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Calculus of Thought

Calculus of Thought
  • Author : Daniel M. Rice
  • Publisher :Unknown
  • Release Date :2013-11-07
  • Total pages :280
  • ISBN : 012410407X
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Summary : 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 :Unknown
  • Release Date :2012
  • Total pages :219
  • ISBN : 9789814383189
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Summary : 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 :Unknown
  • Release Date :2013-10-15
  • Total pages :272
  • ISBN : 9780124104525
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Summary : 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

Calculus of Thought

Calculus of Thought
  • Author : Daniel Rice
  • Publisher :Unknown
  • Release Date :2013
  • Total pages :272
  • ISBN : OCLC:1105778492
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Summary : 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 Offers a new neuromorphic foundation for machine learning based upon the reduced error logistic regression (RELR) method and provides simple examples of RELR computations in toy problems that can be accessed in spreadsheet workbooks through a companion website.

Calculus Of Ideas, A: A Mathematical Study Of Human Thought

Calculus Of Ideas, A: A Mathematical Study Of Human Thought
  • Author : Ulf Grenander
  • Publisher :Unknown
  • Release Date :2012-08-10
  • Total pages :236
  • ISBN : 9789814439114
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Summary : 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.

Engineering Formulas for Thought

Engineering Formulas for Thought
  • Author : Charles M. Bull
  • Publisher :Unknown
  • Release Date :1972
  • Total pages :42
  • ISBN : OCLC:946959429
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Summary :

The Mathematical Imagination

The Mathematical Imagination
  • Author : Matthew Handelman
  • Publisher :Unknown
  • Release Date :2019-03-05
  • Total pages :256
  • ISBN : 9780823283842
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Summary : This book offers an archeology of the undeveloped potential of mathematics for critical theory. As Max Horkheimer and Theodor W. Adorno first conceived of the critical project in the 1930s, critical theory steadfastly opposed the mathematization of thought. Mathematics flattened thought into a dangerous positivism that led reason to the barbarism of World War II. The Mathematical Imagination challenges this narrative, showing how for other German-Jewish thinkers, such as Gershom Scholem, Franz Rosenzweig, and Siegfried Kracauer, mathematics offered metaphors to negotiate the crises of modernity during the Weimar Republic. Influential theories of poetry, messianism, and cultural critique, Handelman shows, borrowed from the philosophy of mathematics, infinitesimal calculus, and geometry in order to refashion cultural and aesthetic discourse. Drawn to the austerity and muteness of mathematics, these friends and forerunners of the Frankfurt School found in mathematical approaches to negativity strategies to capture the marginalized experiences and perspectives of Jews in Germany. Their vocabulary, in which theory could be both mathematical and critical, is missing from the intellectual history of critical theory, whether in the work of second generation critical theorists such as Jürgen Habermas or in contemporary critiques of technology. The Mathematical Imagination shows how Scholem, Rosenzweig, and Kracauer’s engagement with mathematics uncovers a more capacious vision of the critical project, one with tools that can help us intervene in our digital and increasingly mathematical present.

Frames of Mind

Frames of Mind
  • Author : Judith Summerfield,Geoffrey Summerfield
  • Publisher :Unknown
  • Release Date :1986
  • Total pages :378
  • ISBN : 0394337956
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Summary :

