Where Mathematics Come From How The Embodied Mind Brings Mathematics Into Being
Author: George Lakoff
Publisher:
Published: 2000-11-02
Total Pages: 520
ISBN-13:
DOWNLOAD EBOOK →A study of the cognitive science of mathematical ideas.
Lanterna Rally
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Reclaiming Cognition
Author: Rafael E. Núñez
Publisher: Imprint Academic
Published: 1999
Total Pages: 310
ISBN-13: 9780907845065
DOWNLOAD EBOOK →Traditional cognitive science is Cartesian in the sense that it takes as fundamental the distinction between the mental and the physical, the mind and the world. This leads to the claim that cognition is representational and best explained using models derived from AI and computational theory. The authors depart radically from this model.
Embodied Artificial Intelligence
Author: Fumiya Iida
Publisher: Springer
Published: 2004-07-02
Total Pages: 334
ISBN-13: 3540278338
DOWNLOAD EBOOK →Originating from a Dagstuhl seminar, the collection of papers presented in this book constitutes on the one hand a representative state-of-the-art survey of embodied artificial intelligence, and on the other hand the papers identify the important research trends and directions in the field. Following an introductory overview, the 23 papers are organized into topical sections on - philosophical and conceptual issues - information, dynamics, and morphology - principles of embodiment for real-world applications - developmental approaches - artificial evolution and self-reconfiguration
18 Unconventional Essays on the Nature of Mathematics
Author: Reuben Hersh
Publisher: Springer Science & Business Media
Published: 2006-01-16
Total Pages: 346
ISBN-13: 0387298312
DOWNLOAD EBOOK →Collection of the most interesting recent writings on the philosophy of mathematics written by highly respected researchers from philosophy, mathematics, physics, and chemistry Interdisciplinary book that will be useful in several fields—with a cross-disciplinary subject area, and contributions from researchers of various disciplines
How Humans Learn to Think Mathematically
Author: David Tall
Publisher: Cambridge University Press
Published: 2013-09-02
Total Pages: 483
ISBN-13: 1107035708
DOWNLOAD EBOOK →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.
A Mathematician's Lament
Author: Paul Lockhart
Publisher: Bellevue Literary Press
Published: 2009-04-01
Total Pages: 144
ISBN-13: 1934137332
DOWNLOAD EBOOK →“One of the best critiques of current mathematics education I have ever seen.”—Keith Devlin, math columnist on NPR’s Morning Edition A brilliant research mathematician who has devoted his career to teaching kids reveals math to be creative and beautiful and rejects standard anxiety-producing teaching methods. Witty and accessible, Paul Lockhart’s controversial approach will provoke spirited debate among educators and parents alike and it will alter the way we think about math forever. Paul Lockhart, has taught mathematics at Brown University and UC Santa Cruz. Since 2000, he has dedicated himself to K-12 level students at St. Ann’s School in Brooklyn, New York.
How Mathematicians Think
Author: William Byers
Publisher: Princeton University Press
Published: 2010-05-02
Total Pages: 424
ISBN-13: 0691145997
DOWNLOAD EBOOK →To many outsiders, mathematicians appear to think like computers, grimly grinding away with a strict formal logic and moving methodically--even algorithmically--from one black-and-white deduction to another. Yet mathematicians often describe their most important breakthroughs as creative, intuitive responses to ambiguity, contradiction, and paradox. A unique examination of this less-familiar aspect of mathematics, How Mathematicians Think reveals that mathematics is a profoundly creative activity and not just a body of formalized rules and results. Nonlogical qualities, William Byers shows, play an essential role in mathematics. Ambiguities, contradictions, and paradoxes can arise when ideas developed in different contexts come into contact. Uncertainties and conflicts do not impede but rather spur the development of mathematics. Creativity often means bringing apparently incompatible perspectives together as complementary aspects of a new, more subtle theory. The secret of mathematics is not to be found only in its logical structure. The creative dimensions of mathematical work have great implications for our notions of mathematical and scientific truth, and How Mathematicians Think provides a novel approach to many fundamental questions. Is mathematics objectively true? Is it discovered or invented? And is there such a thing as a "final" scientific theory? Ultimately, How Mathematicians Think shows that the nature of mathematical thinking can teach us a great deal about the human condition itself.
Concepts of Modern Mathematics
Author: Ian Stewart
Publisher: Courier Corporation
Published: 2012-05-23
Total Pages: 368
ISBN-13: 0486134954
DOWNLOAD EBOOK →In this charming volume, a noted English mathematician uses humor and anecdote to illuminate the concepts of groups, sets, subsets, topology, Boolean algebra, and other mathematical subjects. 200 illustrations.
Naming Infinity
Author: Loren Graham
Publisher: Harvard University Press
Published: 2009-03-31
Total Pages: 252
ISBN-13: 0674032934
DOWNLOAD EBOOK →In 1913, Russian imperial marines stormed an Orthodox monastery at Mt. Athos, Greece, to haul off monks engaged in a dangerously heretical practice known as Name Worshipping. Exiled to remote Russian outposts, the monks and their mystical movement went underground. Ultimately, they came across Russian intellectuals who embraced Name Worshipping—and who would achieve one of the biggest mathematical breakthroughs of the twentieth century, going beyond recent French achievements. Loren Graham and Jean-Michel Kantor take us on an exciting mathematical mystery tour as they unravel a bizarre tale of political struggles, psychological crises, sexual complexities, and ethical dilemmas. At the core of this book is the contest between French and Russian mathematicians who sought new answers to one of the oldest puzzles in math: the nature of infinity. The French school chased rationalist solutions. The Russian mathematicians, notably Dmitri Egorov and Nikolai Luzin—who founded the famous Moscow School of Mathematics—were inspired by mystical insights attained during Name Worshipping. Their religious practice appears to have opened to them visions into the infinite—and led to the founding of descriptive set theory. The men and women of the leading French and Russian mathematical schools are central characters in this absorbing tale that could not be told until now. Naming Infinity is a poignant human interest story that raises provocative questions about science and religion, intuition and creativity.
Mysticism and Logic
