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How Mathematicians Think
By William Byers Book ID : 1400833957
 Publisher : Princeton University Press
 Pages : 424
 Genre : Mathematics
 Reads : 975
 eBook Format : Pdf, ePub, Mobi, Kindle
 File Pdf: howmathematiciansthink.pdf
Book Summary:
To many outsiders, mathematicians appear to think like computers, grimly grinding away with a strict formal logic and moving methodicallyeven algorithmicallyfrom one blackandwhite 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 lessfamiliar 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.
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 Isbn : 1416594434
 Pages : 320
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 Reads : 503
 File Pdf: isgodamathematician.pdf
Book Summary:
Bestselling author and astrophysicist Mario Livio examines the lives and theories of history’s greatest mathematicians to ask how—if mathematics is an abstract construction of the human mind—it can so perfectly explain the physical world. Nobel Laureate Eugene Wigner once wondered about “the unreasonable effectiveness of mathematics” in the formulation of the laws of nature. Is God a Mathematician? investigates why mathematics is as powerful as it is. From ancient times to the present, scientists and philosophers have marveled at how such a seemingly abstract discipline could so perfectly explain the natural world. More than that—mathematics has often made predictions, for example, about subatomic particles or cosmic phenomena that were unknown at the time, but later were proven to be true. Is mathematics ultimately invented or discovered? If, as Einstein insisted, mathematics is “a product of human thought that is independent of experience,” how can it so accurately describe and even predict the world around us? Physicist and author Mario Livio brilliantly explores mathematical ideas from Pythagoras to the present day as he shows us how intriguing questions and ingenious answers have led to ever deeper insights into our world. This fascinating book will interest anyone curious about the human mind, the scientific world, and the relationship between them.
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 File Pdf: birthofatheorem.pdf
Book Summary:
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 File Pdf: thinkinginproblems.pdf
Book Summary:
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 File Pdf: thesurvivalofamathematician.pdf
Book Summary:
"One of the themes of the book is how to have a fulfilling professional life. In order to achieve this goal, Krantz discusses keeping a vigorous scholarly program going and finding new challenges, as well as dealing with the everyday tasks of research, teaching, and administration." "In short, this is a survival manual for the professional mathematician  both in academics and in industry and government agencies. It is a sequel to the author's A Mathematician's Survival Guide."BOOK JACKET.
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 File Pdf: mathematicalgrammarofbiology.pdf
Book Summary:
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 Reads : 263
 File Pdf: metaphysicsandthephilosophyofscience.pdf
Book Summary:
The question of the proper role of metaphysics in philosophy of science is both significant and contentious. The last few decades have seen considerable engagement with philosophical projects aptly described as "the metaphysics of science:" inquiries into natural laws and properties, natural kinds, causal relations, and dispositions. At the same time, many metaphysicians have begun moving in the direction of more scientificallyinformed ("scientistic" or "naturalistic") metaphysics. And yet many philosophers of science retain a deep suspicion about the significance of metaphysical investigations into science. This volume of new essays explores a broadly methodological question: what role should metaphysics play in our philosophizing about science? These new essays, written by leading philosophers of science, address this question both through groundlevel investigations of particular issues in the metaphysics of science and by more general methodological inquiry.
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 File Pdf: pensees.pdf
Book Summary:
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 File Pdf: analysisii.pdf
Book Summary:
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 File Pdf: eulerspioneeringequation.pdf
Book Summary:
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 Publisher : Princeton University Press
 Isbn : 1400837774
 Pages : 312
 Category : Mathematics
 Reads : 540
 File Pdf: fearlesssymmetry.pdf
Book Summary:
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 File Pdf: thecalculusoffriendship.pdf
Book Summary:
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 File Pdf: mathematicsasascienceofpatterns.pdf
Book Summary:
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 File Pdf: mathematicsandthehistorianscraft.pdf
Book Summary:
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 File Pdf: fourierseries.pdf
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 Pages : 304
 Category : Mathematics
 Reads : 532
 File Pdf: beyondinfinity.pdf
Book Summary:
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 Publisher : Princeton University Press
 Isbn : 1400885523
 Pages : 464
 Category : Mathematics
 Reads : 837
 File Pdf: mathematicswithoutapologies.pdf
Book Summary:
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 Pages : 320
 Category : Mathematics
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 File Pdf: mathematics.pdf
Book Summary:
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 File Pdf: theworldofmathematics.pdf
Book Summary:
Read and download full book The World of Mathematics
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 Publisher : CRC Press
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 Pages : 475
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 File Pdf: usingthemathematicsliterature.pdf
Book Summary:
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 Pages : 572
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 File Pdf: travelingwithphilosophes.pdf
Book Summary:
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 Publisher : Springer Science & Business Media
 Isbn : 0387330828
 Pages : 280
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 File Pdf: analysisandprobability.pdf
Book Summary:
Combines analysis and tools from probability, harmonic analysis, operator theory, and engineering (signal/image processing) Interdisciplinary focus with handson approach, generous motivation and new pedagogical techniques Numerous exercises reinforce fundamental concepts and hone computational skills Separate sections explain engineering terms to mathematicians and operator theory to engineers Fills a gap in the literature
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 Publisher : Springer Science & Business Media
 Isbn : 9400914652
 Pages : 1368
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 File Pdf: internationalhandbookofmathematicseducation.pdf
Book Summary:
ALAN J. BISHOP Monash University, Clayton, Victoria, Australia RATIONALE Mathematics Education is becoming a welldocumented field with many books, journals and international conferences focusing on a variety of aspects relating to theory, research and practice. That documentation also reflects the fact that the field has expanded enormously in the last twenty years. At the 8th International Congress on Mathematics Education (ICME) in Seville, Spain, for example, there were 26 specialist Working Groups and 26 special ist Topic Groups, as well as a host of other group activities. In 1950 the 'Commission Internationale pour I 'Etude et l' Amelioration de l'Enseignement des Mathematiques' (CIEAEM) was formed and twenty years ago another active group, the 'International Group for the Psychology of Mathematics Education' (PME), began at the third ICME at Karlsruhe in 1976. Since then several other specialist groups have been formed, and are also active through regular conferences and publications, as documented in Edward Jacobsen's Chapter 34 in this volume.