Calculus For Dummies

Calculus For Dummies
  • Author : Mark Ryan
  • Publisher :Unknown
  • Release Date :2016-06-07
  • Total pages :384
  • ISBN : 9781119293491
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Summary : Slay the calculus monster with this user-friendly guide Calculus For Dummies, 2nd Edition makes calculus manageable—even if you're one of the many students who sweat at the thought of it. By breaking down differentiation and integration into digestible concepts, this guide helps you build a stronger foundation with a solid understanding of the big ideas at work. This user-friendly math book leads you step-by-step through each concept, operation, and solution, explaining the "how" and "why" in plain English instead of math-speak. Through relevant instruction and practical examples, you'll soon learn that real-life calculus isn't nearly the monster it's made out to be. Calculus is a required course for many college majors, and for students without a strong math foundation, it can be a real barrier to graduation. Breaking that barrier down means recognizing calculus for what it is—simply a tool for studying the ways in which variables interact. It's the logical extension of the algebra, geometry, and trigonometry you've already taken, and Calculus For Dummies, 2nd Edition proves that if you can master those classes, you can tackle calculus and win. Includes foundations in algebra, trigonometry, and pre-calculus concepts Explores sequences, series, and graphing common functions Instructs you how to approximate area with integration Features things to remember, things to forget, and things you can't get away with Stop fearing calculus, and learn to embrace the challenge. With this comprehensive study guide, you'll gain the skills and confidence that make all the difference. Calculus For Dummies, 2nd Edition provides a roadmap for success, and the backup you need to get there.

The Cognitive Connection

The Cognitive Connection
  • Author : Howard Levine,Howard Rheingold
  • Publisher :Unknown
  • Release Date :1987
  • Total pages :276
  • ISBN : UOM:39015012445196
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Summary : Discusses the differences between natural language and programming languages, looks at mathematical logic, and describes the future of computer programming

Evolution of Mathematical Thought

Evolution of Mathematical Thought
  • Author : Herbert Meschkowski
  • Publisher :Unknown
  • Release Date :1965
  • Total pages :157
  • ISBN : UCAL:B4246914
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Summary :

Language as Calculus vs. Language as Universal Medium

Language as Calculus vs. Language as Universal Medium
  • Author : Maren Kusch
  • Publisher :Unknown
  • Release Date :2012-12-06
  • Total pages :362
  • ISBN : 9789400924178
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Summary : I first became interested in Husserl and Heidegger as long ago as 1980, when as an undergraduate at the Freie Universitat Berlin I studied the books by Professor Ernst Tugendhat. Tugendhat's at tempt to bring together analytical and continental philosophy has never ceased to fascinate me, and even though in more recent years other influences have perhaps been stronger, I should like to look upon the present study as still being indebted to Tugendhat's initial incentive. It was my good fortune that for personal reasons I had to con tinue my academic training from 1981 onwards in Finland. Even though Finland is a stronghold of analytical philosophy, it also has a tradition of combining continental and Anglosaxon philosophical thought. Since I had already admired this line of work in Tugendhat, it is hardly surprising that once in Finland I soon became impressed by Professor Jaakko Hintikka's studies on Husserl and intentionality, and by Professor Georg Henrik von Wright's analytical hermeneu tics. While the latter influence has-at least in part-led to a book on the history of hermeneutics, the former influence has led to the present work. My indebtedness to Professor Hintikka is enormous. Not only is the research reported here based on his suggestions, but Hintikka has also commented extensively on different versions of the manuscript, helped me to make important contacts, found a publisher for me, and-last but not least-was a never failing source of encouragement.

Great Currents of Mathematical Thought

Great Currents of Mathematical Thought
  • Author : François Le Lionnais
  • Publisher :Unknown
  • Release Date :2004-01-01
  • Total pages :266
  • ISBN : 0486495795
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Summary : 50 essays by eminent scholars include meditations on "Structures," Disciplines," "Space," "Function," "Group," "Probability," and "The Mathematical Epic" (Volume I) and on "Mathematics and the Human Intellect," "Mathematics and Technology," and "Mathematics and Civilization" (Volume II). 1962 edition.

Calculus and Pizza

Calculus and Pizza
  • Author : Clifford A. Pickover
  • Publisher :Unknown
  • Release Date :2003-06-16
  • Total pages :208
  • ISBN : 0471269875
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Summary : "Setting up residence in a pizza parlor, Clifford Pickover focuses on procedures for solving problems, offering short, easy-to-digest chapters that allow you to quickly get the essence of a technique or question. From exponentials and logarithms to derivatives and multiple integrals, the book utilizes pepperoni, meatballs, and more to make complex topics fun to learn - emphasizing basic, practical principles to help you calculate the speed of tossed pizza dough or the rising cost of eggplant parmigiana. Plus, you'll see how simple math - and a meal - can solve more especially curious and even mind-shattering problems."--BOOK JACKET.

