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Mathematical Discovery
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Book Synopsis Mathematical Discovery on Understanding, Learning, and Teaching Problem Solving by : George Pólya
Download or read book Mathematical Discovery on Understanding, Learning, and Teaching Problem Solving written by George Pólya and published by . This book was released on 2009 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt: George Polya was a Hungarian mathematician. Born in Budapest on 13 December 1887, his original name was Polya Gyorg. He wrote perhaps the most famous book of mathematics ever written, namely "How to Solve It." However, "How to Solve It" is not strictly speaking a math book. It is a book about how to solve problems of any kind, of which math is just one type of problem. The same techniques could in principle be used to solve any problem one encounters in life (such as how to choose the best wife ). Therefore, Polya wrote the current volume to explain how the techniques set forth in "How to Solve It" can be applied to specific areas such as geometry.
Book Synopsis Proofs and Refutations by : Imre Lakatos
Download or read book Proofs and Refutations written by Imre Lakatos and published by Cambridge University Press. This book was released on 1976 with total page 190 pages. Available in PDF, EPUB and Kindle. Book excerpt: Proofs and Refutations is for those interested in the methodology, philosophy and history of mathematics.
Book Synopsis Mathematical Discovery by : Brian Thomson
Download or read book Mathematical Discovery written by Brian Thomson and published by ClassicalRealAnalysis.com. This book was released on 2011-04-28 with total page 267 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an outgrowth of classes given at the University of California, Santa Barbara, mainly for students who had little mathematical background. Many of the students indicated they never understood what mathematics was all about (beyond what they learned in algebra and geometry). Was there any more math-ematics to be discovered or created? How could one actually discover or create new mathematics? In order to give these students some sort of answers to such questions, we designed a course in which the students could actually participate in the discovery of mathematics.
Book Synopsis Experimentation in Mathematics by : Jonathan M. Borwein
Download or read book Experimentation in Mathematics written by Jonathan M. Borwein and published by CRC Press. This book was released on 2004-04-12 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: New mathematical insights and rigorous results are often gained through extensive experimentation using numerical examples or graphical images and analyzing them. Today computer experiments are an integral part of doing mathematics. This allows for a more systematic approach to conducting and replicating experiments. The authors address the role of
Book Synopsis Discovering Patterns in Mathematics and Poetry by : Marcia Birken
Download or read book Discovering Patterns in Mathematics and Poetry written by Marcia Birken and published by BRILL. This book was released on 2008-01-01 with total page 213 pages. Available in PDF, EPUB and Kindle. Book excerpt: You are invited to join a fascinating journey of discovery, as Marcia Birken and Anne C. Coon explore the intersecting patterns of mathematics and poetry — bringing the two fields together in a new way. Setting the tone with humor and illustrating each chapter with countless examples, Birken and Coon begin with patterns we can see, hear, and feel and then move to more complex patterns. Number systems and nursery rhymes lead to the Golden Mean and sestinas. Simple patterns of shape introduce tessellations and concrete poetry. Fractal geometry makes fractal poetry possible. Ultimately, patterns for the mind lead to questions: How do mathematicians and poets conceive of proof, paradox, and infinity? What role does analogy play in mathematical discovery and poetic expression? The book will be of special interest to readers who enjoy looking for connections across traditional disciplinary boundaries. Discovering Patterns in Mathematics and Poetry features centuries of creative work by mathematicians, poets, and artists, including Fibonacci, Albrecht Dürer, M. C. Escher, David Hilbert, Benoit Mandelbrot, William Shakespeare, Edna St. Vincent Millay, Langston Hughes, E.E. Cummings, and many contemporary experimental poets. Original illustrations include digital photographs, mathematical and poetic models, and fractal imagery.
Book Synopsis Discovering Mathematics by : Jiří Gregor
Download or read book Discovering Mathematics written by Jiří Gregor and published by Springer Science & Business Media. This book was released on 2010-12-21 with total page 243 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book contains chapters of structured approach to problem solving in mathematical analysis on an intermediate level. It follows the ideas of G.Polya and others, distinguishing between exercises and problem solving in mathematics. Interrelated concepts are connected by hyperlinks, pointing toward easier or more difficult problems so as to show paths of mathematical reasoning. Basic definitions and theorems can also be found by hyperlinks from relevant places. Problems are open to alternative formulations, generalizations, simplifications, and verification of hypotheses by the reader; this is shown to be helpful in solving problems. The book presents how advanced mathematical software can aid all stages of mathematical reasoning while the mathematical content remains in foreground. The authors show how software can contribute to deeper understanding and to enlarging the scope of teaching for students and teachers of mathematics.
