Turning Points in the History of Mathematics


Author: Hardy Grant,Israel Kleiner
Publisher: Birkhäuser
ISBN: 1493932640
Category: Mathematics
Page: 109
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This book explores some of the major turning points in the history of mathematics, ranging from ancient Greece to the present, demonstrating the drama that has often been a part of its evolution. Studying these breakthroughs, transitions, and revolutions, their stumbling-blocks and their triumphs, can help illuminate the importance of the history of mathematics for its teaching, learning, and appreciation. Some of the turning points considered are the rise of the axiomatic method (most famously in Euclid), and the subsequent major changes in it (for example, by David Hilbert); the “wedding,” via analytic geometry, of algebra and geometry; the “taming” of the infinitely small and the infinitely large; the passages from algebra to algebras, from geometry to geometries, and from arithmetic to arithmetics; and the revolutions in the late nineteenth and early twentieth centuries that resulted from Georg Cantor’s creation of transfinite set theory. The origin of each turning point is discussed, along with the mathematicians involved and some of the mathematics that resulted. Problems and projects are included in each chapter to extend and increase understanding of the material. Substantial reference lists are also provided. Turning Points in the History of Mathematics will be a valuable resource for teachers of, and students in, courses in mathematics or its history. The book should also be of interest to anyone with a background in mathematics who wishes to learn more about the important moments in its development.

Bernhard Riemann 1826–1866

Turning Points in the Conception of Mathematics
Author: Detlef Laugwitz
Publisher: Springer Science & Business Media
ISBN: 0817647775
Category: Mathematics
Page: 357
View: 8601

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The name of Bernard Riemann is well known to mathematicians and physicists around the world. His name is indelibly stamped on the literature of mathematics and physics. This remarkable work, rich in insight and scholarship, is addressed to mathematicians, physicists, and philosophers interested in mathematics. It seeks to draw those readers closer to the underlying ideas of Riemann’s work and to the development of them in their historical context. This illuminating English-language version of the original German edition will be an important contribution to the literature of the history of mathematics.

Greek Mathematical Thought and the Origin of Algebra


Author: Jacob Klein
Publisher: Courier Corporation
ISBN: 0486319814
Category: Mathematics
Page: 384
View: 5364

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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.

A History of Mathematics


Author: Carl B. Boyer,Uta C. Merzbach
Publisher: John Wiley & Sons
ISBN: 0470630566
Category: Mathematics
Page: 688
View: 3868

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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.

Mathematics and the Physical World


Author: Morris Kline
Publisher: Courier Corporation
ISBN: 0486136310
Category: Mathematics
Page: 512
View: 7310

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Stimulating account of development of mathematics from arithmetic, algebra, geometry and trigonometry, to calculus, differential equations, and non-Euclidean geometries. Also describes how math is used in optics, astronomy, and other phenomena.

Mathematics

The Loss of Certainty
Author: Morris Kline
Publisher: Oxford University Press, USA
ISBN: 9780195030853
Category: Mathematics
Page: 366
View: 4085

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Refuting the accepted belief that mathematics is exact and infallible, the author examines the development of conflicting concepts of mathematics and their implications for the physical, applied, social, and computer sciences

The History of Mathematics

A Brief Course
Author: Roger L. Cooke
Publisher: John Wiley & Sons
ISBN: 1118460294
Category: Mathematics
Page: 648
View: 6815

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Praise for the Second Edition "An amazing assemblage of worldwide contributions in mathematics and, in addition to use as a course book, a valuable resource . . . essential." —CHOICE This Third Edition of The History of Mathematics examines the elementary arithmetic, geometry, and algebra of numerous cultures, tracing their usage from Mesopotamia, Egypt, Greece, India, China, and Japan all the way to Europe during the Medieval and Renaissance periods where calculus was developed. Aimed primarily at undergraduate students studying the history of mathematics for science, engineering, and secondary education, the book focuses on three main ideas: the facts of who, what, when, and where major advances in mathematics took place; the type of mathematics involved at the time; and the integration of this information into a coherent picture of the development of mathematics. In addition, the book features carefully designed problems that guide readers to a fuller understanding of the relevant mathematics and its social and historical context. Chapter-end exercises, numerous photographs, and a listing of related websites are also included for readers who wish to pursue a specialized topic in more depth. Additional features of The History of Mathematics, Third Edition include: Material arranged in a chronological and cultural context Specific parts of the history of mathematics presented as individual lessons New and revised exercises ranging between technical, factual, and integrative Individual PowerPoint presentations for each chapter and a bank of homework and test questions (in addition to the exercises in the book) An emphasis on geography, culture, and mathematics In addition to being an ideal coursebook for undergraduate students, the book also serves as a fascinating reference for mathematically inclined individuals who are interested in learning about the history of mathematics.