Deep Thinking

Deep Thinking
  • Author : William Byers
  • Publisher :Unknown
  • Release Date :2014-09-22
  • Total pages :264
  • ISBN : 9789814618052
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Summary : There is more than one way to think. Most people are familiar with the systematic, rule-based thinking that one finds in a mathematical proof or a computer program. But such thinking does not produce breakthroughs in mathematics and science nor is it the kind of thinking that results in significant learning. Deep thinking is a different and more basic way of using the mind. It results in the discontinuous “aha!” experience, which is the essence of creativity. It is at the heart of every paradigm shift or reframing of a problematic situation. The identification of deep thinking as the default state of the mind has the potential to reframe our current approach to technological change, education, and the nature of mathematics and science. For example, there is an unbridgeable gap between deep thinking and computer simulations of thinking. Many people suspect that such a gap exists, but find it difficult to make this intuition precise. This book identifies the way in which the authentic intelligence of deep thinking differs from the artificial intelligence of “big data” and “analytics”. Deep thinking is the essential ingredient in every significant learning experience, which leads to a new way to think about education. It is also essential to the construction of conceptual systems that are at the heart of mathematics and science, and of the technologies that shape the modern world. Deep thinking can be found whenever one conceptual system morphs into another. The sources of this study include the cognitive development of numbers in children, neuropsychology, the study of creativity, and the historical development of mathematics and science. The approach is unusual and original. It comes out of the author's lengthy experience as a mathematician, teacher, and writer of books about mathematics and science, such as How Mathematicians Think: Using Ambiguity, Contradiction, and Paradox to Create Mathematics and The Blind Spot: Science and the Crisis of Uncertainty. Contents:What is Deep Thinking?Conceptual SystemsDeep Thinking in Mathematics and ScienceDeep Thinking in the Mind and the BrainDeep Thinking and CreativityDeep LearningGood TeachingUndergraduate MathematicsWhat the Mind Can Teach Us About MathematicsWhat Mathematics Can Teach Us About the MindReferences Readership: Students, graduate students and researchers with an interest in mathematics, mathematicians, scientists, philosophers, psychologists, and readers who use mathematics in their work. Key Features:In this book, the author, a mathematician, demonstrates the specific difference between creative mathematical thought and the analytic thought of logic and the artificial intelligence of computersThis book shows why learning is a creative activity and demonstrates how teaching and learning must undergo radical changes in this age of rapid technological changeMathematics is a model for how people think and it reveals the essence of intelligenceThe author, a mathematician, demonstrates that creativity is a basic feature of the world. The same phenomenon of creative intelligence underlies the theory of evolution, child development, learning, and scientific and mathematical research. Creativity is so natural that even babies are capable of it but so difficult that adults have great trouble with it. This book explains the reasons behind this apparent paradoxKeywords:Mathematics;Cognitive Development;Thinking;Education;Mathematics Education;Conceptual Systems

The History of the Calculus and Its Conceptual Development

The History of the Calculus and Its Conceptual Development
  • Author : Carl B. Boyer
  • Publisher :Unknown
  • Release Date :2012-10-09
  • Total pages :368
  • ISBN : 9780486175386
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Summary : Fluent description of the development of both the integral and differential calculus — its early beginnings in antiquity, medieval contributions, and a consideration of Newton and Leibniz.

