How To Solve It A New Aspect Of Mathematical Method Princeton Science Library

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How To Solve It

Author : G. Polya
ISBN : 9780691119663
Genre : Mathematics
File Size : 41.81 MB
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Outlines a method of solving mathematical problems for teachers and students based upon the four steps of understanding the problem, devising a plan, carrying out the plan, and checking the results.
Category: Mathematics

Exploring Continued Fractions From The Integers To Solar Eclipses

Author : Andrew J. Simoson
ISBN : 9781470447953
Genre : Continued fractions
File Size : 57.63 MB
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There is a nineteen-year recurrence in the apparent position of the sun and moon against the background of the stars, a pattern observed long ago by the Babylonians. In the course of those nineteen years the Earth experiences 235 lunar cycles. Suppose we calculate the ratio of Earth's period about the sun to the moon's period about Earth. That ratio has 235/19 as one of its early continued fraction convergents, which explains the apparent periodicity. Exploring Continued Fractions explains this and other recurrent phenomena—astronomical transits and conjunctions, lifecycles of cicadas, eclipses—by way of continued fraction expansions. The deeper purpose is to find patterns, solve puzzles, and discover some appealing number theory. The reader will explore several algorithms for computing continued fractions, including some new to the literature. He or she will also explore the surprisingly large portion of number theory connected to continued fractions: Pythagorean triples, Diophantine equations, the Stern-Brocot tree, and a number of combinatorial sequences. The book features a pleasantly discursive style with excursions into music (The Well-Tempered Clavier), history (the Ishango bone and Plimpton 322), classics (the shape of More's Utopia) and whimsy (dropping a black hole on Earth's surface). Andy Simoson has won both the Chauvenet Prize and Pólya Award for expository writing from the MAA and his Voltaire's Riddle was a Choice magazine Outstanding Academic Title. This book is an enjoyable ramble through some beautiful mathematics. For most of the journey the only necessary prerequisites are a minimal familiarity with mathematical reasoning and a sense of fun.
Category: Continued fractions

Teaching Philosophy

Author : Andrea Kenkmann
ISBN : 9781441100771
Genre : Philosophy
File Size : 45.24 MB
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In the current academic climate, teaching is often seen as secondary to research. Teaching Philosophy seeks to bring teaching philosophy higher on the academic agenda. An international team of contributors, all of whom share the view that philosophy is a subject that can transform students, offers practical guidance and advice for teachers of philosophy. The book suggests ways in which the teaching of philosophy at undergraduate level might be facilitated. Some of the essays place the emphasis on individual self discovery, others focus on the wider political context, many offer practical ideas for enhancing the teaching of philosophy through exercises that engage students in often unconventional ways. The integration of students' views on teaching provides a necessary reminder that teaching is not a one-way process, but a project that will ultimately succeed through cooperation and a shared sense of achievement amongst participants. This thoughtful and important book emphasises the responsibility of the philosophy teacher towards his or her students and to society in general.
Category: Philosophy

Invitation To Real Analysis

Author : César Ernesto Silva
ISBN : 9781470449285
Genre : Education
File Size : 67.41 MB
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Preliminaries: Sets, functions and induction; The real numbers and the completeness property; Sequences; Topology of the real numbers and metric spaces; Continuous functions; Differentiable functions; Integration; Series; Sequences and series of functions; Solutions to questions; Bibliographical notes; Bibliography; Index.
Category: Education

Teaching Mathematical Modelling Connecting To Research And Practice

Author : Gloria Ann Stillman
ISBN : 9789400765405
Genre : Education
File Size : 88.23 MB
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This book provides readers with an overview of recent international research and developments in the teaching and learning of modelling and applications from a variety of theoretical and practical perspectives. There is a strong focus on pedagogical issues for teaching and learning of modelling as well as research into teaching and practice. The teaching of applications of mathematics and mathematical modelling from the early years through primary and secondary school and at tertiary level is rising in prominence in many parts of the world commensurate with an ever-increasing usage of mathematics in business, the environment, industry and everyday life. The authors are all members of the International Community of Teachers of Mathematical Modelling and Applications and important researchers in mathematics education and mathematics. The book will be of interest to teachers, practitioners and researchers in universities, polytechnics, teacher education, curriculum and policy.​
Category: Education

Mathematics And Plausible Reasoning Induction And Analogy In Mathematics

Author : G. Polya
ISBN : 0691025096
Genre : Mathematics
File Size : 75.12 MB
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Here the author of How to Solve It explains how to become a "good guesser." Marked by G. Polya's simple, energetic prose and use of clever examples from a wide range of human activities, this two-volume work explores techniques of guessing, inductive reasoning, and reasoning by analogy, and the role they play in the most rigorous of deductive disciplines.
Category: Mathematics