Book Synopsis Discovering Mathematics by : A. Gardiner
Download or read book Discovering Mathematics written by A. Gardiner and published by Courier Corporation. This book was released on 2006-01-26 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: The term "mathematics" usually suggests an array of familiar problems with solutions derived from well-known techniques. Discovering Mathematics: The Art of Investigation takes a different approach, exploring how new ideas and chance observations can be pursued, and focusing on how the process invariably leads to interesting questions that would never have otherwise arisen. With puzzles involving coins, postage stamps, and other commonplace items, students are challenged to account for the simple explanations behind perplexing mathematical phenomena. Elementary methods and solutions allow readers to concentrate on the way in which the material is explored, as well as on strategies for answers that aren't immediately obvious. The problems don't require the kind of sophistication that would put them out of reach of ordinary students, but they're sufficiently complex to capture the essential features of mathematical discovery. Complete solutions appear at the end.
Book Synopsis How Not to Be Wrong by : Jordan Ellenberg
Download or read book How Not to Be Wrong written by Jordan Ellenberg and published by Penguin Press. This book was released on 2014-05-29 with total page 480 pages. Available in PDF, EPUB and Kindle. Book excerpt: A brilliant tour of mathematical thought and a guide to becoming a better thinker, How Not to Be Wrong shows that math is not just a long list of rules to be learned and carried out by rote. Math touches everything we do; It's what makes the world make sense. Using the mathematician's methods and hard-won insights-minus the jargon-professor and popular columnist Jordan Ellenberg guides general readers through his ideas with rigor and lively irreverence, infusing everything from election results to baseball to the existence of God and the psychology of slime molds with a heightened sense of clarity and wonder. Armed with the tools of mathematics, we can see the hidden structures beneath the messy and chaotic surface of our daily lives. How Not to Be Wrong shows us how--Publisher's description.
Book Synopsis Groups and Symmetry: A Guide to Discovering Mathematics by : David W. Farmer
Download or read book Groups and Symmetry: A Guide to Discovering Mathematics written by David W. Farmer and published by American Mathematical Soc.. This book was released on 1996 with total page 112 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics is discovered by looking at examples, noticing patterns, making conjectures, and testing those conjectures. Once discovered, the final results get organized and put in textbooks. The details and the excitement of the discovery are lost. This book introduces the reader to the excitement of the original discovery. By means of a wide variety of tasks, readers are led to find interesting examples, notice patterns, devise rules to explain the patterns, and discover mathematics for themselves. The subject studied here is the mathematics behind the idea of symmetry, but the methods and ideas apply to all of mathematics. The only prerequisites are enthusiasm and a knowledge of basic high-school math. The book is only a guide. It will start you off in the right direction and bring you back if you stray too far. The excitement and the discovery are left to you.
Book Synopsis The Stanford Mathematics Problem Book by : George Polya
Download or read book The Stanford Mathematics Problem Book written by George Polya and published by Courier Corporation. This book was released on 2013-04-09 with total page 82 pages. Available in PDF, EPUB and Kindle. Book excerpt: Based on Stanford University's well-known competitive exam, this excellent mathematics workbook offers students at both high school and college levels a complete set of problems, hints, and solutions. 1974 edition.
Book Synopsis What's Happening in the Mathematical Sciences by : Barry Cipra
Download or read book What's Happening in the Mathematical Sciences written by Barry Cipra and published by American Mathematical Soc.. This book was released on with total page 108 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematicians like to point out that mathematics is universal. In spite of this, most people continue to view it as either mundane (balancing a checkbook) or mysterious (cryptography). This fifth volume of the What's Happening series contradicts that view by showing that mathematics is indeed found everywhere-in science, art, history, and our everyday lives. Here is some of what you'll find in this volume: Mathematics and Science Mathematical biology: Mathematics was key tocracking the genetic code. Now, new mathematics is needed to understand the three-dimensional structure of the proteins produced from that code. Celestial mechanics and cosmology: New methods have revealed a multitude of solutions to the three-body problem. And other new work may answer one of cosmology'smost fundamental questions: What is the size and shape of the universe? Mathematics and Everyday Life Traffic jams: New models are helping researchers understand where traffic jams come from-and maybe what to do about them! Small worlds: Researchers have found a short distance from theory to applications in the study of small world networks. Elegance in Mathematics Beyond Fermat's Last Theorem: Number theorists are reaching higher ground after Wiles' astounding 1994 proof: new developments inthe elegant world of elliptic curves and modular functions. The Millennium Prize Problems: The Clay Mathematics Institute has offered a million dollars for solutions to seven important and difficult unsolved problems. These are just some of the topics of current interest that are covered in thislatest volume of What's Happening in the Mathematical Sciences. The book has broad appeal for a wide spectrum of mathematicians and scientists, from high school students through advanced-level graduates and researchers.
