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 : 52. 77 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.

The Stanford Mathematics Problem Book

Author : G. Polya
ISBN : 9780486318325
Genre : Mathematics
File Size : 76. 16 MB
Format : PDF
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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.

Software Design For Engineers And Scientists

Author : John Allen Robinson
ISBN : 0080474403
Genre : Computers
File Size : 51. 60 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

Rethinking Logic Logic In Relation To Mathematics Evolution And Method

Author : Carlo Cellucci
ISBN : 9789400760912
Genre : Philosophy
File Size : 70. 67 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.

Model Based Reasoning In Science And Technology

Author : Lorenzo Magnani
ISBN : 9783319389837
Genre : Philosophy
File Size : 57. 97 MB
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This book discusses how scientific and other types of cognition make use of models, abduction, and explanatory reasoning in order to produce important or creative changes in theories and concepts. It includes revised contributions presented during the international conference on Model-Based Reasoning (MBR’015), held on June 25-27 in Sestri Levante, Italy. The book is divided into three main parts, the first of which focuses on models, reasoning and representation. It highlights key theoretical concepts from an applied perspective, addressing issues concerning information visualization, experimental methods and design. The second part goes a step further, examining abduction, problem solving and reasoning. The respective contributions analyze different types of reasoning, discussing various concepts of inference and creativity and their relationship with experimental data. In turn, the third part reports on a number of historical, epistemological and technological issues. By analyzing possible contradictions in modern research and describing representative case studies in experimental research, this part aims at fostering new discussions and stimulating new ideas. All in all, the book provides researchers and graduate students in the field of applied philosophy, epistemology, cognitive science and artificial intelligence alike with an authoritative snapshot of current theories and applications of model-based reasoning.

Theories Of Mathematics Education

Author : Bharath Sriraman
ISBN : 9783642007422
Genre : Education
File Size : 46. 85 MB
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Advances in Mathematics Education is a new and innovative book series published by Springer that builds on the success and the rich history of ZDM—The Inter- tional Journal on Mathematics Education (formerly known as Zentralblatt für - daktik der Mathematik). One characteristic of ZDM since its inception in 1969 has been the publication of themed issues that aim to bring the state-of-the-art on c- tral sub-domains within mathematics education. The published issues include a rich variety of topics and contributions that continue to be of relevance today. The newly established monograph series aims to integrate, synthesize and extend papers from previously published themed issues of importance today, by orienting these issues towards the future state of the art. The main idea is to move the ?eld forward with a book series that looks to the future by building on the past by carefully choosing viable ideas that can fruitfully mutate and inspire the next generations. Taking ins- ration from Henri Poincaré (1854–1912), who said “To create consists precisely in not making useless combinations and in making those which are useful and which are only a small minority.

Proofs From The Book

Author : Martin Aigner
ISBN : 9783662442050
Genre : Mathematics
File Size : 20. 14 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.

Handbook Of Writing For The Mathematical Sciences

Author : Nicholas J. Higham
ISBN : 0898719550
Genre : Mathematics
File Size : 44. 87 MB
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This handy volume, enlivened by anecdotes, unusual paper titles, and humorous quotations, provides even more information on the issues you will face when writing a technical paper or talk, from choosing the right journal in which to publish to handling your references. Its overview of the entire publication process is invaluable for anyone hoping to publish in a technical journal.

Concepts Of Modern Mathematics

Author : Ian Stewart
ISBN : 9780486134956
Genre : Mathematics
File Size : 65. 74 MB
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In this charming volume, a noted English mathematician uses humor and anecdote to illuminate the concepts of groups, sets, subsets, topology, Boolean algebra, and other mathematical subjects. 200 illustrations.

Technology For Creativity And Innovation Tools Techniques And Applications

Author : Mesquita, Anabela
ISBN : 9781609605209
Genre : Technology & Engineering
File Size : 65. 23 MB
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"This book provides empirical research findings and best practices on creativity and innovation in business, organizational, and social environments"--Provided by publisher.

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