Foolproof And Other Mathematical Meditations
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Foolproof And Other Mathematical Meditations
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Author : Brian Hayes
language : en
Publisher: MIT Press
Release Date : 2018-10-30
Foolproof And Other Mathematical Meditations written by Brian Hayes and has been published by MIT Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-10-30 with Mathematics categories.
A non-mathematician explores mathematical terrain, reporting accessibly and engagingly on topics from Sudoku to probability. Brian Hayes wants to convince us that mathematics is too important and too much fun to be left to the mathematicians. Foolproof, and Other Mathematical Meditations is his entertaining and accessible exploration of mathematical terrain both far-flung and nearby, bringing readers tidings of mathematical topics from Markov chains to Sudoku. Hayes, a non-mathematician, argues that mathematics is not only an essential tool for understanding the world but also a world unto itself, filled with objects and patterns that transcend earthly reality. In a series of essays, Hayes sets off to explore this exotic terrain, and takes the reader with him. Math has a bad reputation: dull, difficult, detached from daily life. As a talking Barbie doll opined, “Math class is tough.” But Hayes makes math seem fun. Whether he's tracing the genealogy of a well-worn anecdote about a famous mathematical prodigy, or speculating about what would happen to a lost ball in the nth dimension, or explaining that there are such things as quasirandom numbers, Hayes wants readers to share his enthusiasm. That's why he imagines a cinematic treatment of the discovery of the Riemann zeta function (“The year: 1972. The scene: Afternoon tea in Fuld Hall at the Institute for Advanced Study in Princeton, New Jersey”), explains that there is math in Sudoku after all, and describes better-than-average averages. Even when some of these essays involve a hike up the learning curve, the view from the top is worth it.
The Meaning Of Proofs
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Author : Gabriele Lolli
language : en
Publisher: MIT Press
Release Date : 2022-09-27
The Meaning Of Proofs written by Gabriele Lolli and has been published by MIT Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-09-27 with Mathematics categories.
Why mathematics is not merely formulaic: an argument that to write a mathematical proof is tantamount to inventing a story. In The Meaning of Proofs, mathematician Gabriele Lolli argues that to write a mathematical proof is tantamount to inventing a story. Lolli offers not instructions for how to write mathematical proofs, but a philosophical and poetic reflection on mathematical proofs as narrative. Mathematics, imprisoned within its symbols and images, Lolli writes, says nothing if its meaning is not narrated in a story. The minute mathematicians open their mouths to explain something—the meaning of x, how to find y—they are framing a narrative. Every proof is the story of an adventure, writes Lolli, a journey into an unknown land to open a new, connected route; once the road is open, we correct it, expand it. Just as fairy tales offer a narrative structure in which new characters can be inserted into recurring forms of the genre in original ways, in mathematics, each new abstract concept is the protagonist of a different theory supported by the general techniques of mathematical reasoning. In ancient Greece, there was more than an analogy between literature and mathematics, there was direct influence. Euclid’s proofs have roots in poetry and rhetoric. Mathematics, Lolli asserts, is not the mere manipulation of formulas.
The Raven S Hat
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Author : Jonas Peters
language : en
Publisher: MIT Press
Release Date : 2021-02-02
The Raven S Hat written by Jonas Peters and has been published by MIT Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-02-02 with Mathematics categories.
Games that show how mathematics can solve the apparently unsolvable. This book presents a series of engaging games that seem unsolvable--but can be solved when they are translated into mathematical terms. How can players find their ID cards when the cards are distributed randomly among twenty boxes? By applying the theory of permutations. How can a player guess the color of her own hat when she can only see other players' hats? Hamming codes, which are used in communication technologies. Like magic, mathematics solves the apparently unsolvable. The games allow readers, including university students or anyone with high school-level math, to experience the joy of mathematical discovery.
Fundamentals Of Mathematics
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Author :
language : en
Publisher:
Release Date : 1974
Fundamentals Of Mathematics written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1974 with Mathematics categories.
Lectures On The Philosophy Of Mathematics
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Author : Joel David Hamkins
language : en
Publisher: MIT Press
Release Date : 2021-03-09
Lectures On The Philosophy Of Mathematics written by Joel David Hamkins and has been published by MIT Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-03-09 with Mathematics categories.
An introduction to the philosophy of mathematics grounded in mathematics and motivated by mathematical inquiry and practice. In this book, Joel David Hamkins offers an introduction to the philosophy of mathematics that is grounded in mathematics and motivated by mathematical inquiry and practice. He treats philosophical issues as they arise organically in mathematics, discussing such topics as platonism, realism, logicism, structuralism, formalism, infinity, and intuitionism in mathematical contexts. He organizes the book by mathematical themes--numbers, rigor, geometry, proof, computability, incompleteness, and set theory--that give rise again and again to philosophical considerations.
Programming For The Puzzled
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Author : Srini Devadas
language : en
Publisher: MIT Press
Release Date : 2017-11-16
Programming For The Puzzled written by Srini Devadas and has been published by MIT Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-11-16 with Computers categories.
Learning programming with one of “the coolest applications around”: algorithmic puzzles ranging from scheduling selfie time to verifying the six degrees of separation hypothesis. This book builds a bridge between the recreational world of algorithmic puzzles (puzzles that can be solved by algorithms) and the pragmatic world of computer programming, teaching readers to program while solving puzzles. Few introductory students want to program for programming's sake. Puzzles are real-world applications that are attention grabbing, intriguing, and easy to describe. Each lesson starts with the description of a puzzle. After a failed attempt or two at solving the puzzle, the reader arrives at an Aha! moment—a search strategy, data structure, or mathematical fact—and the solution presents itself. The solution to the puzzle becomes the specification of the code to be written. Readers will thus know what the code is supposed to do before seeing the code itself. This represents a pedagogical philosophy that decouples understanding the functionality of the code from understanding programming language syntax and semantics. Python syntax and semantics required to understand the code are explained as needed for each puzzle. Readers need only the rudimentary grasp of programming concepts that can be obtained from introductory or AP computer science classes in high school. The book includes more than twenty puzzles and more than seventy programming exercises that vary in difficulty. Many of the puzzles are well known and have appeared in publications and on websites in many variations. They range from scheduling selfie time with celebrities to solving Sudoku problems in seconds to verifying the six degrees of separation hypothesis. The code for selected puzzle solutions is downloadable from the book's website; the code for all puzzle solutions is available to instructors.
