Evolution Of Mathematical Concepts

Author : Raymond L. Wilder
Publisher : Courier Corporation
Page : 242 pages
File Size : 47,5 Mb
Release : 2013-01-01
Category : Mathematics
ISBN : 9780486490618

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Evolution of Mathematical Concepts by Raymond L. Wilder Pdf

Accessible to students and relevant to specialists, this remarkable book by a prominent educator offers a unique perspective on the evolutionary development of mathematics. Rather than conducting a survey of the history or philosophy of mathematics, Raymond L. Wilder envisions mathematics as a broad cultural phenomenon. His treatment examines and illustrates how such concepts as number and length were affected by historic and social events. Starting with a brief consideration of preliminary notions, this study explores the early evolution of numbers, the evolution of geometry, and the conquest of the infinite as embodied by real numbers. A detailed look at the processes of evolution concludes with an examination of the evolutionary aspects of modern mathematics.

Author : Raymond Louis Wilder
Publisher : International Publication Service
Page : 216 pages
File Size : 43,6 Mb
Release : 1978-01-01
Category : Mathematics
ISBN : 0335002498

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Evolution of Mathematical Concepts by Raymond Louis Wilder Pdf

Author : John A. Walker
Publisher : Springer Science & Business Media
Page : 244 pages
File Size : 44,9 Mb
Release : 2013-03-09
Category : Computers
ISBN : 9781468410365

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Dynamical Systems and Evolution Equations by John A. Walker Pdf

This book grew out of a nine-month course first given during 1976-77 in the Division of Engineering Mechanics, University of Texas (Austin), and repeated during 1977-78 in the Department of Engineering Sciences and Applied Mathematics, Northwestern University. Most of the students were in their second year of graduate study, and all were familiar with Fourier series, Lebesgue integration, Hilbert space, and ordinary differential equa tions in finite-dimensional space. This book is primarily an exposition of certain methods of topological dynamics that have been found to be very useful in the analysis of physical systems but appear to be well known only to specialists. The purpose of the book is twofold: to present the material in such a way that the applications-oriented reader will be encouraged to apply these methods in the study of those physical systems of personal interest, and to make the coverage sufficient to render the current research literature intelligible, preparing the more mathematically inclined reader for research in this particular area of applied mathematics. We present only that portion of the theory which seems most useful in applications to physical systems. Adopting the view that the world is deterministic, we consider our basic problem to be predicting the future for a given physical system. This prediction is to be based on a known equation of evolution, describing the forward-time behavior of the system, but it is to be made without explicitly solving the equation.

Author : Luke Heaton
Publisher : Oxford University Press
Page : 337 pages
File Size : 43,9 Mb
Release : 2017
Category : History
ISBN : 9780190621766

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A Brief History of Mathematical Thought by Luke Heaton Pdf

Emblazoned on many advertisements for the wildly popular game of Sudoku are the reassuring words, -no mathematical knowledge required.- Anxiety about math plagues many of us, and school memories can still summon intense loathing. In A Brief History of Mathematical Thought, Luke Heaton shows that much of what many think-and fear-about mathematics is misplaced, and to overcome our insecurities we need to understand its history. To help, he offers a lively guide into and through the world of mathematics and mathematicians, one in which patterns and arguments are traced through logic in a language grounded in concrete experience. Heaton reveals how Greek and Roman mathematicians like Pythagoras, Euclid, and Archimedes helped shaped the early logic of mathematics; how the Fibonacci sequence, the rise of algebra, and the invention of calculus are connected; how clocks, coordinates, and logical padlocks work mathematically; and how, in the twentieth century, Alan Turing's revolutionary work on the concept of computation laid the groundwork for the modern world. A Brief History of Mathematical Thought situates mathematics as part of, and essential to, lived experience. Understanding it requires not abstract thought or numbing memorization but an historical imagination and a view to its origins. --

Author : E. T. Bell
Publisher : Courier Corporation
Page : 657 pages
File Size : 50,8 Mb
Release : 2012-09-11
Category : Mathematics
ISBN : 9780486152288

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The Development of Mathematics by E. T. Bell Pdf

Time-honored study by a prominent scholar of mathematics traces decisive epochs from the evolution of mathematical ideas in ancient Egypt and Babylonia to major breakthroughs in the 19th and 20th centuries. 1945 edition.

