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How Mathematicians Think

By William Byers
  • ISBN Code: : 1400833957
  • Publisher : Princeton University Press
  • Pages : 424
  • Category : Mathematics
  • Reads : 788
  • Book Compatibility : Pdf, ePub, Mobi, Kindle
  • Pdf : how-mathematicians-think.pdf

Book Excerpt :

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.

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  • File : Pdf, ePub, Mobi, Kindle
  • Publisher : Simon and Schuster
  • Book Code : 1416594434
  • Total of Pages : 320
  • Category : Mathematics
  • Members : 546
  • Pdf File: is-god-a-mathematician.pdf

Book Short 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, ePub, Mobi, Kindle
  • Publisher : Springer Science & Business Media
  • Book Code : 3642136060
  • Total of Pages : 238
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  • Pdf File: mathematical-lives.pdf

Book Short Summary:

Steps forward in mathematics often reverberate in other scientific disciplines, and give rise to innovative conceptual developments or find surprising technological applications. This volume brings to the forefront some of the proponents of the mathematics of the twentieth century, who have put at our disposal new and powerful instruments for investigating the reality around us. The portraits present people who have impressive charisma and wide-ranging cultural interests, who are passionate about defending the importance of their own research, are sensitive to beauty, and attentive to the social and political problems of their times. What we have sought to document is mathematics’ central position in the culture of our day. Space has been made not only for the great mathematicians but also for literary texts, including contributions by two apparent interlopers, Robert Musil and Raymond Queneau, for whom mathematical concepts represented a valuable tool for resolving the struggle between ‘soul and precision.’

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  • Book Code : 0374710236
  • Total of Pages : 272
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  • Pdf File: birth-of-a-theorem.pdf

Book Short Summary:

In 2010, French mathematician Cédric Villani received the Fields Medal, the most coveted prize in mathematics, in recognition of a proof which he devised with his close collaborator Clément Mouhot to explain one of the most surprising theories in classical physics. Birth of a Theorem is Villani's own account of the years leading up to the award. It invites readers inside the mind of a great mathematician as he wrestles with the most important work of his career. But you don't have to understand nonlinear Landau damping to love Birth of a Theorem. It doesn't simplify or overexplain; rather, it invites readers into collaboration. Villani's diaries, emails, and musings enmesh you in the process of discovery. You join him in unproductive lulls and late-night breakthroughs. You're privy to the dining-hall conversations at the world's greatest research institutions. Villani shares his favorite songs, his love of manga, and the imaginative stories he tells his children. In mathematics, as in any creative work, it is the thinker's whole life that propels discovery—and with Birth of a Theorem, Cédric Villani welcomes you into his.

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  • File : Pdf, ePub, Mobi, Kindle
  • Publisher : Springer Science & Business Media
  • Book Code : 0817684069
  • Total of Pages : 405
  • Category : Mathematics
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  • Pdf File: thinking-in-problems.pdf

Book Short Summary:

This concise, self-contained textbook gives an in-depth look at problem-solving from a mathematician’s point-of-view. Each chapter builds off the previous one, while introducing a variety of methods that could be used when approaching any given problem. Creative thinking is the key to solving mathematical problems, and this book outlines the tools necessary to improve the reader’s technique. The text is divided into twelve chapters, each providing corresponding hints, explanations, and finalization of solutions for the problems in the given chapter. For the reader’s convenience, each exercise is marked with the required background level. This book implements a variety of strategies that can be used to solve mathematical problems in fields such as analysis, calculus, linear and multilinear algebra and combinatorics. It includes applications to mathematical physics, geometry, and other branches of mathematics. Also provided within the text are real-life problems in engineering and technology. Thinking in Problems is intended for advanced undergraduate and graduate students in the classroom or as a self-study guide. Prerequisites include linear algebra and analysis.

