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Journey through Mathematics de Enrique A. González-Velasco

Journey through Mathematics

Autor Enrique A. González-Velasco
en Limba Engleză Paperback – 19 aug 2014

Subliniem valoarea acestei ediții din 2011 publicată de Springer, care se distinge prin rigoarea cu care tratează evoluția conceptelor fundamentale, de la trigonometrie la convergență. Journey through Mathematics nu este o simplă cronologie, ci o analiză a procesului de creație matematică, structurată pe șase piloni tematici: trigonometria, logaritmii, numerele complexe, seriile infinite, calculul diferențial și integral, și conceptul de convergență. Notăm cu interes includerea unor surse primare care nu au mai fost traduse anterior în limba engleză, oferind cititorului contactul direct cu gândirea matematicienilor din antichitate și perioada medievală.

Putem afirma că lucrarea completează perspectiva oferită de Mathematics and Its History de John Stillwell, adăugând o analiză mult mai detaliată a surselor non-europene (din Egipt, India și lumea islamică) și concentrându-se pe „episodul” matematic în sine, mai degrabă decât pe o panoramă generală a curriculei. În timp ce The History of Mathematics – A Brief Course de R Cooke oferă o privire de ansamblu culturală, volumul lui Enrique A. González-Velasco se adresează celor care doresc să înțeleagă demonstrația tehnică din spatele marilor descoperiri.

Organizarea cărții urmărește o progresie logică a complexității. Primele capitole pun bazele geometrice și computaționale prin trigonometrie și logaritmi, pregătind terenul pentru saltul conceptual către numerele complexe și seriile infinite. Finalul volumului este dedicat calculului și convergenței, oferind o bază solidă pentru înțelegerea analizei moderne. Tonul este precis, academic dar accesibil, fiind un instrument de studiu esențial pentru viitorii profesori de matematică.

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Specificații

ISBN-13: 9781489988423
ISBN-10: 1489988424
Pagini: 480
Ilustrații: XI, 466 p.
Dimensiuni: 155 x 235 x 26 mm
Greutate: 0.72 kg
Ediția:2011
Editura: Springer
Locul publicării:New York, NY, United States

Public țintă

Lower undergraduate

De ce să citești această carte

Această carte se adresează studenților și profesorilor care doresc să depășească memorarea formulelor, înțelegând geneza lor istorică. Cititorul câștigă o perspectivă profundă asupra modului în care s-au născut concepte precum logaritmii sau calculul integral, având acces la surse primare din culturi diverse. Este un motiv concret pentru a redescoperi matematica nu ca pe un set de reguli fixe, ci ca pe un efort uman continuu și transcontinental.

Despre autor

Enrique A. González-Velasco este un matematician și cercetător cu o experiență vastă în educația academică, fiind recunoscut pentru capacitatea sa de a sintetiza istoria matematicii într-un limbaj clar pentru nivelul universitar (undergraduate). Interesul său se concentrează pe analiza matematică și pe modul în care sursele istorice primare pot fi integrate în predarea modernă. Lucrarea sa publicată la Springer reflectă angajamentul autorului față de rigoarea istorică, utilizând traduceri proprii și interpretări ale textelor clasice pentru a ilumina parcursul intelectual al marilor gânditori, de la Arhimede până la creatorii calculului modern.

Cuprins

Preface.- 1 Trigonometry.- 2 Logarithms.- 3 Complex Numbers.- 4 Infinite Series.- 5 The Calculus.- 6 Convergence.- Bibliography.- Index

