how to solve it a new aspect of mathematical method penguin science

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How To Solve It

Author : G. Polya
ISBN : 9780691119663
Genre : Mathematics
File Size : 87. 79 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.

Software Design For Engineers And Scientists

Author : John Allen Robinson
ISBN : 0080474403
Genre : Computers
File Size : 73. 52 MB
Format : PDF
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Software Design for Engineers and Scientists integrates three core areas of computing: . Software engineering - including both traditional methods and the insights of 'extreme programming' . Program design - including the analysis of data structures and algorithms . Practical object-oriented programming Without assuming prior knowledge of any particular programming language, and avoiding the need for students to learn from separate, specialised Computer Science texts, John Robinson takes the reader from small-scale programing to competence in large software projects, all within one volume. Copious examples and case studies are provided in C++. The book is especially suitable for undergraduates in the natural sciences and all branches of engineering who have some knowledge of computing basics, and now need to understand and apply software design to tasks like data analysis, simulation, signal processing or visualisation. John Robinson introduces both software theory and its application to problem solving using a range of design principles, applied to the creation of medium-sized systems, providing key methods and tools for designing reliable, efficient, maintainable programs. The case studies are presented within scientific contexts to illustrate all aspects of the design process, allowing students to relate theory to real-world applications. Core computing topics - usually found in separate specialised texts - presented to meet the specific requirements of science and engineering students Demonstrates good practice through applications, case studies and worked examples based in real-world contexts

The Stanford Mathematics Problem Book

Author : George Polya
ISBN : 9780486318325
Genre : Mathematics
File Size : 44. 22 MB
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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.

Discourse On Method And Related Writings

Author : Rene Descartes
ISBN : 9781101160503
Genre : Philosophy
File Size : 33. 70 MB
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"It is not enough to have a good mind; it is more important to use it well" René Descartes was a central figure in the scientific revolution of the seventeenth century. In his Discourse on Method he outlined the contrast between mathematics and experimental sciences, and the extent to which each one can achieve certainty. Drawing on his own work in geometry, optics, astronomy and physiology, Descartes developed the hypothetical method that characterizes modern science, and this soon came to replace the traditional techniques derived from Aristotle. Many of Descartes’ most radical ideas—such as the disparity between our perceptions and the realities that cause them—have been highly influential in the development of modern philosophy. This edition sets the Discourse on Method in the wider context of Descartes’ work, with the Rules for Guiding One’s Intelligence in Searching for the Truth (1628), extracts from The World (1633) and selected letters from 1636-9. A companion volume, Meditations and Other Metaphysical Writings, is also published in Penguin Classics.

Proofs From The Book

Author : Martin Aigner
ISBN : 9783662442050
Genre : Mathematics
File Size : 83. 62 MB
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This revised and enlarged fifth edition features four new chapters, which contain highly original and delightful proofs for classics such as the spectral theorem from linear algebra, some more recent jewels like the non-existence of the Borromean rings and other surprises. From the Reviews "... Inside PFTB (Proofs from The Book) is indeed a glimpse of mathematical heaven, where clever insights and beautiful ideas combine in astonishing and glorious ways. There is vast wealth within its pages, one gem after another. ... Aigner and Ziegler... write: "... all we offer is the examples that we have selected, hoping that our readers will share our enthusiasm about brilliant ideas, clever insights and wonderful observations." I do. ... " Notices of the AMS, August 1999 "... This book is a pleasure to hold and to look at: ample margins, nice photos, instructive pictures and beautiful drawings ... It is a pleasure to read as well: the style is clear and entertaining, the level is close to elementary, the necessary background is given separately and the proofs are brilliant. ..." LMS Newsletter, January 1999 "Martin Aigner and Günter Ziegler succeeded admirably in putting together a broad collection of theorems and their proofs that would undoubtedly be in the Book of Erdös. The theorems are so fundamental, their proofs so elegant and the remaining open questio ns so intriguing that every mathematician, regardless of speciality, can benefit from reading this book. ... " SIGACT News, December 2011.

