The Making Of Mathematics
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The Making Of Mathematics
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Author : Carlo Cellucci
language : en
Publisher: Springer Nature
Release Date : 2022-03-07
The Making Of Mathematics written by Carlo Cellucci and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-03-07 with Mathematics categories.
This book offers an alternative to current philosophy of mathematics: heuristic philosophy of mathematics. In accordance with the heuristic approach, the philosophy of mathematics must concern itself with the making of mathematics and in particular with mathematical discovery. In the past century, mainstream philosophy of mathematics has claimed that the philosophy of mathematics cannot concern itself with the making of mathematics but only with finished mathematics, namely mathematics as presented in published works. On this basis, mainstream philosophy of mathematics has maintained that mathematics is theorem proving by the axiomatic method. This view has turned out to be untenable because of Gödel’s incompleteness theorems, which have shown that the view that mathematics is theorem proving by the axiomatic method does not account for a large number of basic features of mathematics. By using the heuristic approach, this book argues that mathematics is not theorem proving by the axiomatic method, but is rather problem solving by the analytic method. The author argues that this view can account for the main items of the mathematical process, those being: mathematical objects, demonstrations, definitions, diagrams, notations, explanations, applicability, beauty, and the role of mathematical knowledge.
The Making Of Mathematics
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Author : Peter C. Brinkworth
language : en
Publisher:
Release Date : 1994
The Making Of Mathematics written by Peter C. Brinkworth and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with Mathematics categories.
Mathematics And The Real World
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Author : Zvi Artstein
language : en
Publisher: Prometheus Books
Release Date : 2014-09-02
Mathematics And The Real World written by Zvi Artstein and has been published by Prometheus Books this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-09-02 with Mathematics categories.
In this accessible and illuminating study of how the science of mathematics developed, a veteran math researcher and educator looks at the ways in which our evolutionary makeup is both a help and a hindrance to the study of math. Artstein chronicles the discovery of important mathematical connections between mathematics and the real world from ancient times to the present. The author then describes some of the contemporary applications of mathematics—in probability theory, in the study of human behavior, and in combination with computers, which give mathematics unprecedented power. The author concludes with an insightful discussion of why mathematics, for most people, is so frustrating. He argues that the rigorous logical structure of math goes against the grain of our predisposed ways of thinking as shaped by evolution, presumably because the talent needed to cope with logical mathematics gave the human race as a whole no evolutionary advantage. With this in mind, he offers ways to overcome these innate impediments in the teaching of math.
Making Mathematics With Needlework
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Author : sarah-marie belcastro
language : en
Publisher: CRC Press
Release Date : 2007-12-12
Making Mathematics With Needlework written by sarah-marie belcastro and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-12-12 with Mathematics categories.
Mathematical craftwork has become extremely popular, and mathematicians and crafters alike are fascinated by the relationship between their crafts. The focus of this book, written for mathematicians, needleworkers, and teachers of mathematics, is on the relationship between mathematics and the fiber arts (including knitting, crocheting, cross-stitch, and quilting). Each chapter starts with an overview of the mathematics and the needlework at a level understandable to both mathematicians and needleworkers, followed by more technical sections discussing the mathematics, how to introduce the mathematics in the classroom through needlework, and how to make the needlework project, including patterns and instructions.
Making Up Numbers A History Of Invention In Mathematics
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Author : Ekkehard Kopp
language : en
Publisher: Open Book Publishers
Release Date : 2020-10-23
Making Up Numbers A History Of Invention In Mathematics written by Ekkehard Kopp and has been published by Open Book Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-10-23 with Mathematics categories.
Making up Numbers: A History of Invention in Mathematics offers a detailed but accessible account of a wide range of mathematical ideas. Starting with elementary concepts, it leads the reader towards aspects of current mathematical research. The book explains how conceptual hurdles in the development of numbers and number systems were overcome in the course of history, from Babylon to Classical Greece, from the Middle Ages to the Renaissance, and so to the nineteenth and twentieth centuries. The narrative moves from the Pythagorean insistence on positive multiples to the gradual acceptance of negative numbers, irrationals and complex numbers as essential tools in quantitative analysis. Within this chronological framework, chapters are organised thematically, covering a variety of topics and contexts: writing and solving equations, geometric construction, coordinates and complex numbers, perceptions of ‘infinity’ and its permissible uses in mathematics, number systems, and evolving views of the role of axioms. Through this approach, the author demonstrates that changes in our understanding of numbers have often relied on the breaking of long-held conventions to make way for new inventions at once providing greater clarity and widening mathematical horizons. Viewed from this historical perspective, mathematical abstraction emerges as neither mysterious nor immutable, but as a contingent, developing human activity. Making up Numbers will be of great interest to undergraduate and A-level students of mathematics, as well as secondary school teachers of the subject. In virtue of its detailed treatment of mathematical ideas, it will be of value to anyone seeking to learn more about the development of the subject.