Wittgenstein and the Turning Point in the Philosophy of Mathematics
By Stuart Shanker Format : Pdf, ePub, Mobi, Kindle
 Publisher : State University of New York Press
 Isbn : 1438419538
 Pages : 376
 Category : Philosophy
 Reads : 822
 File Pdf: wittgensteinandtheturningpointinthephilosophyofmathematics.pdf
Book Summary:
Shanker exposes the confusions underlying the currently prevailing interpretations of Wittgenstein. He shows how such approaches and their underlying critical frameworks are incapable of coming to terms with Wittgensteins arguments in the philosophy of mathematics. This book explains not only Wittgensteins approach, which was justly heralded as causing a turning point in the philosophy of mathematics, but also the philosophy of mathematics in general.
The Pragmatics of Mathematics Education
By Tim Rowland Format : Pdf, ePub, Mobi, Kindle
 Publisher : Routledge
 Isbn : 1135698333
 Pages : 256
 Category : Education
 Reads : 144
 File Pdf: thepragmaticsofmathematicseducation.pdf
Book Summary:
Drawing on philosophy of language and recent linguistic theory, Rowland surveys several approaches to classroom communication in mathematics. Are students intimidated by the nature of mathematics teaching? Many students appear fearful of voicing their understanding  is fear of error part of the linguistics of mathematics? The approaches explored here provide a rationale and a method for exploring and understanding speakers' motives in classroom mathematics talk. Teacherstudent interactions in mathematics are analysed, and this provides a toolkit that teachers can use to respond to the intellectual vulnerability of their students.
Mathematicians and their Gods
By Snezana Lawrence,Mark McCartney Format : Pdf, ePub, Mobi, Kindle
 Publisher : OUP Oxford
 Isbn : 0191007544
 Pages : 320
 Category : Mathematics
 Reads : 701
 File Pdf: mathematiciansandtheirgods.pdf
Book Summary:
To open a newspaper or turn on the television it would appear that science and religion are polar opposites  mutually exclusive bedfellows competing for hearts and minds. There is little indication of the rich interaction between religion and science throughout history, much of which continues today. From ancient to modern times, mathematicians have played a key role in this interaction. This is a book on the relationship between mathematics and religious beliefs. It aims to show that, throughout scientific history, mathematics has been used to make sense of the 'big' questions of life, and that religious beliefs sometimes drove mathematicians to mathematics to help them make sense of the world. Containing contributions from a wide array of scholars in the fields of philosophy, history of science and history of mathematics, this book shows that the intersection between mathematics and theism is rich in both culture and character. Chapters cover a fascinating range of topics including the Sect of the Pythagoreans, Newton's views on the apocalypse, Charles Dodgson's Anglican faith and Gödel's proof of the existence of God.
Both Flesh and Not
By David Foster Wallace Format : Pdf, ePub, Mobi, Kindle
 Publisher : Little, Brown
 Isbn : 0316214698
 Pages : 336
 Category : Literary Collections
 Reads : 465
 File Pdf: bothfleshandnot.pdf
Book Summary:
Brilliant, dazzling, neverbeforecollected nonfiction writings by "one of America's most daring and talented writers" (Los Angeles Times Book Review): Both Flesh and Not gathers fifteen of Wallace's seminal essays, all published in book form for the first time. Never has Wallace's seemingly endless curiosity been more evident than in this compilation of work spanning nearly 20 years of writing. Here, Wallace turns his critical eye with equal enthusiasm toward Roger Federer and Jorge Luis Borges; Terminator 2 and The Best of the Prose Poem; the nature of being a fiction writer and the quandary of defining the essay; the best underappreciated novels and the English language's most irksome misused words; and much more. Both Flesh and Not restores Wallace's essays as originally written, and it includes a selection from his personal vocabulary list, an assembly of unusual words and definitions.
