en-US Fri, 11 Nov 2022 14:00:22 -0800 60 144 41 /images/layout/goodreads_logo_144.jpg 32889394
Mathematics is one of humanity's most successful yet puzzling endeavors. It is a model of precision and objectivity, but appears distinct from the empirical sciences because it seems to deliver nonexperiential knowledge of a nonphysical reality of numbers, sets, and functions. How can these two aspects of mathematics be reconciled? This concise book provides a systematic yet accessible introduction to the field that is trying to answer that the philosophy of mathematics.

Written by Øystein Linnebo, one of the world's leading scholars on the subject, the book introduces all of the classical approaches to the field, including logicism, formalism, intuitionism, empiricism, and structuralism. It also contains accessible introductions to some more specialized issues, such as mathematical intuition, potential infinity, the iterative conception of sets, and the search for new mathematical axioms. The groundbreaking work of German mathematician and philosopher Gottlob Frege, one of the founders of analytic philosophy, figures prominently throughout the book. Other important thinkers whose work is introduced and discussed include Immanuel Kant, John Stuart Mill, David Hilbert, Kurt Gödel, W. V. Quine, Paul Benacerraf, and Hartry H. Field.

Sophisticated but clear and approachable, this is an essential introduction for all students and teachers of philosophy, as well as mathematicians and others who want to understand the foundations of mathematics.]]> 216 Øystein Linnebo 0691161402 RA 0 to-read 3.84
author: Øystein Linnebo
name: RA
average rating: 3.84
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]]> 1795589
Colin Adams’s The Knot Book is the first book to make cutting-edge research in knot theory accessible to a non-specialist audience. Starting with the simplest knots, Adams guides readers through increasingly more intricate twists and turns of knot theory, exploring problems and theorems mathematicians can now solve, as well as those that remain open. He also explores how knot theory is providing important insights in biology, chemistry, physics, and other fields. The new paperback edition has been updated to include the latest research results, and includes hundreds of illustrations of knots, as well as worked examples, exercises and problems.

With a simple piece of string, an elementary mathematical background, and The Knot Book , anyone can start learning about some of the most advanced ideas in contemporary mathematics.]]> 306 Colin Conrad Adams 0716742195 RA 4 4.04 1994
author: Colin Conrad Adams
name: RA
average rating: 4.04
book published: 1994
rating: 4
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date added: 2022/02/01
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]]> 3114618 Educational math textbook. 160 William G. Chinn 0883856182 RA 4 3.69 1966
author: William G. Chinn
name: RA
average rating: 3.69
book published: 1966
rating: 4
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date added: 2022/02/01
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This book was very illuminating for me.it�� shows how from elementary analysis the topological concepts came out.the introduction of this book clearly try to explain what Topology is and why we care about it.we care about topology because it helps us solve equations,ok not quite find a method form solving but to ensure what we are trying to find is really is there! this book argues that topological concepts allow us derive many kind of "existence theorems". Theorems like Brouwers fixed point theorem,Borsuk-Ulam theorem,Existence of roots of complex polynomials�� are all existence theorems and can be proved by the help some basic theorems. " This is not a metaphysical question becomes clear if we consider the history of famous problems of trisecting an angle and squaring the circle using only straightedge and compass". I remember the two videos about 3blue1brown about Topology and those two are also about existence of something! This book is not the first book one should read about this subject rather one should keep it besides while reading other books.the analysis are hard somewhere but it becomes easier by second reading after a while.Recommended for those who love to learn about topology(atleast read the introduction)."topology is not a branch of analysis. Instead it is a kind of geometry.it is not an advanced form of geometry such as projective or differential geometries,but rather a primitive, rudimentary form - one which underlies all geometries"
]]> 208764 338 J. Scott Carter 9810220669 RA 1 2.33 1995
author: J. Scott Carter
name: RA
average rating: 2.33
book published: 1995
rating: 1
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date added: 2022/01/31
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I was overwhelmed by the amazing drawings of this book! But unfortunately this book didn't do much for me.I found this book quite unreadable, their is no practice problem to actually solidify the topics the author is presented in each chapter, i was very excited to learn about sphere eversion in details but i counldn't understand that much,perheps i should give it a shot after some time has passed
]]> 25499274 305 Eugenia Cheng 1782830820 RA 4 3.90 2015
author: Eugenia Cheng
name: RA
average rating: 3.90
book published: 2015
rating: 4
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date added: 2021/11/15
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]]> 1484211 432 David W. Henderson 0131437488 RA 0 to-read 3.86 2004
author: David W. Henderson
name: RA
average rating: 3.86
book published: 2004
rating: 0
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date added: 2021/08/03
shelves: to-read
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]]> 599877 408 Jeffrey R. Weeks 0824707095 RA 0 4.41 1985
author: Jeffrey R. Weeks
name: RA
average rating: 4.41
book published: 1985
rating: 0
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date added: 2021/08/03
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]]> 51456682 166 Tai-Danae Bradley 0262539357 RA 0 to-read 4.44 2020
author: Tai-Danae Bradley
name: RA
average rating: 4.44
book published: 2020
rating: 0
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date added: 2021/08/03
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]]> 211199 80 John Milnor 0691048339 RA 0 to-read 4.53 1997
author: John Milnor
name: RA
average rating: 4.53
book published: 1997
rating: 0
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date added: 2021/08/03
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]]> 35535406 'This is the book I wish I could have written but am very glad I've read' Jim Al-Khalili