An Introduction to the Language of Category Theory


Author: Steven Roman
Publisher: Birkhäuser
ISBN: 331941917X
Category: Mathematics
Page: 169
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This textbook provides an introduction to elementary category theory, with the aim of making what can be a confusing and sometimes overwhelming subject more accessible. In writing about this challenging subject, the author has brought to bear all of the experience he has gained in authoring over 30 books in university-level mathematics. The goal of this book is to present the five major ideas of category theory: categories, functors, natural transformations, universality, and adjoints in as friendly and relaxed a manner as possible while at the same time not sacrificing rigor. These topics are developed in a straightforward, step-by-step manner and are accompanied by numerous examples and exercises, most of which are drawn from abstract algebra. The first chapter of the book introduces the definitions of category and functor and discusses diagrams,duality, initial and terminal objects, special types of morphisms, and some special types of categories,particularly comma categories and hom-set categories. Chapter 2 is devoted to functors and naturaltransformations, concluding with Yoneda's lemma. Chapter 3 presents the concept of universality and Chapter 4 continues this discussion by exploring cones, limits, and the most common categorical constructions – products, equalizers, pullbacks and exponentials (along with their dual constructions). The chapter concludes with a theorem on the existence of limits. Finally, Chapter 5 covers adjoints and adjunctions. Graduate and advanced undergraduates students in mathematics, computer science, physics, or related fields who need to know or use category theory in their work will find An Introduction to Category Theory to be a concise and accessible resource. It will be particularly useful for those looking for a more elementary treatment of the topic before tackling more advanced texts.

The Development of Mathematics


Author: E. T. Bell
Publisher: Courier Corporation
ISBN: 0486152286
Category: Mathematics
Page: 656
View: 3162

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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.

History of Topology


Author: I.M. James
Publisher: Elsevier
ISBN: 9780080534077
Category: Mathematics
Page: 1056
View: 9630

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Topology, for many years, has been one of the most exciting and influential fields of research in modern mathematics. Although its origins may be traced back several hundred years, it was Poincaré who "gave topology wings" in a classic series of articles published around the turn of the century. While the earlier history, sometimes called the prehistory, is also considered, this volume is mainly concerned with the more recent history of topology, from Poincaré onwards. As will be seen from the list of contents the articles cover a wide range of topics. Some are more technical than others, but the reader without a great deal of technical knowledge should still find most of the articles accessible. Some are written by professional historians of mathematics, others by historically-minded mathematicians, who tend to have a different viewpoint.

A Source Book in Mathematics


Author: David Eugene Smith
Publisher: Courier Corporation
ISBN: 0486158292
Category: Mathematics
Page: 736
View: 2062

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The writings of Newton, Leibniz, Pascal, Riemann, Bernoulli, and others in a comprehensive selection of 125 treatises dating from the Renaissance to the late 19th century — most unavailable elsewhere.

A Concise History of Mathematics

Fourth Revised Edition
Author: Dirk J. Struik
Publisher: Courier Corporation
ISBN: 0486138887
Category: Science
Page: 256
View: 1607

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Compact, well-written survey ranges from the ancient Near East to 20th-century computer theory, covering Archimedes, Pascal, Gauss, Hilbert, and many others. "A work which is unquestionably one of the best." — Nature.

Statistics for Mathematicians

A Rigorous First Course
Author: Victor M. Panaretos
Publisher: Birkhäuser
ISBN: 3319283413
Category: Mathematics
Page: 177
View: 6020

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This textbook provides a coherent introduction to the main concepts and methods of one-parameter statistical inference. Intended for students of Mathematics taking their first course in Statistics, the focus is on Statistics for Mathematicians rather than on Mathematical Statistics. The goal is not to focus on the mathematical/theoretical aspects of the subject, but rather to provide an introduction to the subject tailored to the mindset and tastes of Mathematics students, who are sometimes turned off by the informal nature of Statistics courses. This book can be used as the basis for an elementary semester-long first course on Statistics with a firm sense of direction that does not sacrifice rigor. The deeper goal of the text is to attract the attention of promising Mathematics students.

