A Calculus of Ideas

Author: Ulf Grenander
Publisher: World Scientific
ISBN: 9814383198
Format: PDF, Docs
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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.

A Calculus of Ideas

Author: Ulf Grenander
Publisher: World Scientific
ISBN: 9814439118
Format: PDF
Download Now
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. Contents:An Architecture for the Mind:IntroductionCreating Thoughts: Algebra of ThinkingPersonality of a Mind:A Mind EquationTwo Personalities:Building a GOLEM, a Thinking MachineAs Thinking DevelopsRealizing a Mind:MIND and BrainReflectionsDoubts and CertaintiesAppendics:Some Famous Mind TheoriesConsistency of Probability MeasureA Modality LatticeDynamics of Random Process of ThinkingSoftware for GOLEM Readership: Graduate students in applied mathematics, statistics and cognitive science as well as postgraduates and researchers in these fields. Keywords:Thinking;Pattern Theory;Language;SoftwareKey Features:Unconventional speculative approach using thought experimentsQuite different from other studies of human thoughtWritten by the inventor of pattern theoryDue to the controversial nature of the theory presented, it will appeal to the adventure-minded researchers in applied mathematics, statistics and cognitive function

How Humans Learn to Think Mathematically

Author: David Tall
Publisher: Cambridge University Press
ISBN: 1107035708
Format: PDF, Mobi
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How Humans Learn to Think Mathematically describes the development of mathematical thinking from the young child to the sophisticated adult. Professor David Tall reveals the reasons why mathematical concepts that make sense in one context may become problematic in another. For example, a child's experience of whole number arithmetic successively affects subsequent understanding of fractions, negative numbers, algebra, and the introduction of definitions and proof. Tall's explanations for these developments are accessible to a general audience while encouraging specialists to relate their areas of expertise to the full range of mathematical thinking. The book offers a comprehensive framework for understanding mathematical growth, from practical beginnings through theoretical developments, to the continuing evolution of mathematical thinking at the highest level.

Where Mathematics Comes from

Author: George Lakoff
Publisher: Basic Books (AZ)
ISBN:
Format: PDF, Mobi
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Provides an in-depth analysis of the cognitive science of mathematical ideas that argues that conceptual metaphor plays a definitive role in mathematical ideas, exploring such concepts as arithmetic, algebra, sets, logic, and infinity. 20,000 first printing.

Infinitesimal

Author: Amir Alexander
Publisher: Oneworld Publications
ISBN: 1780745338
Format: PDF, ePub, Mobi
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On August 10, 1632, five leading Jesuits convened in a sombre Roman palazzo to pass judgment on a simple idea: that a continuous line is composed of distinct and limitlessly tiny parts. The doctrine would become the foundation of calculus, but on that fateful day the judges ruled that it was forbidden. With the stroke of a pen they set off a war for the soul of the modern world. Amir Alexander takes us from the bloody religious strife of the sixteenth century to the battlefields of the English civil war and the fierce confrontations between leading thinkers like Galileo and Hobbes. The legitimacy of popes and kings, as well as our modern beliefs in human liberty and progressive science, hung in the balance; the answer hinged on the infinitesimal. Pulsing with drama and excitement, Infinitesimal will forever change the way you look at a simple line.

Simplicity

Author: Craig Dilworth
Publisher: Rowman & Littlefield
ISBN: 0739177230
Format: PDF
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Simplicity provides a new logic with which to approach intellectual situations. Using the simplicity way of thinking as a tool helps clarify intellectual standpoints and conceptually problematic situations in philosophy, mathematics and physics.

What is Mathematics

Author: Richard Courant
Publisher: Oxford University Press, USA
ISBN: 9780195105193
Format: PDF, ePub, Docs
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A discussion of fundamental mathematical principles from algebra to elementary calculus designed to promote constructive mathematical reasoning.

The Tangled Origins of the Leibnizian Calculus

Author: Richard C. Brown
Publisher: World Scientific
ISBN: 9814390798
Format: PDF, ePub, Docs
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1. Evolution or revolution in mathematics -- 2. Issues in seventeenth century mathematics -- 3. Isaac Barrow: a foil to Leibniz -- 4. A young central European polymath -- 5. First steps in mathematics -- 6. The creation of calculus -- 7. Logic -- 8. The universal characteristic -- 9. The baroque cultural context -- 10. Epilogue -- 11. Some concluding remarks on mathematical change -- Appendices.

Mathematics

Author: Morris Kline
Publisher: Oxford University Press, USA
ISBN: 9780195030853
Format: PDF, Docs
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Refuting the accepted belief that mathematics is exact and infallible, the author examines the development of conflicting concepts of mathematics and their implications for the physical, applied, social, and computer sciences

Mathematics in Western Culture

Author: Morris Kline
Publisher: Oxford University Press
ISBN: 9780195345452
Format: PDF, ePub, Mobi
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This book gives a remarkably fine account of the influences mathematics has exerted on the development of philosophy, the physical sciences, religion, and the arts in Western life.