‘I think I can safely say that nobody understands quantum mechanics.��
Richard Feynman wrote this in 1965 �� the year he was awarded the Nobel prize in physics for his work on quantum mechanics.

Quantum physics is regarded as one of the most obscure and impenetrable subjects in all of science. But when Feynman said he didn’t understand quantum mechanics, he didn’t mean that he couldn’t do it �� he meant that’s all he could do. He didn’t understand what the maths was saying: what quantum mechanics tells us about reality.

Over the past decade or so, the enigma of quantum mechanics has come into sharper focus. We now realise that quantum mechanics is less about particles and waves, uncertainty and fuzziness, than a theory about information: about what can be known and how.

This is more disturbing than our bad habit of describing the quantum world as ‘things behaving weirdly�� suggests. It calls into question the meanings and limits of space and time, cause and effect, and knowledge itself.

The quantum world isn’t a different world: it is our world, and if anything deserves to be called ‘weird��, it’s us. This exhilarating book is about what quantum maths really means �� and what it ��DZ����’t mean.]]> 384 Philip Ball 1847924573 RA 0 to-read 4.04 2018
author: Philip Ball
name: RA
average rating: 4.04
book published: 2018
rating: 0
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date added: 2021/03/09
shelves: to-read
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]]> 12043542 236 Sue E. Goodman 0821847961 RA 5 5.00 2004
author: Sue E. Goodman
name: RA
average rating: 5.00
book published: 2004
rating: 5
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date added: 2021/03/09
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]]> 155777 432 Morris W. Hirsch 0123497035 RA 0 to-read 3.68 2003
author: Morris W. Hirsch
name: RA
average rating: 3.68
book published: 2003
rating: 0
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]]> 51456721
This book offers an introduction to the art and craft of proof-writing. The author, a leading research mathematician, presents a series of engaging and compelling mathematical statements with interesting elementary proofs. These proofs capture a wide range of topics, including number theory, combinatorics, graph theory, the theory of games, geometry, infinity, order theory, and real analysis. The goal is to show students and aspiring mathematicians how to write proofs with elegance and precision.]]> 240 Joel David Hamkins 0262539799 RA 0 to-read 4.36
author: Joel David Hamkins
name: RA
average rating: 4.36
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date added: 2020/06/10
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]]> 2238557 272 Stan Wagon 0521457041 RA 0 to-read 4.50 1985
author: Stan Wagon
name: RA
average rating: 4.50
book published: 1985
rating: 0
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date added: 2020/05/22
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]]> 695429 Principia Mathematica and Related Systems." This revolutionary paper challenged certain basic assumptions underlying much research in mathematics and logic. Gödel received public recognition of his work in 1951 when he was awarded the first Albert Einstein Award for achievement in the natural sciences--perhaps the highest award of its kind in the United States. The award committee described his work in mathematical logic as "one of the greatest contributions to the sciences in recent times."

However, few mathematicians of the time were equipped to understand the young scholar's complex proof. Ernest Nagel and James Newman provide a readable and accessible explanation to both scholars and non-specialists of the main ideas and broad implications of Gödel's discovery. It offers every educated person with a taste for logic and philosophy the chance to understand a previously difficult and inaccessible subject.