Featured Reviews in Mathematical Reviews 1997-1999

With Selected Reviews of Classic Books and Papers from 1940-1969
Author: Donald G. Babbitt,Jane E. Kister
Publisher: American Mathematical Soc.
ISBN: 9780821896709
Category: Mathematics
Page: 541
View: 8895

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This second volume of Featured Reviews makes available special detailed reviews of some of the most important mathematical articles and books published from 1997 through 1999. Also included are excellent reviews of several classic books and articles published prior to 1970. Among those reviews, for example, are the following: Homological Algebra by Henri Cartan and Samuel Eilenberg, reviewed by G. Hochschild; Faisceaux algebriques coherents by Jean-Pierre Serre, reviewed by C. Chevalley; and On the Theory of General Partial Differential Operators by Lars Hormander, reviewed by J. L. Lions. In particular, those seeking information on current developments outside their own area of expertise will find the volume very useful. By identifying some of the best publications, papers, and books that have had or are expected to have a significant impact in applied and pure mathematics, this volume will serve as a comprehensive guide to important new research across all fields covered by MR.

Mathematics and Its History


Author: John Stillwell
Publisher: Springer Science & Business Media
ISBN: 144196052X
Category: Mathematics
Page: 662
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From a review of the second edition: "This book covers many interesting topics not usually covered in a present day undergraduate course, as well as certain basic topics such as the development of the calculus and the solution of polynomial equations. The fact that the topics are introduced in their historical contexts will enable students to better appreciate and understand the mathematical ideas involved...If one constructs a list of topics central to a history course, then they would closely resemble those chosen here." (David Parrott, Australian Mathematical Society) This book offers a collection of historical essays detailing a large variety of mathematical disciplines and issues; it’s accessible to a broad audience. This third edition includes new chapters on simple groups and new sections on alternating groups and the Poincare conjecture. Many more exercises have been added as well as commentary that helps place the exercises in context.

Journey through genius

the great theorems of mathematics
Author: William Dunham
Publisher: Egully.com
ISBN: N.A
Category: Mathematics
Page: 300
View: 1685

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A rare combination of the historical, biographical, and mathematicalgenius, this book is a fascinating introduction to a neglected field of human creativity. Dunham places mathematical theorem, along with masterpieces of art, music, and literature and gives them the attention they deserve.

What's Happening in the Mathematical Sciences


Author: Barry Cipra
Publisher: American Mathematical Soc.
ISBN: 9780821889985
Category: Science
Page: 51
View: 8002

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After rave reviews for last year's issue of What's Happening, volume 2 has been eagerly awaited. Very well written, '' said one reader of volume 1. The writing is brilliant, positively brilliant.'' A terrific publication, '' said another. This is a wonderful tool for showing people what mathematics is about and what mathematicians can do.'' One reader called it a must for all mathematics department reading and coffee lounges.'' Volume 2 of What's Happening features the same lively writing and all new topics. Here you can read about a new class of solitons, the contributions wavelets are making to solving scientific problems, how mathematics is improving medical imaging, and Andrew Wiles's acclaimed work on Fermat's Last Theorem. What's Happening is great for mathematics undergraduates, graduate students, and mathematics clubs---not to mention mathematics faculty, who will enjoy reading about recent developments in fields other than their own. Highlighting the excitement and wonder of mathematics, What's Happening is in a class by itself.

The Mathematics of Various Entertaining Subjects

Research in Games, Graphs, Counting, and Complexity
Author: Jennifer Beineke,Jason Rosenhouse
Publisher: Princeton University Press
ISBN: 1400889138
Category: Mathematics
Page: 408
View: 3067

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The history of mathematics is filled with major breakthroughs resulting from solutions to recreational problems. Problems of interest to gamblers led to the modern theory of probability, for example, and surreal numbers were inspired by the game of Go. Yet even with such groundbreaking findings and a wealth of popular-level books, research in recreational mathematics has often been neglected. The Mathematics of Various Entertaining Subjects now returns with a brand-new compilation of fascinating problems and solutions in recreational mathematics. This latest volume gathers together the top experts in recreational math and presents a compelling look at board games, card games, dice, toys, computer games, and much more. The book is divided into five parts: puzzles and brainteasers, geometry and topology, graph theory, games of chance, and computational complexity. Readers will discover what origami, roulette wheels, and even the game of Trouble can teach about math. Essays contain new results, and the contributors include short expositions on their topic’s background, providing a framework for understanding the relationship between serious mathematics and recreational games. Mathematical areas explored include combinatorics, logic, graph theory, linear algebra, geometry, topology, computer science, operations research, probability, game theory, and music theory. Investigating an eclectic mix of games and puzzles, The Mathematics of Various Entertaining Subjects is sure to entertain, challenge, and inspire academic mathematicians and avid math enthusiasts alike.