A Calculus Of Ideas PDF Download
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| Author | : Ulf Grenander |
| Publisher | : World Scientific |
| Total Pages | : 236 |
| Release | : 2012 |
| Genre | : Computers |
| ISBN | : 9814383198 |
Download A Calculus of Ideas Book in PDF, ePub and Kindle
This monograph reports a thought experiment with a mathematical structure intended to illustrate the workings of a mind. It presents a mathematical theory of human thought based on pattern theory with a graph-based approach to thinking. The method illustrated and produced by extensive computer simulations is related to neural networks. Based mainly on introspection, it is speculative rather than empirical such that it differs radically in attitude from the conventional wisdom of current cognitive science.
| Author | : Ulf Grenander |
| Publisher | : World Scientific |
| Total Pages | : 236 |
| Release | : 2012 |
| Genre | : Computers |
| ISBN | : 981438318X |
Download A Calculus of Ideas Book in PDF, ePub and Kindle
This monograph reports a thought experiment with a mathematical structure intended to illustrate the workings of a mind. It presents a mathematical theory of human thought based on pattern theory with a graph-based approach to thinking. The method illustrated and produced by extensive computer simulations is related to neural networks. Based mainly on introspection, it is speculative rather than empirical such that it differs radically in attitude from the conventional wisdom of current cognitive science.
| Author | : David M. Bressoud |
| Publisher | : Princeton University Press |
| Total Pages | : 242 |
| Release | : 2021-05-04 |
| Genre | : Mathematics |
| ISBN | : 0691218781 |
Download Calculus Reordered Book in PDF, ePub and Kindle
Calculus Reordered takes readers on a remarkable journey through hundreds of years to tell the story of how calculus grew to what we know today. David Bressoud explains why calculus is credited to Isaac Newton and Gottfried Leibniz in the seventeenth century, and how its current structure is based on developments that arose in the nineteenth century. Bressoud argues that a pedagogy informed by the historical development of calculus presents a sounder way for students to learn this fascinating area of mathematics. Delving into calculus's birth in the Hellenistic Eastern Mediterranean--especially Syracuse in Sicily and Alexandria in Egypt--as well as India and the Islamic Middle East, Bressoud considers how calculus developed in response to essential questions emerging from engineering and astronomy. He looks at how Newton and Leibniz built their work on a flurry of activity that occurred throughout Europe, and how Italian philosophers such as Galileo Galilei played a particularly important role. In describing calculus's evolution, Bressoud reveals problems with the standard ordering of its curriculum: limits, differentiation, integration, and series. He contends instead that the historical order--which follows first integration as accumulation, then differentiation as ratios of change, series as sequences of partial sums, and finally limits as they arise from the algebra of inequalities--makes more sense in the classroom environment. Exploring the motivations behind calculus's discovery, Calculus Reordered highlights how this essential tool of mathematics came to be.
| Author | : Fima C. Klebaner |
| Publisher | : Imperial College Press |
| Total Pages | : 431 |
| Release | : 2005 |
| Genre | : Mathematics |
| ISBN | : 1860945554 |
Download Introduction to Stochastic Calculus with Applications Book in PDF, ePub and Kindle
This book presents a concise treatment of stochastic calculus and its applications. It gives a simple but rigorous treatment of the subject including a range of advanced topics, it is useful for practitioners who use advanced theoretical results. It covers advanced applications, such as models in mathematical finance, biology and engineering.Self-contained and unified in presentation, the book contains many solved examples and exercises. It may be used as a textbook by advanced undergraduates and graduate students in stochastic calculus and financial mathematics. It is also suitable for practitioners who wish to gain an understanding or working knowledge of the subject. For mathematicians, this book could be a first text on stochastic calculus; it is good companion to more advanced texts by a way of examples and exercises. For people from other fields, it provides a way to gain a working knowledge of stochastic calculus. It shows all readers the applications of stochastic calculus methods and takes readers to the technical level required in research and sophisticated modelling.This second edition contains a new chapter on bonds, interest rates and their options. New materials include more worked out examples in all chapters, best estimators, more results on change of time, change of measure, random measures, new results on exotic options, FX options, stochastic and implied volatility, models of the age-dependent branching process and the stochastic Lotka-Volterra model in biology, non-linear filtering in engineering and five new figures.Instructors can obtain slides of the text from the author.
| Author | : Ulf Grenander |
| Publisher | : World Scientific |
| Total Pages | : 236 |
| Release | : 2012-08-10 |
| Genre | : Mathematics |
| ISBN | : 9814439118 |
Download Calculus Of Ideas, A: A Mathematical Study Of Human Thought Book in PDF, ePub and Kindle
This monograph reports a thought experiment with a mathematical structure intended to illustrate the workings of a mind. It presents a mathematical theory of human thought based on pattern theory with a graph-based approach to thinking. The method illustrated and produced by extensive computer simulations is related to neural networks. Based mainly on introspection, it is speculative rather than empirical such that it differs radically in attitude from the conventional wisdom of current cognitive science.