New York University Press is proud to publish this special edition of one of its bestselling books. With a new introduction by Douglas R. Hofstadter, this book will appeal to students, scholars, and professionals in the fields of mathematics, computer science, logic and philosophy, and science.]]> 125 Ernest Nagel 0814758169 RA 5 4.18 1958
author: Ernest Nagel
name: RA
average rating: 4.18
book published: 1958
rating: 5
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date added: 2020/05/20
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]]> 38820046 In Sapiens, he explored our past. In Homo Deus, he looked to our future. Now, one of the most innovative thinkers on the planet turns to the present to make sense of today's most pressing issues.

How do computers and robots change the meaning of being human? How do we deal with the epidemic of fake news? Are nations and religions still relevant? What should we teach our children?

Yuval Noah Harari's 21 Lessons for the 21st Century is a probing and visionary investigation into today's most urgent issues as we move into the uncharted territory of the future. As technology advances faster than our understanding of it, hacking becomes a tactic of war, and the world feels more polarized than ever, Harari addresses the challenge of navigating life in the face of constant and disorienting change and raises the important questions we need to ask ourselves in order to survive.

In twenty-one accessible chapters that are both provocative and profound, Harari builds on the ideas explored in his previous books, untangling political, technological, social, and existential issues and offering advice on how to prepare for a very different future from the world we now live in: How can we retain freedom of choice when Big Data is watching us? What will the future workforce look like, and how should we ready ourselves for it? How should we deal with the threat of terrorism? Why is liberal democracy in crisis?

Harari's unique ability to make sense of where we have come from and where we are going has captured the imaginations of millions of readers. Here he invites us to consider values, meaning, and personal engagement in a world full of noise and uncertainty. When we are deluged with irrelevant information, clarity is power. Presenting complex contemporary challenges clearly and accessibly, 21 Lessons for the 21st Century is essential reading.]]> 372 Yuval Noah Harari 0525512179 RA 3 to-read 4.15 2018
author: Yuval Noah Harari
name: RA
average rating: 4.15
book published: 2018
rating: 3
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date added: 2020/05/14
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]]> 22529392 “A delightful meta-biography--playful indeed--of a brilliant iconoclast.�� --James Gleick, author of The Information

John Horton Conway is a singular mathematician with a lovely loopy brain. He is Archimedes, Mick Jagger, Salvador Dali, and Richard Feynman all rolled into one--he boasts a rock star’s charisma, a slyly bent sense of humor, a polymath’s promiscuous curiosity, and an insatiable compulsion to explain everything about the world to everyone in it. At Cambridge, Conway wrestled with "Monstrous Moonshine," discovered the aptly named surreal numbers, and invented the cult classic Game of Life--more than just a cool fad, Life demonstrates how simplicity generates complexity and provides an analogy for mathematics and the entire universe. As a "mathemagician" at Princeton, he used ropes, dice, pennies, coat hangers, even the occasional Slinky, as props to extend his winning imagination and share his many nerdish delights. He granted Roberts full access to his idiosyncrasies and intellect both, though not without the occasional "Oh hell," he’d say. "You’re not going to put that in the book. Are you?!?"]]> 480 Siobhan Roberts 1620405938 RA 4 3.94 2015
author: Siobhan Roberts
name: RA
average rating: 3.94
book published: 2015
rating: 4
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date added: 2020/05/14
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]]> 433439

The Second Edition of this fundamental textbook maintains the book's tradition of clear, thought-provoking instruction. Readers are provided once again with an instructive mix of mathematics, physics, statistics, and information theory.

All the essential topics in information theory are covered in detail, including entropy, data compression, channel capacity, rate distortion, network information theory, and hypothesis testing. The authors provide readers with a solid understanding of the underlying theory and applications. Problem sets and a telegraphic summary at the end of each chapter further assist readers. The historical notes that follow each chapter recap the main points.