Recenzii

From the reviews:
“This book is certainly to be recommended to any student of the history of mathematics who has a particular interest in any of the topics covered, particularly those whose history is less usually taught in detail at undergraduate level … . the friendly writing style, interesting tangents on etymology and biography, and the chance to discover the work of some less celebrated mathematicians still make Journey through mathematics a very agreeable read.” (Katherine Steiner, BSHM Bulletin, Vol. 28 (1), 2013)
Choice - Outstanding Academic Title in 2012
“This detailed, carefully written volume is a selective history of mathematics, up to what might be considered the ‘early modern period’ … with emphasis on 17th- and 18th-century advances. … the book particularly suitable for undergraduate mathematics students, including those planning to teach in secondary schools. The volume contains an extensive bibliography with many original sources … . A worthwhile addition to the literature. Summing Up: Highly recommended. Upper-division undergraduates through researchers/faculty.” (S. J. Colley, Choice, Vol. 49 (7), March, 2012)
“Describes the history of mathematics that gave rise to our modern concepts in calculus … . González-Velasco has done a marvelous job by sketching this very readable historical tale. … not only compulsory reading for a course on the history of mathematics, but everyone teaching a calculus course should be aware of the roots and the wonderful achievements of the mathematical giants of the past centuries. They boldly went where nobody had gone before and paved the road for what we take for granted today.” (A. Bultheel, The European Mathematical Society, March, 2012)
“González-Velasco has put together an immense amount of material that can be used in teaching some central topics in mathematics using the words of the originators. He is to be commended for all of his researchand his use of sources that are not easily available. … this book will have readers who will benefit from it, most of those will be mature readers very experienced in mathematics and its history.” (Victor J. Katz, Mathematical Reviews, Issue 2012 g)
“The book is affectionately written and one feels on nearly every page that the author eventually fell in love with his subjects. … Many illustrations from that sources as well as modern drawings and copper engravings of the mathematicians involved contribute to the readability of the text and invite the reader rummaging in the book. This is an honest book. … Students of mathematics, mathematicians with an inclination towards the history of their subject, and teachers of mathematics will profit much from this book.” (Thomas Sonar, Zentralblatt MATH, Vol. 1243, 2012)
“The book basically consists of the history of six well-known branches of mathematics … . Throughout the book there is cultural, political and biographical background as a context for the historical enquiry. There are many illustrations and excerpts from primary sources, and the author provides a feel for the way in which mathematics was created, why it was created, and how it was expressed. … this book is a highly recommended addition to the existing literature.” (P. N. Ruane, MAA Reviews, December, 2011)

Notă biografică

Enrique A. González-Velasco is a professor of mathematics at the University of Massachusetts at Lowell. His specialty is the history of math. He has also published a textbook on Fourier analysis and boundary value problems with a historical focus.

Textul de pe ultima copertă

This book offers an accessible and in-depth look at some of the most  important episodes of two thousand years of mathematical history. Beginning with trigonometry and moving on through logarithms, complex numbers, infinite series, and calculus, this book profiles some of the lesser known but crucial contributors to modern day mathematics. It is unique in its use of primary sources as well as its accessibility; a knowledge of first-year calculus is the only prerequisite. But undergraduate and graduate students alike will appreciate this glimpse into the fascinating process of mathematical creation.
The history of math is an intercontinental journey, and this book showcases brilliant mathematicians from Greece, Egypt, and India, as well as Europe and the Islamic world. Several of the primary sources have never before been translated into English. Their interpretation is thorough and readable, and offers an excellent background for teachers of high school mathematics as well as anyone interested in the history of math.
Features of this book include:
-Dozens of diagrams and photographs of original sources
-Original translation of Rafael Bombelli's contribution to the study of complex numbers
-A detailed history of the calculus as it was being written, and a new analysis of Leibniz's writings on the subject
-The first English translation of the first published proof of the fundamental theorem of Calculus, given by James Gregory in 1668
-An accessible discussion of James Gregory's work, including his invention of Taylor series forty years before Taylor
-An original English translation of extended portions of works by José Anastácio da Cunha, a little known but important contributor to the convergence of series and the differential calculus, some of whose ideas were later attributed to Cauchy

Caracteristici

An accessible and in-depth look at some of the most important episodes of about two thousand years of mathematical history Interpretation and analysis of dozens of primary sources, and several never-before-seen documents translated into English Requires only a knowledge of first-year calculus--an excellent resource for undergraduates, high school teachers, and anyone interested in the history of math Includes supplementary material: sn.pub/extras