Calculus of Thought

Calculus of Thought
Author: Daniel M. Rice
Publisher:
Total Pages: 280
Release: 2013-11-07
Genre: Mathematics
ISBN: 9780124104075

A must-read for all scientists about a very simple computation method designed to simulate big-data neural processing. This book is inspired by the Calculus Ratiocinator idea of Gottfried Leibniz, which is that machine computation should be developed to simulate human cognitive processes, thus avoiding problematic subjective bias in analytic solutions to practical and scientific problems. The reduced error logistic regression (RELR) method is proposed as such a "Calculus of Thought."

A Calculus of Ideas

A Calculus of Ideas
Author: Ulf Grenander
Publisher: World Scientific
Total Pages: 236
Release: 2012
Genre: Computers
ISBN: 9814383198

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.

Calculus of Thought

Calculus of Thought
Author: Daniel M Rice
Publisher: Academic Press
Total Pages: 295
Release: 2013-10-15
Genre: Mathematics
ISBN: 0124104525

Calculus of Thought: Neuromorphic Logistic Regression in Cognitive Machines is a must-read for all scientists about a very simple computation method designed to simulate big-data neural processing. This book is inspired by the Calculus Ratiocinator idea of Gottfried Leibniz, which is that machine computation should be developed to simulate human cognitive processes, thus avoiding problematic subjective bias in analytic solutions to practical and scientific problems. The reduced error logistic regression (RELR) method is proposed as such a "Calculus of Thought." This book reviews how RELR's completely automated processing may parallel important aspects of explicit and implicit learning in neural processes. It emphasizes the fact that RELR is really just a simple adjustment to already widely used logistic regression, along with RELR's new applications that go well beyond standard logistic regression in prediction and explanation. Readers will learn how RELR solves some of the most basic problems in today's big and small data related to high dimensionality, multi-colinearity, and cognitive bias in capricious outcomes commonly involving human behavior. - Provides a high-level introduction and detailed reviews of the neural, statistical and machine learning knowledge base as a foundation for a new era of smarter machines - Argues that smarter machine learning to handle both explanation and prediction without cognitive bias must have a foundation in cognitive neuroscience and must embody similar explicit and implicit learning principles that occur in the brain

A Brief History of Mathematical Thought

A Brief History of Mathematical Thought
Author: Luke Heaton
Publisher: Oxford University Press
Total Pages: 337
Release: 2017
Genre: History
ISBN: 0190621761

A compelling and readable book that situates mathematics in human experience and history.

From Calculus to Cohomology

From Calculus to Cohomology
Author: Ib H. Madsen
Publisher: Cambridge University Press
Total Pages: 302
Release: 1997-03-13
Genre: Mathematics
ISBN: 9780521589567

An introductory textbook on cohomology and curvature with emphasis on applications.

How Not to Be Wrong

How Not to Be Wrong
Author: Jordan Ellenberg
Publisher: Penguin Press
Total Pages: 480
Release: 2014-05-29
Genre: Mathematics
ISBN: 1594205221

A brilliant tour of mathematical thought and a guide to becoming a better thinker, How Not to Be Wrong shows that math is not just a long list of rules to be learned and carried out by rote. Math touches everything we do; It's what makes the world make sense. Using the mathematician's methods and hard-won insights-minus the jargon-professor and popular columnist Jordan Ellenberg guides general readers through his ideas with rigor and lively irreverence, infusing everything from election results to baseball to the existence of God and the psychology of slime molds with a heightened sense of clarity and wonder. Armed with the tools of mathematics, we can see the hidden structures beneath the messy and chaotic surface of our daily lives. How Not to Be Wrong shows us how--Publisher's description.

Calculus on Manifolds

Calculus on Manifolds
Author: Michael Spivak
Publisher: Westview Press
Total Pages: 164
Release: 1965
Genre: Science
ISBN: 9780805390216

This book uses elementary versions of modern methods found in sophisticated mathematics to discuss portions of "advanced calculus" in which the subtlety of the concepts and methods makes rigor difficult to attain at an elementary level.

A Tour of the Calculus

A Tour of the Calculus
Author: David Berlinski
Publisher: Vintage
Total Pages: 353
Release: 2011-04-27
Genre: Mathematics
ISBN: 030778973X

Were it not for the calculus, mathematicians would have no way to describe the acceleration of a motorcycle or the effect of gravity on thrown balls and distant planets, or to prove that a man could cross a room and eventually touch the opposite wall. Just how calculus makes these things possible and in doing so finds a correspondence between real numbers and the real world is the subject of this dazzling book by a writer of extraordinary clarity and stylistic brio. Even as he initiates us into the mysteries of real numbers, functions, and limits, Berlinski explores the furthest implications of his subject, revealing how the calculus reconciles the precision of numbers with the fluidity of the changing universe. "An odd and tantalizing book by a writer who takes immense pleasure in this great mathematical tool, and tries to create it in others."--New York Times Book Review