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Author: Raymond L. Wilder Publisher: Courier Corporation ISBN: 0486490610 Category : Mathematics Languages : en Pages : 242
Book Description
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 L. Wilder Publisher: Courier Corporation ISBN: 0486490610 Category : Mathematics Languages : en Pages : 242
Book Description
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: John A. Walker Publisher: Springer Science & Business Media ISBN: 1468410369 Category : Computers Languages : en Pages : 244
Book Description
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: E. T. Bell Publisher: Courier Corporation ISBN: 0486152286 Category : Mathematics Languages : en Pages : 657
Book Description
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: Zvi Artstein Publisher: Prometheus Books ISBN: 1616145463 Category : Mathematics Languages : en Pages : 428
Book Description
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.
Author: Isabella Bashmakova Publisher: American Mathematical Soc. ISBN: 1470457229 Category : Mathematics Languages : en Pages : 196
Book Description
The elements of algebra were known to the ancient mesopotamians at least 4000 years ago. Today, algebra stands as one of the cornerstones of modern mathematics. How then did the subject evolve? An illuminating read for historians of mathematics and working algebraists looking into the history of their subject.
Author: Michael J. Crowe Publisher: Courier Corporation ISBN: 0486679101 Category : Mathematics Languages : en Pages : 306
Book Description
Prize-winning study traces the rise of the vector concept from the discovery of complex numbers through the systems of hypercomplex numbers to the final acceptance around 1910 of the modern system of vector analysis.
Author: Sean H. Rice Publisher: Sinauer Associates Incorporated ISBN: 9780878937028 Category : Mathematics Languages : en Pages : 370
Book Description
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: John Stillwell Publisher: Springer Nature ISBN: 3030551938 Category : Mathematics Languages : en Pages : 400
Book Description
This textbook provides a unified and concise exploration of undergraduate mathematics by approaching the subject through its history. Readers will discover the rich tapestry of ideas behind familiar topics from the undergraduate curriculum, such as calculus, algebra, topology, and more. Featuring historical episodes ranging from the Ancient Greeks to Fermat and Descartes, this volume offers a glimpse into the broader context in which these ideas developed, revealing unexpected connections that make this ideal for a senior capstone course. The presentation of previous versions has been refined by omitting the less mainstream topics and inserting new connecting material, allowing instructors to cover the book in a one-semester course. This condensed edition prioritizes succinctness and cohesiveness, and there is a greater emphasis on visual clarity, featuring full color images and high quality 3D models. As in previous editions, a wide array of mathematical topics are covered, from geometry to computation; however, biographical sketches have been omitted. Mathematics and Its History: A Concise Edition is an essential resource for courses or reading programs on the history of mathematics. Knowledge of basic calculus, algebra, geometry, topology, and set theory is assumed. From reviews of previous editions: “Mathematics and Its History is a joy to read. The writing is clear, concise and inviting. The style is very different from a traditional text. I found myself picking it up to read at the expense of my usual late evening thriller or detective novel.... The author has done a wonderful job of tying together the dominant themes of undergraduate mathematics.” Richard J. Wilders, MAA, on the Third Edition "The book...is presented in a lively style without unnecessary detail. It is very stimulating and will be appreciated not only by students. Much attention is paid to problems and to the development of mathematics before the end of the nineteenth century.... This book brings to the non-specialist interested in mathematics many interesting results. It can be recommended for seminars and will be enjoyed by the broad mathematical community." European Mathematical Society, on the Second Edition
Author: Elizabeth de Freitas Publisher: Cambridge University Press ISBN: 1107134633 Category : Education Languages : en Pages : 301
Book Description
Leading thinkers in mathematics, philosophy and education offer new insights into the fundamental question: what is a mathematical concept?
Author: Raymond L. Wilder
Author: Raymond L. Wilder
Author: John A. Walker
Author: E. T. Bell
Author: Zvi Artstein
Author: Isabella Bashmakova
Author: Luke Heaton
Author: Michael J. Crowe
Author: Sean H. Rice
Author: John Stillwell
Author: Elizabeth de Freitas