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  • File : Pdf, ePub, Mobi, Kindle
  • Publisher : American Mathematical Soc.
  • Book Code : 0821846299
  • Total of Pages : 310
  • Category : Mathematics
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  • Pdf File: the-survival-of-a-mathematician.pdf

Book Short 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, ePub, Mobi, Kindle
  • Publisher : Springer
  • Book Code : 3319626892
  • Total of Pages : 82
  • Category : Mathematics
  • Members : 833
  • Pdf File: mathematical-grammar-of-biology.pdf

Book Short Summary:

This seminal, multidisciplinary book shows how mathematics can be used to study the first principles of DNA. Most importantly, it enriches the so-called “Chargaff’s grammar of biology” by providing the conceptual theoretical framework necessary to generalize Chargaff’s rules. Starting with a simple example of DNA mathematical modeling where human nucleotide frequencies are associated to the Fibonacci sequence and the Golden Ratio through an optimization problem, its breakthrough is showing that the reverse, complement and reverse-complement operators defined over oligonucleotides induce a natural set partition of DNA words of fixed-size. These equivalence classes, when organized into a matrix form, reveal hidden patterns within the DNA sequence of every living organism. Intended for undergraduate and graduate students both in mathematics and in life sciences, it is also a valuable resource for researchers interested in studying invariant genomic properties.

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  • Pdf File: metaphysics-and-the-philosophy-of-science.pdf

Book Short 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 scientifically-informed ("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 ground-level investigations of particular issues in the metaphysics of science and by more general methodological inquiry.

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  • Pdf File: pensees.pdf

Book Short Summary:

Blaise Pascal, the precociously brilliant contemporary of Descartes, was a gifted mathematician and physicist, but it is his unfinished apologia for the Christian religion upon which his reputation now rests. The Penseés is a collection of philosohical fragments, notes and essays in which Pascal explores the contradictions of human nature in pscyhological, social, metaphysical and - above all - theological terms. Mankind emerges from Pascal's analysis as a wretched and desolate creature within an impersonal universe, but who can be transformed through faith in God's grace.

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  • Pdf File: analysis-ii.pdf

Book Short Summary:

This is part two of a two-volume book on real analysis and is intended for senior undergraduate students of mathematics who have already been exposed to calculus. The emphasis is on rigour and foundations of analysis. Beginning with the construction of the number systems and set theory, the book discusses the basics of analysis (limits, series, continuity, differentiation, Riemann integration), through to power series, several variable calculus and Fourier analysis, and then finally the Lebesgue integral. These are almost entirely set in the concrete setting of the real line and Euclidean spaces, although there is some material on abstract metric and topological spaces. The book also has appendices on mathematical logic and the decimal system. The entire text (omitting some less central topics) can be taught in two quarters of 25–30 lectures each. The course material is deeply intertwined with the exercises, as it is intended that the student actively learn the material (and practice thinking and writing rigorously) by proving several of the key results in the theory.

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  • File : Pdf, ePub, Mobi, Kindle
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  • Total of Pages : 200
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  • Pdf File: euler-s-pioneering-equation.pdf

Book Short Summary:

In 1988 The Mathematical Intelligencer, a quarterly mathematics journal, carried out a poll to find the most beautiful theorem in mathematics. Twenty-four theorems were listed and readers were invited to award each a 'score for beauty'. While there were many worthy competitors, the winner was 'Euler's equation'. In 2004 Physics World carried out a similar poll of 'greatest equations', and found that among physicists Euler's mathematical result came second only to Maxwell's equations. The Stanford mathematician Keith Devlin reflected the feelings of many in describing it as "like a Shakespearian sonnet that captures the very essence of love, or a painting which brings out the beauty of the human form that is far more than just skin deep, Euler's equation reaches down into the very depths of existence". What is it that makes Euler's identity, eiπ + 1 = 0, so special? In Euler's Pioneering Equation Robin Wilson shows how this simple, elegant, and profound formula links together perhaps the five most important numbers in mathematics, each associated with a story in themselves: the number 1, the basis of our counting system; the concept of zero, which was a major development in mathematics, and opened up the idea of negative numbers; π an irrational number, the basis for the measurement of circles; the exponential e, associated with exponential growth and logarithms; and the imaginary number i, the square root of -1, the basis of complex numbers. Following a chapter on each of the elements, Robin Wilson discusses how the startling relationship between them was established, including the several near misses to the discovery of the formula.