Calculus for the Utterly Confused

Calculus for the Utterly Confused
  • Author : Robert Oman,Daniel Oman
  • Publisher :Unknown
  • Release Date :1998-07-22
  • Total pages :208
  • ISBN : 0071368728
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Summary : When it comes to understanding one of your most intimidating courses--calculus--even good students can be confused. Intended primarily for the non-engineering calculus student (though the more serious calculus student will also benefit), Calculus for the Utterly Confused is your ticket to success. Calculus concepts are explained and applied in such diverse fields as business, medicine, finance, economics, chemistry, sociology, physics, and health and environmental sciences. The message of Calculus for the Utterly Confused is simple: You donÕt have to be confused anymore. With the wealth of expert advice from the authors who have taught many, many confused students, youÕll discover a newer, fresher, clearer way to look at calculus. DonÕt wait another minute--get on the road to higher grades and greater confidence, and go from utterly confused to totally prepared in no time!

A History of European Thought in the Nineteenth Century: Philosophical thought. 2 v

A History of European Thought in the Nineteenth Century: Philosophical thought. 2 v
  • Author : John Theodore Merz
  • Publisher :Unknown
  • Release Date :1965
  • Total pages :229
  • ISBN : STANFORD:36105002452535
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Summary :

Techniques in Differentiation

Techniques in Differentiation
  • Author : S.T. Simms
  • Publisher :Unknown
  • Release Date :2015-03-23
  • Total pages :142
  • ISBN : 0987528912
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Summary : The discovery of calculus in the seventeenth century by Isaac Newton and Gottfried Leibniz, helped usher in a revolution in mathematics and science that had a profound and far-reaching effect on the world. Calculus provided a powerful tool that enabled the fledgling science of physics to break new ground in our understanding of the workings of the natural universe. Indeed, calculus is virtually synonymous with physics as it is the mathematics of infinitesimal change. As the world about us appears to be a continuity punctuated by discrete things, then calculus is vital in understanding the behavior of a quantitative change relative to another, from one instant to the next. The intellectual endeavor of mathematics can be thought of as a tree, with calculus one of its boughs. This bough consisting of two major branches, one entwined about the other-differentiation and integration. This book focuses on the discovery, methods and applications of the mathematics of differentiation. Differential calculus, as opposed to integral calculus, considers variable quantitative relationships to one another in the form of tangents. Techniques in Differentiation is based on material written for high school calculus students. However, the book is suitable for any elementary calculus student at either high school or university level. It aims to give calculus students a deeper understanding of the subject. This is achieved by, in part, providing more historical background and development than is offered by most calculus textbooks. A common failing of many technical textbooks is to skim over mathematical workings that get to some result. Mathematical and scientific textbooks typically assume the student has the required mathematical skill to provide the missing details for themselves. This is an ongoing major complaint of students and can make the study of a mathematics textbook particularly frustrating. The author of Techniques in Differentiation in contrast, provides detailed line-by-line working in proofs and examples. Another complaint of mathematics students is textbooks that provide too few exercises, or overly simple questions with which to practice. The author provides a large number of exercise questions, ranging in level of difficulty from easy to challenging. In addition, Techniques in Differentiation includes the answers to all the questions in the exercises at the end of each chapter. It is particularly irksome when a textbook does not provide answers to exercises-students find it frustrating when they are unable to see if they have adequately mastered the concepts and techniques outlined in a mathematics book. The dedicated student will find in calculus a powerful analytical tool with applications in the physical sciences, engineering and technology. And like all areas of mathematics, it can also be appreciated for its own inherent beauty. Techniques in Differentiation will provide mathematics students with the technical skills with which to explore and appreciate calculus and its applications.

The Calculus Lifesaver

The Calculus Lifesaver
  • Author : Adrian Banner
  • Publisher :Unknown
  • Release Date :2007-03-25
  • Total pages :728
  • ISBN : 9780691130880
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Summary : For many students, calculus can be the most mystifying and frustrating course they will ever take. Based upon Adrian Banner's popular calculus review course at Princeton University, this book provides students with the essential tools they need not only to learn calculus, but also to excel at it.

Why Can't Dogs Do Calculus?

Why Can't Dogs Do Calculus?
  • Author : Murray Weiner
  • Publisher :Unknown
  • Release Date :2002
  • Total pages :229
  • ISBN : 9671608477
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Summary :