The Ancient Tradition of Geometric Problems

Author: Wilbur Richard Knorr

Publisher: Courier Corporation

ISBN: 0486675327

Category: Mathematics

Page: 410

View: 816

Illustrated study focuses on attempts by ancient Greeks to solve three classical problems: cube duplication, angle trisection, and circle quadrature. Origins of the study of conics, introduction of special mechanical curves, more. 1986 edition.

Exploring Classical Greek Construction Problems with Interactive Geometry Software

Author: Ad Meskens,Paul Tytgat

Publisher: Birkhäuser

ISBN: 3319428632

Category: Mathematics

Page: 185

View: 5138

In this book the classical Greek construction problems are explored in a didactical, enquiry based fashion using Interactive Geometry Software (IGS). The book traces the history of these problems, stating them in modern terminology. By focusing on constructions and the use of IGS the reader is confronted with the same problems that ancient mathematicians once faced. The reader can step into the footsteps of Euclid, Viète and Cusanus amongst others and then by experimenting and discovering geometric relationships far exceed their accomplishments. Exploring these problems with the neusis-method lets him discover a class of interesting curves. By experimenting he will gain a deeper understanding of how mathematics is created. More than 100 exercises guide him through methods which were developed to try and solve the problems. The exercises are at the level of undergraduate students and only require knowledge of elementary Euclidean geometry and pre-calculus algebra. It is especially well-suited for those students who are thinking of becoming a mathematics teacher and for mathematics teachers.

History of Mathematics

A Supplement

Author: Craig Smorynski

Publisher: Springer Science & Business Media

ISBN: 0387754814

Category: Mathematics

Page: 274

View: 9390

General textbooks, attempting to cover three thousand or so years of mathematical history, must necessarily oversimplify just about everything, the practice of which can scarcely promote a critical approach to the subject. To counter this, History of Mathematics offers deeper coverage of key select topics, providing students with material that could encourage more critical thinking. It also includes the proofs of important results which are typically neglected in the modern history of mathematics curriculum.

Mathematical Logic

Author: Stephen Cole Kleene

Publisher: Courier Corporation

ISBN: 0486317072

Category: Mathematics

Page: 416

View: 5531

Contents include an elementary but thorough overview of mathematical logic of 1st order; formal number theory; surveys of the work by Church, Turing, and others, including Gödel's completeness theorem, Gentzen's theorem, more.

Using History to Teach Mathematics

An International Perspective

Author: Victor J. Katz

Publisher: Cambridge University Press

ISBN: 9780883851630

Category: Mathematics

Page: 261

View: 6856

This volume examines how the history of mathematics can find application in the teaching of mathematics itself.

Mathematical Expeditions

Chronicles by the Explorers

Author: Reinhard Laubenbacher,David Pengelley

Publisher: Springer Science & Business Media

ISBN: 9780387984339

Category: Mathematics

Page: 278

View: 7155

The stories of five mathematical journeys into new realms, pieced together from the writings of the explorers themselves. Some were guided by mere curiosity and the thrill of adventure, others by more practical motives. In each case the outcome was a vast expansion of the known mathematical world and the realisation that still greater vistas remain to be explored. The authors tell these stories by guiding readers through the very words of the mathematicians at the heart of these events, providing an insightinto the art of approaching mathematical problems. The five chapters are completely independent, with varying levels of mathematical sophistication, and will attract students, instructors, and the intellectually curious reader. By working through some of the original sources and supplementary exercises, which discuss and solve -- or attempt to solve -- a great problem, this book helps readers discover the roots of modern problems, ideas, and concepts, even whole subjects. Students will also see the obstacles that earlier thinkers had to clear in order to make their respective contributions to five central themes in the evolution of mathematics.

Mathematics celestial and terrestrial

Festschrift für Menso Folkerts zum 65. Geburtstag

Author: Joseph Warren Dauben

Publisher: N.A

ISBN: 9783804724822

Category: Mathematics

Page: 823

View: 811

Acta historica Leopoldina

Author: Joseph Warren Dauben

Publisher: N.A

ISBN: 9783804724822

Category: Natural history

Page: 823

View: 3182

Greek Mathematical Thought and the Origin of Algebra

Author: Jacob Klein

Publisher: Courier Corporation

ISBN: 9780486272894

Category: Mathematics

Page: 360

View: 7093

Important study focuses on the revival and assimilation of ancient Greek mathematics in the 13th–16th centuries, via Arabic science, and the 16th-century development of symbolic algebra. This brought about the crucial change in the concept of number that made possible modern science — in which the symbolic "form" of a mathematical statement is completely inseparable from its "content" of physical meaning. Includes a translation of Vieta's Introduction to the Analytical Art. 1968 edition. Bibliography.

Philosophy of Mathematics and Deductive Structure in Euclid's Elements

Author: Ian Mueller

Publisher: Dover Books on Mathematics


Category: Mathematics

Page: 378

View: 5226

A survey of Euclid's Elements, this text provides an understanding of the classical Greek conception of mathematics. It offers a well-rounded perspective, examining similarities to modern views as well as differences. Rather than focusing strictly on historical and mathematical issues, the book examines philosophical, foundational, and logical questions. Although comprehensive in its treatment, this study represents a less cumbersome, more streamlined approach than the classic three-volume reference by Sir Thomas L. Heath (also available from Dover Publications). To make reading easier and to facilitate access to individual analyses and discussions, the author has included helpful appendixes. These list special symbols and additional propositions, along with all of the assumptions and propositions of the Elements and notations of their discussion within this volume.