Making Mathematics More Practical
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Author : Yew Hoong Leong
language : en
Publisher: World Scientific Publishing Company
Release Date : 2013-09-04
Making Mathematics More Practical written by Yew Hoong Leong and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-09-04 with Mathematics categories.
The book Making Mathematics Practical (published by World Scientific in 2011) proposes a new paradigm in teaching problem solving in secondary school mathematics classrooms. It is a report of the research project “Mathematical Problem Solving for Everyone” (MProSE), which attempts to provide all the necessary resources for teachers to teach problem solving in schools. This book reports as a follow-up on the actual enactment of the proposed MProSE problem solving curriculum in five Singapore schools. The experimental schools, which span across the entire spectrum of all Singapore secondary schools, report how they tweak the MProSE proposal to fit into their school curriculum, together with issues, challenges and success stories in implementing such an innovative curriculum in Singapore schools. It is an ideal handbook for educators who believe in problem solving as the core of mathematics curriculum and who wish to implement such an approach in their schools.
Mathematics In The Making
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Author : Lancelot Thomas Hogben
language : en
Publisher:
Release Date : 1973
Mathematics In The Making written by Lancelot Thomas Hogben and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1973 with Mathematics categories.
Making Mathematics Practical
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Author : Tin Lam Toh
language : en
Publisher: World Scientific Publishing Company
Release Date : 2011-03-08
Making Mathematics Practical written by Tin Lam Toh and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-03-08 with Mathematics categories.
This book is the first of its kind, as it includes both mathematics content and pedagogy. It is a professional instructional manual on how mathematical problem solving curriculum can be implemented in the classrooms. The book develops from the theoretical work of Polya and Schoenfeld, and explicates how these can be translated to the actual implementation in schools. It represents the work of a group of researchers from the Singapore National Institute of Education, after experimenting with it in the Singapore school classrooms. This book includes a set of scheme of work, lesson plans and a choice of mathematics problems that teachers can actually use in teaching problem solving. Certain pedagogical considerations are developed and suggested in this book. In addition, the book includes an assessment framework on how mathematical problem solving can be assessed.
Making Images With Mathematics
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Author : Alexei Sourin
language : en
Publisher: Springer Nature
Release Date : 2021-06-01
Making Images With Mathematics written by Alexei Sourin and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-06-01 with Computers categories.
This textbook teaches readers how to turn geometry into an image on a computer screen. This exciting journey begins in the schools of the ancient Greek philosophers, and describes the major events that changed people’s perception of geometry. The readers will learn how to see geometry and colors beyond simple mathematical formulas and how to represent geometric shapes, transformations and motions by digital sampling of various mathematical functions. Special multiplatform visualization software developed by the author will allow readers to explore the exciting world of visual immersive mathematics, and the book software repository will provide a starting point for their own sophisticated visualization applications. Making Images with Mathematics serves as a self-contained text for a one-semester computer graphics and visualization course for computer science and engineering students, as well as a reference manual for researchers and developers.
Making Mathematics Practical
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Author : Tin Lam Toh
language : en
Publisher: World Scientific
Release Date : 2011
Making Mathematics Practical written by Tin Lam Toh and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with Mathematics categories.
This book is the first of its kind, as it includes both mathematics content and pedagogy. It is a professional instructional manual on how mathematical problem solving curriculum can be implemented in the classrooms. The book develops from the theoretical work of Polya and Schoenfeld, and explicates how these can be translated to the actual implementation in schools. It represents the work of a group of researchers from the Singapore National Institute of Education, after experimenting with it in the Singapore school classrooms. This book includes a set of scheme of work, lesson plans and a choice of mathematics problems that teachers can actually use in teaching problem solving. Certain pedagogical considerations are developed and suggested in this book. In addition, the book includes an assessment framework on how mathematical problem solving can be assessed.