History of Mathematics: a Source-Based Approach, Volume 2

Häftad, Engelska, 2022

AvJune Barrow-Green,Jeremy Gray,Robin Wilson

1 349 kr

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The History of Mathematics: A Source-Based Approach is a comprehensive history of the development of mathematics. This, the second volume of a two-volume set, takes the reader from the invention of the calculus to the beginning of the twentieth century. The initial discoverers of calculus are given thorough investigation, and special attention is also paid to Newton's Principia. The eighteenth century is presented as primarily a period of the development of calculus, particularly in differential equations and applications of mathematics. Mathematics blossomed in the nineteenth century and the book explores progress in geometry, analysis, foundations, algebra, and applied mathematics, especially celestial mechanics. The approach throughout is markedly historiographic: How do we know what we know? How do we read the original documents? What are the institutions supporting mathematics? Who are the people of mathematics? The reader learns not only the history of mathematics, but also how to think like a historian. The two-volume set was designed as a textbook for the authors' acclaimed year-long course at the Open University. It is, in addition to being an innovative and insightful textbook, an invaluable resource for students and scholars of the history of mathematics. The authors, each among the most distinguished mathematical historians in the world, have produced over fifty books and earned scholarly and expository prizes from the major mathematical societies of the English-speaking world.

Produktinformation

Utgivningsdatum2022-12-23
FormatHäftad
SpråkEngelska
SerieAMS/MAA Textbooks
Antal sidor687
FörlagAmerican Mathematical Society
ISBN9781470472993

Tillhör följande kategorier

Matematik inom Naturvetenskap och teknik

IntroductionThe 17th and 18th centuries: Introduction: The 17th and 18th centuriesThe invention of the calculusNewton and LeibnizThe development of the calculusNewtons' $\textit{Principia Mathematica}$The spread of the calculusThe 18th century18th-century number theory and geometryEuler, Lagrange, and 18th-century calculus18th-century applied mathematics18th-century celestial mechanicsThe 19th century: Introduction: The 19th centuryThe profession of mathematicsNon-Euclidean geometryProjective geometry and the axiomatisation of mathematicsThe rigorisation of analysisThe foundations of mathematicsAlgebra and number theoryGroup theoryApplied mathematicsPoincare and celestial mechanicsCodaExercisesReferencesIndex

This volume picks up where the authors left off in their first volume (2019), from about 1650 to the start of the 20th century. The intent of these books is to ask: Who did the mathematics, and why? How was the work disseminated (or not)? How did it emerge from the culture of the time, and why is it still relevant today? The approach is to use extensive quotations from original sources as the best way to answer some of those questions. The book concludes uniquely with dozens of suggested essay exercises that are ""firmly historical, rather than primarily mathematical;"" some call for supporting or contesting claims about mathematical discoveries. The two volumes were designed for a year-long course, and they provide excellent material for a senior-level course to help students survey the mathematics that they have learned and put it into cultural and scientific context."" - Mathematics Magazine""...this volume (and the series as a whole) is an outstanding addition to the body of history of mathematics texts now available to instructors and students, providing a wonderfully rich treasure trove of primary source material. While few may choose this book as a text for a one-semester survey course on the history of mathematics, it is certainly an excellent option for those who wish to focus solely on the modern era from a professional historical perspective."" - Calvin Jongsma, Dordt University