The History of Mathematics

Brief Version

Author: Victor J. Katz

Publisher: Addison-Wesley


Category: Mathematics

Page: 560

View: 8840

One of the leading historians in the mathematics field, Victor Katz provides a world view of mathematics, balancing ancient, early modern, and modern history. Egypt and Mesopotamia, Greek Mathematics to the Time of Euclid, Greek Mathematics from Archimedes to Ptolemy, Diophantus to Hypatia, Ancient and Medieval China, Ancient and Medieval India, The Mathematics of Islam, Mathematics in Medieval Europe, Mathematics in the Renaissance, Precalculus in the Seventeenth Century, Calculus in the Seventeenth Century, Analysis in the Eighteenth Century, Probability and Statistics in the Eighteenth Century, Algebra and Number Theory in the Eighteenth Century, Geometry in the Eighteenth Century, Algebra and Number Theory in the Nineteenth Century, Analysis in the Nineteenth Century, Statistics in the Nineteenth Century, Geometry in the Nineteenth Century, Aspects of the Twentieth Century For all readers interested in the history of mathematics.

Science and Its Times

Understanding the Social Significance of Scientific Discovery

Author: Neil Schlager

Publisher: Gale / Cengage Learning


Category: Science

Page: 429

View: 2184

Combining essays on people, theories, discoveries and concepts with overviews, primary documents and chronological elements, this reference offers a way to understand the impact of science on the course of human history and how science affects everyday life.

A Profile of Mathematical Logic

Author: Howard DeLong

Publisher: Courier Corporation

ISBN: 0486139158

Category: Mathematics

Page: 320

View: 8289

This introduction to mathematical logic explores philosophical issues and Gödel's Theorem. Its widespread influence extends to the author of Gödel, Escher, Bach, whose Pulitzer Prize–winning book was inspired by this work.

A History of Mathematics

An Introduction

Author: Victor J. Katz

Publisher: Addison-Wesley Longman


Category: Mathematics

Page: 976

View: 3743

Key Message: A History of Mathematics, Third Edition, provides a solid background in the history of mathematics, helping readers gain a deeper understanding of mathematical concepts in their historical context. This book's global perspective covers how contributions from Chinese, Indian, and Islamic mathematicians shaped our modern understanding of mathematics. This book also includes discussions of important historical textbooks and primary sources to help readers further understand the development of modern mathematics. Key Topics: Ancient Mathematics: Egypt and Mesopotamia, The Beginnings of Mathematics in Greece, Euclid, Archimedes and Apollonius, Mathematical Methods in Hellenistic Times, The Final Chapter of Greek Mathematics; Medieval Mathematics: Ancient and Medieval China, Ancient and Medieval India, The Mathematics of Islam, Medieval Europe, Mathematics Elsewhere; Early Modern Mathematics: Algebra in the Renaissance, Mathematical Methods in the Renaissance, Geometry, Algebra and Probability in the Seventeenth Century, The Beginnings of Calculus, Newton and Leibniz; Modern Mathematics: Analysis in the Eighteenth Century, Probability and Statistics in the Eighteenth Century, Algebra and Number Theory in the Eighteenth Century, Geometry in the Eighteenth Century, Algebra and Number Theory in the Nineteenth Century, Analysis in the Nineteenth Century, Probability and Statistics in the Nineteenth Century, Geometry in the Nineteenth Century, Aspects of the Twentieth Century Market: For all readers interested in the history of mathematics.

Classics of Mathematics

Author: Ronald Calinger

Publisher: Pearson College Division

ISBN: 9780023183423

Category: Mathematics

Page: 793

View: 4834

Appropriate for undergraduate and select graduate courses in the history of mathematics, and in the history of science. This edited volume of readings contains more than 130 selections from eminent mathematicians from A `h-mose' to Hilbert and Noether. The chapter introductions comprise a concise history of mathematics based on critical textual analysis and the latest scholarship. Each reading is preceded by a substantial biography of its author.

An Introduction to Harmonic Analysis

Author: Yitzhak Katznelson

Publisher: Courier Dover Publications

ISBN: 9780486633312

Category: Mathematics

Page: 264

View: 8141

This concrete approach to harmonic analysis begins with the circle group T and deals with classical Fourier series in the first five chapters, turning to the real line in chapter six, locally compact abelian groups in chapter seven, and commutative Banach algebras in final chapter.

MAA Notes

Author: N.A

Publisher: The Mathematical Association of America


Category: Education

Page: N.A

View: 2233

New Dictionary of Scientific Biography

Author: Noretta Koertge

Publisher: Scribner

ISBN: 9780684313214

Category: Science

Page: 7

View: 8041

Also available online as part of the Gale Virtual Reference Library under the title Complete dictionary of scientific biography.

From Discrete to Continuous

The Broadening of Number Concepts in Early Modern England

Author: K. Neal

Publisher: Springer Science & Business Media

ISBN: 940170077X

Category: Mathematics

Page: 175

View: 7257

In the early modern period, a crucial transformation occurred in the classical conception of number and magnitude. Traditionally, numbers were merely collections of discrete units that measured some multiple. Magnitude, on the other hand, was usually described as being continuous, or being divisible into parts that are infinitely divisible. This traditional idea of discrete number versus continuous magnitude was challenged in the early modern period in several ways. This detailed study explores how the development of algebraic symbolism, logarithms, and the growing practical demands for an expanded number concept all contributed to a broadening of the number concept in early modern England. An interest in solving practical problems was not, in itself, enough to cause a generalisation of the number concept. It was the combined impact of novel practical applications together with the concomitant development of such mathematical advances as algebraic notation and logarithms that produced a broadened number concept.