Author : Britannica Educational Publishing
Publisher : Britannica Educational Publishing
Page : 311 pages
File Size : 43,5 Mb
Release : 2010-04-01
Category : Juvenile Nonfiction
ISBN : 9781615302215

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The Britannica Guide to The History of Mathematics by Britannica Educational Publishing Pdf

The field of mathematics today represents an ongoing global effort, spanning both countries and centuries. Through this in-depth narrative, students will learn how major mathematical concepts were first derived, as well as how they evolved with the advent of later thinkers shedding new light on various applications. Everything from Euclidean geometry to the philosophy of mathematics is illuminated as readers are transported to the ancient civilizations of Mesopotamia, Egypt, and beyond to discover the history of mathematical thought

Author : Elizabeth de Freitas,Nathalie Sinclair,Alf Coles
Publisher : Cambridge University Press
Page : 301 pages
File Size : 43,9 Mb
Release : 2017-06-22
Category : Education
ISBN : 9781107134638

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What is a Mathematical Concept? by Elizabeth de Freitas,Nathalie Sinclair,Alf Coles Pdf

Leading thinkers in mathematics, philosophy and education offer new insights into the fundamental question: what is a mathematical concept?

Author : Sean H. Rice
Publisher : Sinauer Associates Incorporated
Page : 370 pages
File Size : 40,6 Mb
Release : 2004
Category : Mathematics
ISBN : 0878937021

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Evolutionary Theory by Sean H. Rice Pdf

Evolutionary Theory is for graduate students, researchers, and advanced undergraduates who want an understanding of the mathematical and biological reasoning that underlies evolutionary theory. The book covers all of the major theoretical approaches used to study the mechanics of evolution, including classical one- and two-locus models, diffusion theory, coalescent theory, quantitative genetics, and game theory. There are also chapters on theoretical approaches to the evolution of development and on multilevel selection theory. Each subject is illustrated by focusing on those results that have the greatest power to influence the way that we think about how evolution works. These major results are developed in detail, with many accompanying illustrations, showing exactly how they are derived and how the mathematics relates to the biological insights that they yield. In this way, the reader learns something of the actual machinery of different branches of theory while gaining a deeper understanding of the evolutionary process. Roughly half of the book focuses on gene-based models, the other half being concerned with general phenotype-based theory. Throughout, emphasis is placed on the fundamental relationships between the different branches of theory, illustrating how all of these branches are united by a few basic, universal, principles. The only mathematical background assumed is basic calculus. More advanced mathematical methods are explained, with the help of an extensive appendix, when they are needed.

Author : S. Restivo
Publisher : Springer Science & Business Media
Page : 215 pages
File Size : 44,6 Mb
Release : 2013-12-01
Category : Science
ISBN : 9789401129442

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Mathematics in Society and History by S. Restivo Pdf

This is the first book by a sociologist devoted exclusively to a general sociology of mathematics. The author provides examples of different ways of thinking about mathematics sociologically. The survey of mathematical traditions covers ancient China, the Arabic-Islamic world, India, and Europe. Following the leads of classical social theorists such as Emile Durkheim, Restivo develops the idea that mathematical concepts and ideas are collective representations, and that it is mathematical communities that create mathematics, not individual mathematicians. The implications of the sociology of mathematics, and especially of pure mathematics, for a sociology of mind are also explored. In general, the author's objective is to explore, conjecture, suggest, and stimulate in order to introduce the sociological perspective on mathematics, and to broaden and deepen the still narrow, shallow path that today carries the sociology of mathematics. This book will interest specialists in the philosophy, history, and sociology of mathematics, persons interested in mathematics education, students of science and society, and people interested in current developments in the social and cultural analysis of science and mathematics.

Author : Misha Gromov
Publisher : Birkhäuser
Page : 202 pages
File Size : 54,9 Mb
Release : 2018-08-11
Category : Mathematics
ISBN : 9783319530499

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Great Circle of Mysteries by Misha Gromov Pdf

This visionary and engaging book provides a mathematical perspective on the fundamental ideas of numbers, space, life, evolution, the brain and the mind. The author suggests how a development of mathematical concepts in the spirit of category theory may lead to unravelling the mystery of the human mind and the design of universal learning algorithms. The book is divided into two parts, the first of which describes the ideas of great mathematicians and scientists, those who saw sparks of light in the dark sea of unknown. The second part, Memorandum Ergo, reflects on how mathematics can contribute to the understanding of the mystery of thought. It argues that the core of the human mind is a structurally elaborated object that needs a creation of a broad mathematical context for its understanding. Readers will discover the main properties of the expected mathematical objects within this context, called ERGO-SYSTEMS, and readers will see how these “systems” may serve as prototypes for design of universal learning computer programs. This is a work of great, poetical insight and is richly illustrated. It is a highly attractive read for all those who welcome a mathematical and scientific way of thinking about the world.