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  • Pdf File: fearless-symmetry.pdf

Book Short Summary:

Mathematicians solve equations, or try to. But sometimes the solutions are not as interesting as the beautiful symmetric patterns that lead to them. Written in a friendly style for a general audience, Fearless Symmetry is the first popular math book to discuss these elegant and mysterious patterns and the ingenious techniques mathematicians use to uncover them. Hidden symmetries were first discovered nearly two hundred years ago by French mathematician évariste Galois. They have been used extensively in the oldest and largest branch of mathematics--number theory--for such diverse applications as acoustics, radar, and codes and ciphers. They have also been employed in the study of Fibonacci numbers and to attack well-known problems such as Fermat's Last Theorem, Pythagorean Triples, and the ever-elusive Riemann Hypothesis. Mathematicians are still devising techniques for teasing out these mysterious patterns, and their uses are limited only by the imagination. The first popular book to address representation theory and reciprocity laws, Fearless Symmetry focuses on how mathematicians solve equations and prove theorems. It discusses rules of math and why they are just as important as those in any games one might play. The book starts with basic properties of integers and permutations and reaches current research in number theory. Along the way, it takes delightful historical and philosophical digressions. Required reading for all math buffs, the book will appeal to anyone curious about popular mathematics and its myriad contributions to everyday life.

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  • Pdf File: the-calculus-of-friendship.pdf

Book Short Summary:

The Calculus of Friendship is the story of an extraordinary connection between a teacher and a student, as chronicled through more than thirty years of letters between them. What makes their relationship unique is that it is based almost entirely on a shared love of calculus. For them, calculus is more than a branch of mathematics; it is a game they love playing together, a constant when all else is in flux. The teacher goes from the prime of his career to retirement, competes in whitewater kayaking at the international level, and loses a son. The student matures from high school math whiz to Ivy League professor, suffers the sudden death of a parent, and blunders into a marriage destined to fail. Yet through it all they take refuge in the haven of calculus--until a day comes when calculus is no longer enough. Like calculus itself, The Calculus of Friendship is an exploration of change. It's about the transformation that takes place in a student's heart, as he and his teacher reverse roles, as they age, as they are buffeted by life itself. Written by a renowned teacher and communicator of mathematics, The Calculus of Friendship is warm, intimate, and deeply moving. The most inspiring ideas of calculus, differential equations, and chaos theory are explained through metaphors, images, and anecdotes in a way that all readers will find beautiful, and even poignant. Math enthusiasts, from high school students to professionals, will delight in the offbeat problems and lucid explanations in the letters. For anyone whose life has been changed by a mentor, The Calculus of Friendship will be an unforgettable journey.

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  • Book Code : 0191519006
  • Total of Pages : 298
  • Category : Philosophy
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  • Pdf File: mathematics-as-a-science-of-patterns.pdf

Book Short Summary:

Mathematics as a Science of Patterns is the definitive exposition of a system of ideas about the nature of mathematics which Michael Resnik has been elaborating for a number of years. In calling mathematics a science he implies that it has a factual subject-matter and that mathematical knowledge is on a par with other scientific knowledge; in calling it a science of patterns he expresses his commitment to a structuralist philosophy of mathematics. He links this to a defence of realism about the metaphysics of mathematics—the view that mathematics is about things that really exist. Resnik's distinctive philosophy of mathematics is here presented in an accessible and systematic form: it will be of value not only to specialists in this area, but to philosophers, mathematicians, and logicians interested in the relationship between these three disciplines, or in truth, realism, and epistemology.