The Reflection of Life
By A. H. Louie Format : Pdf, ePub, Mobi, Kindle
 Publisher : Springer Science & Business Media
 Isbn : 1461469287
 Pages : 243
 Category : Mathematics
 Reads : 138
 File Pdf: thereflectionoflife.pdf
Book Summary:
A. H. Louie’s The Reflection of Life: Functional Entailment and Imminence in Relational Biology is a continuation of the exploratory journey in relational biology which began with his 2009 monograph More Than Life Itself: A Synthetic Continuation in Relational Biology. The theme of his first book was ‘What is life?’; the theme of this sequel is “How do two life forms interact?” Biology is a subject concerned with organization of relations. Relational biology is the approach that advocates ‘function dictates structure”, rather than ‘structure implies function’. It is mathematics decoded into biological realizations. The book demonstrates some of the powers of the approach of relational biology, and illustrates how pertinent problems in biology can be better addressed this way. In the first volume the theory was developed by using partially ordered sets, lattices, simulations, models, Aristotle’s four causes, graphs, categories, simple and complex systems, anticipatory systems, and metabolismrepair [(M,R)] systems. Here in the second volume, these tools are expanded to employ setvalued mappings, adjacency matrices, random graphs, and interacting entailment networks. The theory of setvalued mappings culminates in the imminence mapping, which equips the further investigation of functional entailment in complex relational networks. Imminence in (M,R)networks that model living systems addresses the topics of biogenesis and natural selection. Interacting (M,R)networks with mutually entailing processes serve as models in the study of symbiosis and pathophysiology. The formalism also provides a natural framework for a relational theory of virology and oncology. This book will serve researchers and graduate students in mathematics and biology.
Mathematical Reasoning
By Raymond Nickerson Format : Pdf, ePub, Mobi, Kindle
 Publisher : Psychology Press
 Isbn : 1136945385
 Pages : 596
 Category : Psychology
 Reads : 228
 File Pdf: mathematicalreasoning.pdf
Book Summary:
The development of mathematical competence  both by humans as a species over millennia and by individuals over their lifetimes  is a fascinating aspect of human cognition. This book explores when and why the rudiments of mathematical capability first appeared among human beings, what its fundamental concepts are, and how and why it has grown into the richly branching complex of specialties that it is today. It discusses whether the ‘truths’ of mathematics are discoveries or inventions, and what prompts the emergence of concepts that appear to be descriptive of nothing in human experience. Also covered is the role of esthetics in mathematics: What exactly are mathematicians seeing when they describe a mathematical entity as ‘beautiful’? There is discussion of whether mathematical disability is distinguishable from a general cognitive deficit and whether the potential for mathematical reasoning is best developed through instruction. This volume is unique in the vast range of psychological questions it covers, as revealed in the work habits and products of numerous mathematicians. It provides fascinating reading for researchers and students with an interest in cognition in general and mathematical cognition in particular. Instructors of mathematics will also find the book’s insights illuminating.
Gaither's Dictionary of Scientific Quotations
By Carl C. Gaither,Alma E. CavazosGaither Format : Pdf, ePub, Mobi, Kindle
 Publisher : Springer Science & Business Media
 Isbn : 1461411149
 Pages : 2867
 Category : Science
 Reads : 729
 File Pdf: gaithersdictionaryofscientificquotations.pdf
Book Summary:
This unprecedented collection of 27,000 quotations is the most comprehensive and carefully researched of its kind, covering all fields of science and mathematics. With this vast compendium you can readily conceptualize and embrace the written images of scientists, laymen, politicians, novelists, playwrights, and poets about humankind's scientific achievements. Approximately 9000 highquality entries have been added to this new edition to provide a rich selection of quotations for the student, the educator, and the scientist who would like to introduce a presentation with a relevant quotation that provides perspective and historical background on his subject. Gaither's Dictionary of Scientific Quotations, Second Edition, provides the finest reference source of science quotations for all audiences. The new edition adds greater depth to the number of quotations in the various thematic arrangements and also provides new thematic categories.
A Course in Number Theory and Cryptography
By Neal Koblitz Format : Pdf, ePub, Mobi, Kindle
 Publisher : Springer Science & Business Media
 Isbn : 1441985921
 Pages : 235
 Category : Mathematics
 Reads : 544
 File Pdf: acourseinnumbertheoryandcryptography.pdf
Book Summary:
This is a substantially revised and updated introduction to arithmetic topics, both ancient and modern, that have been at the centre of interest in applications of number theory, particularly in cryptography. As such, no background in algebra or number theory is assumed, and the book begins with a discussion of the basic number theory that is needed. The approach taken is algorithmic, emphasising estimates of the efficiency of the techniques that arise from the theory, and one special feature is the inclusion of recent applications of the theory of elliptic curves. Extensive exercises and careful answers are an integral part all of the chapters.