Author : Johann Pfanzagl
Publisher : Springer
Page : 316 pages
File Size : 52,5 Mb
Release : 2017-10-23
Category : Mathematics
ISBN : 9783642310843

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Mathematical Statistics by Johann Pfanzagl Pdf

This book presents a detailed description of the development of statistical theory. In the mid twentieth century, the development of mathematical statistics underwent an enduring change, due to the advent of more refined mathematical tools. New concepts like sufficiency, superefficiency, adaptivity etc. motivated scholars to reflect upon the interpretation of mathematical concepts in terms of their real-world relevance. Questions concerning the optimality of estimators, for instance, had remained unanswered for decades, because a meaningful concept of optimality (based on the regularity of the estimators, the representation of their limit distribution and assertions about their concentration by means of Anderson’s Theorem) was not yet available. The rapidly developing asymptotic theory provided approximate answers to questions for which non-asymptotic theory had found no satisfying solutions. In four engaging essays, this book presents a detailed description of how the use of mathematical methods stimulated the development of a statistical theory. Primarily focused on methodology, questionable proofs and neglected questions of priority, the book offers an intriguing resource for researchers in theoretical statistics, and can also serve as a textbook for advanced courses in statisticc.

Author : Jont Allen
Publisher : Springer Nature
Page : 394 pages
File Size : 55,9 Mb
Release : 2020-09-22
Category : Technology & Engineering
ISBN : 9783030537593

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An Invitation to Mathematical Physics and Its History by Jont Allen Pdf

This state of the art book takes an applications based approach to teaching mathematics to engineering and applied sciences students. The book lays emphasis on associating mathematical concepts with their physical counterparts, training students of engineering in mathematics to help them learn how things work. The book covers the concepts of number systems, algebra equations and calculus through discussions on mathematics and physics, discussing their intertwined history in a chronological order. The book includes examples, homework problems, and exercises. This book can be used to teach a first course in engineering mathematics or as a refresher on basic mathematical physics. Besides serving as core textbook, this book will also appeal to undergraduate students with cross-disciplinary interests as a supplementary text or reader.

Author : Raymond L. Wilder
Publisher : Unknown
Page : 216 pages
File Size : 41,6 Mb
Release : 1974
Category : Electronic
ISBN : OCLC:1072097502

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Evolution of mathematical concepts by Raymond L. Wilder Pdf

Author : Carl B. Boyer,Uta C. Merzbach
Publisher : John Wiley & Sons
Page : 695 pages
File Size : 52,5 Mb
Release : 2011-01-11
Category : Mathematics
ISBN : 9780470525487

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A History of Mathematics by Carl B. Boyer,Uta C. Merzbach Pdf

The updated new edition of the classic and comprehensive guide to the history of mathematics For more than forty years, A History of Mathematics has been the reference of choice for those looking to learn about the fascinating history of humankind’s relationship with numbers, shapes, and patterns. This revised edition features up-to-date coverage of topics such as Fermat’s Last Theorem and the Poincaré Conjecture, in addition to recent advances in areas such as finite group theory and computer-aided proofs. Distills thousands of years of mathematics into a single, approachable volume Covers mathematical discoveries, concepts, and thinkers, from Ancient Egypt to the present Includes up-to-date references and an extensive chronological table of mathematical and general historical developments. Whether you're interested in the age of Plato and Aristotle or Poincaré and Hilbert, whether you want to know more about the Pythagorean theorem or the golden mean, A History of Mathematics is an essential reference that will help you explore the incredible history of mathematics and the men and women who created it.

Author : I. G. Bashmakova,G. S. Smirnova
Publisher : Cambridge University Press
Page : 200 pages
File Size : 50,5 Mb
Release : 2000-04-27
Category : Mathematics
ISBN : 0883853299

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The Beginnings and Evolution of Algebra by I. G. Bashmakova,G. S. Smirnova Pdf

An examination of the evolution of one of the cornerstones of modern mathematics.