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  • Total of Pages : 358
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  • Pdf File: mathematics-and-the-historian-s-craft.pdf

Book Short Summary:

The Kenneth May Lectures have never before been published in book form Important contributions to the history of mathematics by well-known historians of science Should appeal to a wide audience due to its subject area and accessibility

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  • Category : Mathematics
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  • Pdf File: fourier-series.pdf

Book Short Summary:

Classic graduate-level text discusses the Fourier series in Hilbert space, examines further properties of trigonometrical Fourier series, and concludes with a detailed look at the applications of previously outlined theorems. 1956 edition.

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  • Book Code : 0465094821
  • Total of Pages : 304
  • Category : Mathematics
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  • Pdf File: beyond-infinity.pdf

Book Short Summary:

"[Cheng] does a great service by showing us non-mathematician schlubs how real mathematical creativity works." --Wall Street Journal How big is the universe? How many numbers are there? And is infinity + 1 is the same as 1 + infinity? Such questions occur to young children and our greatest minds. And they are all the same question: What is infinity? In Beyond Infinity, Eugenia Cheng takes us on a staggering journey from elemental math to its loftiest abstractions. Along the way, she considers how to use a chessboard to plan a worldwide dinner party, how to make a chicken-sandwich sandwich, and how to create infinite cookies from a finite ball of dough. Beyond Infinity shows how one little symbol holds the biggest idea of all.

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  • Book Code : 1400885523
  • Total of Pages : 464
  • Category : Mathematics
  • Members : 205
  • Pdf File: mathematics-without-apologies.pdf

Book Short Summary:

An insightful reflection on the mathematical soul What do pure mathematicians do, and why do they do it? Looking beyond the conventional answers—for the sake of truth, beauty, and practical applications—this book offers an eclectic panorama of the lives and values and hopes and fears of mathematicians in the twenty-first century, assembling material from a startlingly diverse assortment of scholarly, journalistic, and pop culture sources. Drawing on his personal experiences and obsessions as well as the thoughts and opinions of mathematicians from Archimedes and Omar Khayyám to such contemporary giants as Alexander Grothendieck and Robert Langlands, Michael Harris reveals the charisma and romance of mathematics as well as its darker side. In this portrait of mathematics as a community united around a set of common intellectual, ethical, and existential challenges, he touches on a wide variety of questions, such as: Are mathematicians to blame for the 2008 financial crisis? How can we talk about the ideas we were born too soon to understand? And how should you react if you are asked to explain number theory at a dinner party? Disarmingly candid, relentlessly intelligent, and richly entertaining, Mathematics without Apologies takes readers on an unapologetic guided tour of the mathematical life, from the philosophy and sociology of mathematics to its reflections in film and popular music, with detours through the mathematical and mystical traditions of Russia, India, medieval Islam, the Bronx, and beyond.

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  • Pdf File: mathematics.pdf

Book Short Summary:

To understand why mathematics exists and why it is perpetuated one must know something of its history and of the lives and results of famous mathematicians. This three-volume collection of entertaining articles will captivate those with a special interest in mathematics as well as arouse those with even the slightest curiosity about the most sophisticated sciences.

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  • Pdf File: the-world-of-mathematics.pdf

Book Short Summary:

Read and download full book The World of Mathematics

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Book Short Summary:

This reference serves as a reader-friendly guide to every basic tool and skill required in the mathematical library and helps mathematicians find resources in any format in the mathematics literature. It lists a wide range of standard texts, journals, review articles, newsgroups, and Internet and database tools for every major subfield in mathemati

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Book Short Summary:

Join a fellow traveler on a walkabout through Paris and London, and then travel with him across England, Scotland and Wales. After those walkabouts, accompany him as he journeys across America and follows the equator to Australia. Finally, wander with him along the corridors of modern and postmodern philosophy, and as he travels with old and new Philosophes, who all voiced an opinion as regards this travel book. It is a book that people won't buy, won't read and won't praise. Mark Twain After reading only a few pages, I gave up the study of philosophy forever. Voltaire I cannot look upon the book without shedding tears. Bertrand Russell If I could only make a travel book like that, I would be perfectly willing to die-even anxious. John Dewey I have seen a great many travel books in my time, but none that this one reminds me of. Will Durant This travel book is one-third fabrication, one-third prevarication and one-third barefaced lies. However, the rest of the book is the unadulterated truth. Dr. Morris A. Nussbaum

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  • Pdf File: analysis-and-probability.pdf

Book Short Summary:

Combines analysis and tools from probability, harmonic analysis, operator theory, and engineering (signal/image processing) Interdisciplinary focus with hands-on 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
  • Book Code : 9400914652
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  • Pdf File: international-handbook-of-mathematics-education.pdf

Book Short Summary:

ALAN J. BISHOP Monash University, Clayton, Victoria, Australia RATIONALE Mathematics Education is becoming a well-documented 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
  • File : Pdf, ePub, Mobi, Kindle
  • Publisher : State University of New York Press
  • Book Code : 1438419538
  • Total of Pages : 376
  • Category : Philosophy
  • Members : 925
  • Pdf File: wittgenstein-and-the-turning-point-in-the-philosophy-of-mathematics.pdf

Book Short 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 Wittgenstein’s arguments in the philosophy of mathematics. This book explains not only Wittgenstein’s 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
  • File : Pdf, ePub, Mobi, Kindle
  • Publisher : Routledge
  • Book Code : 1135698333
  • Total of Pages : 256
  • Category : Education
  • Members : 848
  • Pdf File: the-pragmatics-of-mathematics-education.pdf

Book Short 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. Teacher-student interactions in mathematics are analysed, and this provides a toolkit that teachers can use to respond to the intellectual vulnerability of their students.

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  • File : Pdf, ePub, Mobi, Kindle
  • Publisher : OUP Oxford
  • Book Code : 0191007544
  • Total of Pages : 320
  • Category : Mathematics
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  • Pdf File: mathematicians-and-their-gods.pdf

Book Short 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
  • File : Pdf, ePub, Mobi, Kindle
  • Publisher : Little, Brown
  • Book Code : 0316214698
  • Total of Pages : 336
  • Category : Literary Collections
  • Members : 218
  • Pdf File: both-flesh-and-not.pdf

Book Short Summary:

Brilliant, dazzling, never-before-collected 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
  • File : Pdf, ePub, Mobi, Kindle
  • Publisher : Springer Science & Business Media
  • Book Code : 1461469287
  • Total of Pages : 243
  • Category : Mathematics
  • Members : 927
  • Pdf File: the-reflection-of-life.pdf

Book Short 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 metabolism-repair [(M,R)-] systems. Here in the second volume, these tools are expanded to employ set-valued mappings, adjacency matrices, random graphs, and interacting entailment networks. The theory of set-valued 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
  • File : Pdf, ePub, Mobi, Kindle
  • Publisher : Psychology Press
  • Book Code : 1136945385
  • Total of Pages : 596
  • Category : Psychology
  • Members : 213
  • Pdf File: mathematical-reasoning.pdf

Book Short 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. Cavazos-Gaither
  • File : Pdf, ePub, Mobi, Kindle
  • Publisher : Springer Science & Business Media
  • Book Code : 1461411149
  • Total of Pages : 2867
  • Category : Science
  • Members : 178
  • Pdf File: gaither-s-dictionary-of-scientific-quotations.pdf

Book Short 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 high-quality 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
  • File : Pdf, ePub, Mobi, Kindle
  • Publisher : Springer Science & Business Media
  • Book Code : 1441985921
  • Total of Pages : 235
  • Category : Mathematics
  • Members : 852
  • Pdf File: a-course-in-number-theory-and-cryptography.pdf

Book Short 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.