The Penguin Dictionary Of Curious And Interesting Numbers

Author : David Wells
ISBN : 0140261494
Genre : Mathematics
File Size : 67. 62 MB
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Provides information on numbers and what makes particular ones noteworthy

Rethinking Logic Logic In Relation To Mathematics Evolution And Method

Author : Carlo Cellucci
ISBN : 9789400760912
Genre : Philosophy
File Size : 43. 27 MB
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This volume examines the limitations of mathematical logic and proposes a new approach to logic intended to overcome them. To this end, the book compares mathematical logic with earlier views of logic, both in the ancient and in the modern age, including those of Plato, Aristotle, Bacon, Descartes, Leibniz, and Kant. From the comparison it is apparent that a basic limitation of mathematical logic is that it narrows down the scope of logic confining it to the study of deduction, without providing tools for discovering anything new. As a result, mathematical logic has had little impact on scientific practice. Therefore, this volume proposes a view of logic according to which logic is intended, first of all, to provide rules of discovery, that is, non-deductive rules for finding hypotheses to solve problems. This is essential if logic is to play any relevant role in mathematics, science and even philosophy. To comply with this view of logic, this volume formulates several rules of discovery, such as induction, analogy, generalization, specialization, metaphor, metonymy, definition, and diagrams. A logic based on such rules is basically a logic of discovery, and involves a new view of the relation of logic to evolution, language, reason, method and knowledge, particularly mathematical knowledge. It also involves a new view of the relation of philosophy to knowledge. This book puts forward such new views, trying to open again many doors that the founding fathers of mathematical logic had closed historically.

Proofs And Refutations

Author : Imre Lakatos
ISBN : 9781316425336
Genre : Science
File Size : 85. 43 MB
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Imre Lakatos's Proofs and Refutations is an enduring classic, which has never lost its relevance. Taking the form of a dialogue between a teacher and some students, the book considers various solutions to mathematical problems and, in the process, raises important questions about the nature of mathematical discovery and methodology. Lakatos shows that mathematics grows through a process of improvement by attempts at proofs and critiques of these attempts, and his work continues to inspire mathematicians and philosophers aspiring to develop a philosophy of mathematics that accounts for both the static and the dynamic complexity of mathematical practice. With a specially commissioned Preface written by Paolo Mancosu, this book has been revived for a new generation of readers.

How Not To Be Wrong

Author : Jordan Ellenberg
ISBN : 9780698163843
Genre : Mathematics
File Size : 49. 83 MB
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The Freakonomics of math—a math-world superstar unveils the hidden beauty and logic of the world and puts its power in our hands The math we learn in school can seem like a dull set of rules, laid down by the ancients and not to be questioned. In How Not to Be Wrong, Jordan Ellenberg shows us how terribly limiting this view is: Math isn’t confined to abstract incidents that never occur in real life, but rather touches everything we do—the whole world is shot through with it. Math allows us to see the hidden structures underneath the messy and chaotic surface of our world. It’s a science of not being wrong, hammered out by centuries of hard work and argument. Armed with the tools of mathematics, we can see through to the true meaning of information we take for granted: How early should you get to the airport? What does “public opinion” really represent? Why do tall parents have shorter children? Who really won Florida in 2000? And how likely are you, really, to develop cancer? How Not to Be Wrong presents the surprising revelations behind all of these questions and many more, using the mathematician’s method of analyzing life and exposing the hard-won insights of the academic community to the layman—minus the jargon. Ellenberg chases mathematical threads through a vast range of time and space, from the everyday to the cosmic, encountering, among other things, baseball, Reaganomics, daring lottery schemes, Voltaire, the replicability crisis in psychology, Italian Renaissance painting, artificial languages, the development of non-Euclidean geometry, the coming obesity apocalypse, Antonin Scalia’s views on crime and punishment, the psychology of slime molds, what Facebook can and can’t figure out about you, and the existence of God. Ellenberg pulls from history as well as from the latest theoretical developments to provide those not trained in math with the knowledge they need. Math, as Ellenberg says, is “an atomic-powered prosthesis that you attach to your common sense, vastly multiplying its reach and strength.” With the tools of mathematics in hand, you can understand the world in a deeper, more meaningful way. How Not to Be Wrong will show you how.

A Mind For Numbers

Author : Barbara A. Oakley
ISBN : 9780399165245
Genre : Business & Economics
File Size : 68. 54 MB
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An engineering professor who started out doing poorly in mathematical and technical subjects in school offers tools, tips and techniques to learning the creative and analytical thought processes that will lead to achievement in math and science. Original.

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