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Perfect Rigour

Author: Masha Gessen

Publisher: Icon Books Ltd

Published: 2011-03-03

Total Pages: 119

ISBN-13: 1848313098

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.

Perfect Rigor

Author: Masha Gessen

Publisher: HarperCollins

Published: 2009-11-11

Total Pages: 259

ISBN-13: 0547427565

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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.

Leadership Rigor!

Author: Erica Peitler

Publisher: Circle Takes the Square

Published: 2014-07-15

Total Pages: 0

ISBN-13: 9780981512426

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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?

Mathematical Rigour and Informal Proof

Author: Fenner Stanley Tanswell

Publisher: Cambridge University Press

Published: 2024-03-28

Total Pages: 158

ISBN-13: 1009325132

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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.

Curves and Surfaces in Geometric Modeling

Author: Jean H. Gallier

Publisher: Morgan Kaufmann

Published: 2000

Total Pages: 512

ISBN-13: 9781558605992

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"Curves and Surfaces in Geometric Modeling: Theory and Algorithms offers a theoretically unifying understanding of polynomial curves and surfaces as well as an effective approach to implementation that you can apply to your own work as a graduate student, scientist, or practitioner." "The focus here is on blossoming - the process of converting a polynomial to its polar form - as a natural, purely geometric explanation of the behavior of curves and surfaces. This insight is important for more than just its theoretical elegance - the author demonstrates the value of blossoming as a practical algorithmic tool for generating and manipulating curves and surfaces that meet many different criteria. You'll learn to use this and other related techniques drawn from affine geometry for computing and adjusting control points, deriving the continuity conditions for splines, creating subdivision surfaces, and more." "It will be an essential acquisition for readers in many different areas, including computer graphics and animation, robotics, virtual reality, geometric modeling and design, medical imaging, computer vision, and motion planning."--BOOK JACKET.Title Summary field provided by Blackwell North America, Inc. All Rights Reserved

Brownian Motion Calculus

Author: Ubbo F. Wiersema

Publisher: John Wiley & Sons

Published: 2008-12-08

Total Pages: 342

ISBN-13: 0470021705

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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.

The Pleasures of Counting

Author: T. W. Körner

Publisher: Cambridge University Press

Published: 1996-12-05

Total Pages: 548

ISBN-13: 1316025454

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What is the connection between the outbreak of cholera in Victorian Soho, the Battle of the Atlantic, African Eve and the design of anchors? One answer is that they are all examples chosen by Dr Tom Körner to show how a little mathematics can shed light on the world around us, and deepen our understanding of it. Dr Körner, an experienced author, describes a variety of topics which continue to interest professional mathematicians, like him. He does this using relatively simple terms and ideas, yet confronting difficulties (which are often the starting point for new discoveries) and avoiding condescension. If you have ever wondered what it is that mathematicians do, and how they go about it, then read on. If you are a mathematician wanting to explain to others how you spend your working days (and nights), then seek inspiration here.

Topology, Geometry, and Gauge Fields

Author: Gregory L. Naber

Publisher: Springer Science & Business Media

Published: 2013-04-17

Total Pages: 410

ISBN-13: 1475727429

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Like any books on a subject as vast as this, this book has to have a point-of-view to guide the selection of topics. Naber takes the view that the rekindled interest that mathematics and physics have shown in each other of late should be fostered, and that this is best accomplished by allowing them to cohabit. The book weaves together rudimentary notions from the classical gauge theory of physics with the topological and geometrical concepts that became the mathematical models of these notions. The reader is asked to join the author on some vague notion of what an electromagnetic field might be, to be willing to accept a few of the more elementary pronouncements of quantum mechanics, and to have a solid background in real analysis and linear algebra and some of the vocabulary of modern algebra. In return, the book offers an excursion that begins with the definition of a topological space and finds its way eventually to the moduli space of anti-self-dual SU(2) connections on S4 with instanton number -1.

Pierre Duhem

Author: R. Niall D. Martin

Publisher: Open Court Publishing

Published: 1991

Total Pages: 292

ISBN-13: 9780812691603

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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

Published: 2015-04-30

Total Pages: 336

ISBN-13: 0191057665

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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.