| Author | : Sean Carroll |
| Publisher | : Penguin |
| Total Pages | : 305 |
| Release | : 2022-09-20 |
| Genre | : Science |
| ISBN | : 0593186583 |
Download The Biggest Ideas in the Universe Book in PDF, ePub and Kindle
INSTANT NEW YORK TIMES BESTSELLER “Most appealing... technical accuracy and lightness of tone... Impeccable.”—Wall Street Journal “A porthole into another world.”—Scientific American “Brings science dissemination to a new level.”—Science The most trusted explainer of the most mind-boggling concepts pulls back the veil of mystery that has too long cloaked the most valuable building blocks of modern science. Sean Carroll, with his genius for making complex notions entertaining, presents in his uniquely lucid voice the fundamental ideas informing the modern physics of reality. Physics offers deep insights into the workings of the universe but those insights come in the form of equations that often look like gobbledygook. Sean Carroll shows that they are really like meaningful poems that can help us fly over sierras to discover a miraculous multidimensional landscape alive with radiant giants, warped space-time, and bewilderingly powerful forces. High school calculus is itself a centuries-old marvel as worthy of our gaze as the Mona Lisa. And it may come as a surprise the extent to which all our most cutting-edge ideas about black holes are built on the math calculus enables. No one else could so smoothly guide readers toward grasping the very equation Einstein used to describe his theory of general relativity. In the tradition of the legendary Richard Feynman lectures presented sixty years ago, this book is an inspiring, dazzling introduction to a way of seeing that will resonate across cultural and generational boundaries for many years to come.
| Author | : Dan Umbarger |
| Publisher | : |
| Total Pages | : 176 |
| Release | : 2011-05-01 |
| Genre | : Mathematics |
| ISBN | : 9780983397304 |
Download Twenty Key Ideas in Beginning Calculus Book in PDF, ePub and Kindle
A high-school mathematics teacher who learned how to sequence and present ideas during his 30-year career presents a bridge for beginning calculus students to study independently in preparation for a traditional calculus curriculum or as supplemental material for students who are currently in a calculus class.
| Author | : Steven Strogatz |
| Publisher | : Princeton University Press |
| Total Pages | : 181 |
| Release | : 2011-03-07 |
| Genre | : Mathematics |
| ISBN | : 1400830885 |
Download The Calculus of Friendship Book in PDF, ePub and Kindle
The Calculus of Friendship is the story of an extraordinary connection between a teacher and a student, as chronicled through more than thirty years of letters between them. What makes their relationship unique is that it is based almost entirely on a shared love of calculus. For them, calculus is more than a branch of mathematics; it is a game they love playing together, a constant when all else is in flux. The teacher goes from the prime of his career to retirement, competes in whitewater kayaking at the international level, and loses a son. The student matures from high school math whiz to Ivy League professor, suffers the sudden death of a parent, and blunders into a marriage destined to fail. Yet through it all they take refuge in the haven of calculus--until a day comes when calculus is no longer enough. Like calculus itself, The Calculus of Friendship is an exploration of change. It's about the transformation that takes place in a student's heart, as he and his teacher reverse roles, as they age, as they are buffeted by life itself. Written by a renowned teacher and communicator of mathematics, The Calculus of Friendship is warm, intimate, and deeply moving. The most inspiring ideas of calculus, differential equations, and chaos theory are explained through metaphors, images, and anecdotes in a way that all readers will find beautiful, and even poignant. Math enthusiasts, from high school students to professionals, will delight in the offbeat problems and lucid explanations in the letters. For anyone whose life has been changed by a mentor, The Calculus of Friendship will be an unforgettable journey.
| Author | : Günther Palm |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 258 |
| Release | : 2012-12-06 |
| Genre | : Medical |
| ISBN | : 3642709117 |
Download Brain Theory Book in PDF, ePub and Kindle
The present collection of papers forms the Proceedings of the First Meeting on Brain Theory, held October 1-4, 1984 at the International Centre for Theoretical Physics in Trieste, Italy. The Meeting was organized with the aim of bringing together brain theorists who are willing to put their own research in the perspective of the general development of neuroscience. Such a meeting was considered necessary since the explosion of experi mental work in neuroscience during the last decades has not been accompanied by an adequate development on the theoretical side. The intensity of the discussions during the Meeting is prob ably reflected best in the report of the organizers, reprinted here following the Preface. During the Meeting it was decided that a workshop of this kind should be repeated at regular intervals of approximately 2 years. The International Centre for Theoretical Physics in Trieste has kindly agreed to act as host for future meetings. The present Meeting was supported by grants from the In ternational Centre for Theoretical Physics and the International School for Advanced Studies in Trieste, IBM-Germany through the "Stifterverband fur die Deutsche Wissenschaft" and the Max Planck-Institute for Biological Cybernetics.
| Author | : Ben Orlin |
| Publisher | : Black Dog & Leventhal |
| Total Pages | : 320 |
| Release | : 2019-10-08 |
| Genre | : Mathematics |
| ISBN | : 031650906X |
Download Change Is the Only Constant Book in PDF, ePub and Kindle
The next book from Ben Orlin, the popular math blogger and author of the underground bestseller Math With Bad Drawings. Change Is The Only Constant is an engaging and eloquent exploration of the intersection between calculus and daily life, complete with Orlin's sly humor and wonderfully bad drawings. Change is the Only Constant is an engaging and eloquent exploration of the intersection between calculus and daily life, complete with Orlin's sly humor and memorably bad drawings. By spinning 28 engaging mathematical tales, Orlin shows us that calculus is simply another language to express the very things we humans grapple with every day -- love, risk, time, and most importantly, change. Divided into two parts, "Moments" and "Eternities," and drawing on everyone from Sherlock Holmes to Mark Twain to David Foster Wallace, Change is the Only Constant unearths connections between calculus, art, literature, and a beloved dog named Elvis. This is not just math for math's sake; it's math for the sake of becoming a wiser and more thoughtful human.