Rigor And Structure

Author : John P. Burgess
ISBN : 9780191033605
Genre : Philosophy
File Size : 36.57 MB
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While we are commonly told that the distinctive method of mathematics is rigorous proof, and that the special topic of mathematics is abstract structure, there has been no agreement among mathematicians, logicians, or philosophers as to just what either of these assertions means. John P. Burgess clarifies the nature of mathematical rigor and of mathematical structure, and above all of the relation between the two, taking into account some of the latest developments in mathematics, including the rise of experimental mathematics on the one hand and computerized formal proofs on the other hand. The main theses of Rigor and Structure are that the features of mathematical practice that a large group of philosophers of mathematics, the structuralists, have attributed to the peculiar nature of mathematical objects are better explained in a different way, as artefacts of the manner in which the ancient ideal of rigor is realized in modern mathematics. Notably, the mathematician must be very careful in deriving new results from the previous literature, but may remain largely indifferent to just how the results in the previous literature were obtained from first principles. Indeed, the working mathematician may remain largely indifferent to just what the first principles are supposed to be, and whether they are set-theoretic or category-theoretic or something else. Along the way to these conclusions, a great many historical developments in mathematics, philosophy, and logic are surveyed. Yet very little in the way of background knowledge on the part of the reader is presupposed.
Category: Philosophy

Mathematical Reviews

Author :
ISBN : UOM:39015067268402
Genre : Mathematics
File Size : 53.23 MB
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Category: Mathematics

Mathematics And Plausible Reasoning

Author : George Pólya
ISBN : 0691080054
Genre : Logic, Symbolic and mathematical
File Size : 39.7 MB
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"Here the author of How to Solve It explains how to become a "good guesser." Marked by G. Polya's simple, energetic prose and use of clever examples from a wide range of human activities, this two-volume work explores techniques of guessing, inductive reasoning, and reasoning by analogy, and the role they play in the most rigorous of deductive disciplines."--Book cover.
Category: Logic, Symbolic and mathematical

Isoperimetric Inequalities In Mathematical Physics

Author : György Pólya
ISBN : 0691079889
Genre : Mathematics
File Size : 23.19 MB
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The description for this book, Isoperimetric Inequalities in Mathematical Physics. (AM-27), Volume 27, will be forthcoming.
Category: Mathematics

Library Journal

Author :
ISBN : UOM:39015082964266
Genre : Libraries
File Size : 64.69 MB
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Includes, beginning Sept. 15, 1954 (and on the 15th of each month, Sept.-May) a special section: School library journal, ISSN 0000-0035, (called Junior libraries, 1954-May 1961). Also issued separately.
Category: Libraries

Library Of Congress Catalog

Author : Library of Congress
ISBN : MINN:31951001977098U
Genre : Subject catalogs
File Size : 72.83 MB
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Beginning with 1953, entries for Motion pictures and filmstrips, Music and phonorecords form separate parts of the Library of Congress catalogue. Entries for Maps and atlases were issued separately 1953-1955.
Category: Subject catalogs

The Mathematical Century

Author : Piergiorgio Odifreddi
ISBN : 0691128057
Genre : Mathematics
File Size : 37.38 MB
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The twentieth century was a time of unprecedented development in mathematics, as well as in all sciences: more theorems were proved and results found in a hundred years than in all of previous history. In The Mathematical Century, Piergiorgio Odifreddi distills this unwieldy mass of knowledge into a fascinating and authoritative overview of the subject. He concentrates on thirty highlights of pure and applied mathematics. Each tells the story of an exciting problem, from its historical origins to its modern solution, in lively prose free of technical details. Odifreddi opens by discussing the four main philosophical foundations of mathematics of the nineteenth century and ends by describing the four most important open mathematical problems of the twenty-first century. In presenting the thirty problems at the heart of the book he devotes equal attention to pure and applied mathematics, with applications ranging from physics and computer science to biology and economics. Special attention is dedicated to the famous "23 problems" outlined by David Hilbert in his address to the International Congress of Mathematicians in 1900 as a research program for the new century, and to the work of the winners of the Fields Medal, the equivalent of a Nobel prize in mathematics. This eminently readable book will be treasured not only by students and their teachers but also by all those who seek to make sense of the elusive macrocosm of twentieth-century mathematics.
Category: Mathematics