The Best Writing On Mathematics 2019
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Author : Mircea Pitici
language : en
Publisher: Princeton University Press
Release Date : 2019-11-05
The Best Writing On Mathematics 2019 written by Mircea Pitici and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-11-05 with Crafts & Hobbies categories.
An anthology of the year's finest writing on mathematics from around the world, featuring promising new voices as well as some of the foremost names in mathematics.
The Best Writing On Mathematics 2018
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Author : Mircea Pitici
language : en
Publisher: Princeton University Press
Release Date : 2018-12-04
The Best Writing On Mathematics 2018 written by Mircea Pitici and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-12-04 with Mathematics categories.
The year’s finest mathematical writing from around the world This annual anthology brings together the year’s finest mathematics writing from around the world. Featuring promising new voices alongside some of the foremost names in the field, The Best Writing on Mathematics 2018 makes available to a wide audience many pieces not easily found anywhere else—and you don’t need to be a mathematician to enjoy them. These essays delve into the history, philosophy, teaching, and everyday aspects of math, offering surprising insights into its nature, meaning, and practice—and taking readers behind the scenes of today’s hottest mathematical debates. James Grime shows how to build subtly mischievous dice for playing slightly unfair games and Michael Barany traces how our appreciation of the societal importance of mathematics has developed since World War II. In other essays, Francis Su extolls the inherent values of learning, doing, and sharing mathematics, and Margaret Wertheim takes us on a mathematical exploration of the mind and the world—with glimpses at science, philosophy, music, art, and even crocheting. And there’s much, much more. In addition to presenting the year’s most memorable math writing, this must-have anthology includes an introduction by the editor and a bibliography of other notable pieces on mathematics. This is a must-read for anyone interested in where math has taken us—and where it is headed.
Turing S Vision
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Author : Chris Bernhardt
language : en
Publisher: MIT Press
Release Date : 2016-05-13
Turing S Vision written by Chris Bernhardt and has been published by MIT Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-05-13 with Computers categories.
In 1936, when he was just twenty-four years old, Alan Turing wrote a remarkable paper in which he outlined the theory of computation, laying out the ideas that underlie all modern computers. This groundbreaking and powerful theory now forms the basis of computer science. In Turing's Vision, Chris Bernhardt explains the theory, Turing's most important contribution, for the general reader. Bernhardt argues that the strength of Turing's theory is its simplicity, and that, explained in a straightforward manner, it is eminently understandable by the nonspecialist. As Marvin Minsky writes, "The sheer simplicity of the theory's foundation and extraordinary short path from this foundation to its logical and surprising conclusions give the theory a mathematical beauty that alone guarantees it a permanent place in computer theory." Bernhardt begins with the foundation and systematically builds to the surprising conclusions. He also views Turing's theory in the context of mathematical history, other views of computation (including those of Alonzo Church), Turing's later work, and the birth of the modern computer. In the paper, "On Computable Numbers, with an Application to the Entscheidungsproblem," Turing thinks carefully about how humans perform computation, breaking it down into a sequence of steps, and then constructs theoretical machines capable of performing each step. Turing wanted to show that there were problems that were beyond any computer's ability to solve; in particular, he wanted to find a decision problem that he could prove was undecidable. To explain Turing's ideas, Bernhardt examines three well-known decision problems to explore the concept of undecidability; investigates theoretical computing machines, including Turing machines; explains universal machines; and proves that certain problems are undecidable, including Turing's problem concerning computable numbers.
On The Brink Of Paradox
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Author : Agustin Rayo
language : en
Publisher: MIT Press
Release Date : 2019-04-02
On The Brink Of Paradox written by Agustin Rayo and has been published by MIT Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-04-02 with Mathematics categories.
An introduction to awe-inspiring ideas at the brink of paradox: infinities of different sizes, time travel, probability and measure theory, and computability theory. This book introduces the reader to awe-inspiring issues at the intersection of philosophy and mathematics. It explores ideas at the brink of paradox: infinities of different sizes, time travel, probability and measure theory, computability theory, the Grandfather Paradox, Newcomb's Problem, the Principle of Countable Additivity. The goal is to present some exceptionally beautiful ideas in enough detail to enable readers to understand the ideas themselves (rather than watered-down approximations), but without supplying so much detail that they abandon the effort. The philosophical content requires a mind attuned to subtlety; the most demanding of the mathematical ideas require familiarity with college-level mathematics or mathematical proof. The book covers Cantor's revolutionary thinking about infinity, which leads to the result that some infinities are bigger than others; time travel and free will, decision theory, probability, and the Banach-Tarski Theorem, which states that it is possible to decompose a ball into a finite number of pieces and reassemble the pieces so as to get two balls that are each the same size as the original. Its investigation of computability theory leads to a proof of Gödel's Incompleteness Theorem, which yields the amazing result that arithmetic is so complex that no computer could be programmed to output every arithmetical truth and no falsehood. Each chapter is followed by an appendix with answers to exercises. A list of recommended reading points readers to more advanced discussions. The book is based on a popular course (and MOOC) taught by the author at MIT.