tragic early death in England at the age of thirty-four. Her work spans an astonishing variety of subjects, from ancient Greek philosophy and Christianity to oppression, political freedom and French national identity. Intimations of Christianity Among the Ancient Greeks sees Weil apply her unique and piercing intellect to early Greek thought, where she finds fundamental precursors to Christian religious ideas. She argues, provocatively, that concepts fundamental to Christianity such as incarnation, redemption, suffering and resurrection are Greek as well as Christian and that there is much we can learn, spiritually and philosophically, from their entwinement. This Routledge Classics edition includes a new Foreword by Christopher Hamilton.

Measure, Integration & Real Analysis

Author : Sheldon Axler
Publisher : Springer Nature
ISBN 13 : 3030331431
Total Pages : 430 pages
Book Rating : 4.0/5 (33 download)

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Book Synopsis Measure, Integration & Real Analysis by : Sheldon Axler

Download or read book Measure, Integration & Real Analysis written by Sheldon Axler and published by Springer Nature. This book was released on 2019-11-29 with total page 430 pages. Available in PDF, EPUB and Kindle. Book excerpt: This open access textbook welcomes students into the fundamental theory of measure, integration, and real analysis. Focusing on an accessible approach, Axler lays the foundations for further study by promoting a deep understanding of key results. Content is carefully curated to suit a single course, or two-semester sequence of courses, creating a versatile entry point for graduate studies in all areas of pure and applied mathematics. Motivated by a brief review of Riemann integration and its deficiencies, the text begins by immersing students in the concepts of measure and integration. Lebesgue measure and abstract measures are developed together, with each providing key insight into the main ideas of the other approach. Lebesgue integration links into results such as the Lebesgue Differentiation Theorem. The development of products of abstract measures leads to Lebesgue measure on Rn. Chapters on Banach spaces, Lp spaces, and Hilbert spaces showcase major results such as the Hahn–Banach Theorem, Hölder’s Inequality, and the Riesz Representation Theorem. An in-depth study of linear maps on Hilbert spaces culminates in the Spectral Theorem and Singular Value Decomposition for compact operators, with an optional interlude in real and complex measures. Building on the Hilbert space material, a chapter on Fourier analysis provides an invaluable introduction to Fourier series and the Fourier transform. The final chapter offers a taste of probability. Extensively class tested at multiple universities and written by an award-winning mathematical expositor, Measure, Integration & Real Analysis is an ideal resource for students at the start of their journey into graduate mathematics. A prerequisite of elementary undergraduate real analysis is assumed; students and instructors looking to reinforce these ideas will appreciate the electronic Supplement for Measure, Integration & Real Analysis that is freely available online. For errata and updates, visit https://measure.axler.net/

Simplicity: Ideals of Practice in Mathematics and the Arts

Author : Roman Kossak
Publisher : Springer
ISBN 13 : 3319533851
Total Pages : 305 pages
Book Rating : 4.3/5 (195 download)

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Book Synopsis Simplicity: Ideals of Practice in Mathematics and the Arts by : Roman Kossak

Download or read book Simplicity: Ideals of Practice in Mathematics and the Arts written by Roman Kossak and published by Springer. This book was released on 2017-06-28 with total page 305 pages. Available in PDF, EPUB and Kindle. Book excerpt: To find "criteria of simplicity" was the goal of David Hilbert's recently discovered twenty-fourth problem on his renowned list of open problems given at the 1900 International Congress of Mathematicians in Paris. At the same time, simplicity and economy of means are powerful impulses in the creation of artworks. This was an inspiration for a conference, titled the same as this volume, that took place at the Graduate Center of the City University of New York in April of 2013. This volume includes selected lectures presented at the conference, and additional contributions offering diverse perspectives from art and architecture, the philosophy and history of mathematics, and current mathematical practice.