Book Synopsis A Mathematical Mystery Tour by : A. K. Dewdney
Download or read book A Mathematical Mystery Tour written by A. K. Dewdney and published by Wiley. This book was released on 2001-05-23 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Praise for A. K. Dewdney Yes, We Have No Neutrons "We need more books like this-especially if they're this much fun to read." -Wired "Dewdney manages to make this catalog of error entertaining as well as instructive; good medicine for both skeptics and true believers." -Kirkus Reviews "Written with wit and a touch of pathos-and sure to please science lovers." -Publishers Weekly 200% of Nothing "It is impossible to read this timely, important book without enjoyment and eye-opening enlightenment." -Martin Gardner "An entertaining, stinging exposé." -Publishers Weekly
Book Synopsis The Mathematical Experience, Study Edition by : Philip Davis
Download or read book The Mathematical Experience, Study Edition written by Philip Davis and published by Springer Science & Business Media. This book was released on 2011-10-28 with total page 522 pages. Available in PDF, EPUB and Kindle. Book excerpt: Winner of the 1983 National Book Award! "...a perfectly marvelous book about the Queen of Sciences, from which one will get a real feeling for what mathematicians do and who they are. The exposition is clear and full of wit and humor..." - The New Yorker (1983 National Book Award edition) Mathematics has been a human activity for thousands of years. Yet only a few people from the vast population of users are professional mathematicians, who create, teach, foster, and apply it in a variety of situations. The authors of this book believe that it should be possible for these professional mathematicians to explain to non-professionals what they do, what they say they are doing, and why the world should support them at it. They also believe that mathematics should be taught to non-mathematics majors in such a way as to instill an appreciation of the power and beauty of mathematics. Many people from around the world have told the authors that they have done precisely that with the first edition and they have encouraged publication of this revised edition complete with exercises for helping students to demonstrate their understanding. This edition of the book should find a new generation of general readers and students who would like to know what mathematics is all about. It will prove invaluable as a course text for a general mathematics appreciation course, one in which the student can combine an appreciation for the esthetics with some satisfying and revealing applications. The text is ideal for 1) a GE course for Liberal Arts students 2) a Capstone course for perspective teachers 3) a writing course for mathematics teachers. A wealth of customizable online course materials for the book can be obtained from Elena Anne Marchisotto ([email protected]) upon request.
Book Synopsis Pattern Discovery in Bioinformatics by : Laxmi Parida
Download or read book Pattern Discovery in Bioinformatics written by Laxmi Parida and published by CRC Press. This book was released on 2007-07-04 with total page 512 pages. Available in PDF, EPUB and Kindle. Book excerpt: The computational methods of bioinformatics are being used more and more to process the large volume of current biological data. Promoting an understanding of the underlying biology that produces this data, Pattern Discovery in Bioinformatics: Theory and Algorithms provides the tools to study regularities in biological data. Taking a systema
Book Synopsis Science and Method by : Henri Poincaré
Download or read book Science and Method written by Henri Poincaré and published by Courier Corporation. This book was released on 2003-01-01 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: Classic account of basic methodology and psychology of scientific discovery explains how scientists analyze and choose their working facts and explores the nature of experimentation, theory, and the mind. 1914 edition.
Book Synopsis The Art of Conjecturing, Together with Letter to a Friend on Sets in Court Tennis by : Jacob Bernoulli
Download or read book The Art of Conjecturing, Together with Letter to a Friend on Sets in Court Tennis written by Jacob Bernoulli and published by JHU Press. This book was released on 2006 with total page 468 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Part I reprints and reworks Huygens's On Reckoning in Games of Chance. Part II offers a thorough treatment of the mathematics of combinations and permutations, including the numbers since known as "Bernoulli numbers." In Part III, Bernoulli solves more complicated problems of games of chance using that mathematics. In the final part, Bernoulli's crowning achievement in mathematical probability becomes manifest he applies the mathematics of games of chance to the problems of epistemic probability in civil, moral, and economic matters, proving what we now know as the weak law of large numbers."
Book Synopsis A History of the Circle by : Ernest Zebrowski
Download or read book A History of the Circle written by Ernest Zebrowski and published by Rutgers University Press. This book was released on 1999 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ranging from ancient times to twentieth-century theories of time and space, looks at how exploring the circle has lead to increased knowledge about the physical universe.