The Second Edition features:
* Chapters reorganized to improve teaching
* 200 new problems
* New material on source coding, portfolio theory, and feedback capacity
* Updated references

Now current and enhanced, the Second Edition of Elements of Information Theory remains the ideal textbook for upper-level undergraduate and graduate courses in electrical engineering, statistics, and telecommunications.]]> 784 Thomas M. Cover 0471241954 RA 3 4.22 1991
author: Thomas M. Cover
name: RA
average rating: 4.22
book published: 1991
rating: 3
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date added: 2020/03/27
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]]> 661828 304 Michael H. Albert 1568812779 RA 3 4.19 2007
author: Michael H. Albert
name: RA
average rating: 4.19
book published: 2007
rating: 3
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date added: 2020/03/27
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]]> 50991527 87 Tsugumi Ohba RA 3 3.94 2020
author: Tsugumi Ohba
name: RA
average rating: 3.94
book published: 2020
rating: 3
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date added: 2020/02/27
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]]> 24113 777 Douglas R. Hofstadter 0465026567 RA 5 4.29 1979
author: Douglas R. Hofstadter
name: RA
average rating: 4.29
book published: 1979
rating: 5
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date added: 2020/01/05
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]]> 36204378
"Correlation is not causation." This mantra, chanted by scientists for more than a century, has led to a virtual prohibition on causal talk. Today, that taboo is dead. The causal revolution, instigated by Judea Pearl and his colleagues, has cut through a century of confusion and established causality -- the study of cause and effect -- on a firm scientific basis. His work explains how we can know easy things, like whether it was rain or a sprinkler that made a sidewalk wet; and how to answer hard questions, like whether a drug cured an illness. Pearl's work enables us to know not just whether one thing causes another: it lets us explore the world that is and the worlds that could have been. It shows us the essence of human thought and key to artificial intelligence. Anyone who wants to understand either needs The Book of Why .]]> 432 Judea Pearl 046509760X RA 4 3.93 2018
author: Judea Pearl
name: RA
average rating: 3.93
book published: 2018
rating: 4
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date added: 2019/08/09
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]]> 117047 ***30th Anniversary Edition***

Cover note: Each copy of the anniversary edition of The Blind Watchmaker features a unique biomorph. No two covers are exactly alike.

Acclaimed as the most influential work on evolution written in the last hundred years, The Blind Watchmaker offers an inspiring and accessible introduction to one of the most important scientific discoveries of all time. A brilliant and controversial book which demonstrates that evolution by natural selection - the unconscious, automatic, blind yet essentially non-random process discovered by Darwin - is the only answer to the biggest question of all: why do we exist?]]> 466 Richard Dawkins 0141026162 RA 4 4.09 1986
author: Richard Dawkins
name: RA
average rating: 4.09
book published: 1986
rating: 4
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]]> 5597902 Complexity: A Guided Tour--winner of the 2010 Phi Beta Kappa Book Award in Science--offers a wide-ranging overview of the ideas underlying complex systems science, the current research at the forefront of this field, and the prospects for its contribution to solving some of the most important scientific questions of our time.
]]> 368 Melanie Mitchell 0195124413 RA 4 4.11 2009
author: Melanie Mitchell
name: RA
average rating: 4.11
book published: 2009
rating: 4
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date added: 2019/07/10
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]]> 249849
Chaitin’s revolutionary discovery, the Omega number, is an exquisitely complex representation of unknowability in mathematics. His investigations shed light on what we can ultimately know about the universe and the very nature of life. In an infectious and enthusiastic narrative, Chaitin delineates the specific intellectual and intuitive steps he took toward the discovery. He takes us to the very frontiers of scientific thinking, and helps us to appreciate the art—and the sheer beauty—in the science of math.]]> 240 Gregory Chaitin 1400077974 RA 3 3.71 2005
author: Gregory Chaitin
name: RA
average rating: 3.71
book published: 2005
rating: 3
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date added: 2019/06/26
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]]> 13151411 ��
For years it has been received wisdom among most scientists that, just as Darwin claimed, all of the Earth’s life-forms evolved by blind chance. But does Darwin’s theory function on a purely mathematical level? Has there been enough time for evolution to produce the remarkable biological diversity we see around us? It’s a question no one has yet answered—in fact, no one has even attempted to answer it until now.
��
In this illuminating and provocative book, Gregory Chaitin argues that we can’t be sure evolution makes sense without a mathematical theory. He elucidates the mathematical scheme he’s developed that can explain life itself, and examines the works of mathematical pioneers John von Neumann and Alan Turing through the lens of biology. Chaitin presents an accessible introduction to metabiology, a new way of thinking about biological science that highlights the mathematical structures underpinning the biological world. Fascinating and thought-provoking, Proving Darwin makes clear how biology may have found its greatest ally in mathematics.]]> 144 Gregory Chaitin 0375423141 RA 3 2.79 2012
author: Gregory Chaitin
name: RA
average rating: 2.79
book published: 2012
rating: 3
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date added: 2019/06/13
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]]>