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Mathematics and Its History de John Stillwell

Mathematics and Its History

Autor John Stillwell
en Limba Engleză Paperback – 13 oct 2012

Descoperim în această ediție concisă a lucrării Mathematics and Its History o abordare structurată riguros în jurul problemelor fundamentale care au modelat gândirea matematică. Reținem că prioritatea autorului nu este simpla cronologie, ci modul în care episoadele istorice — de la grecii antici la Fermat și Descartes — explică logica din spatele conceptelor de calcul, algebră sau topologie. Această versiune din 2020 a fost rafinată pentru a servi drept suport de curs pentru un singur semestru, eliminând detaliile biografice și subiectele marginale pentru a se concentra pe conexiunile neașteptate dintre ramurile matematicii. Observăm o evoluție clară în prezentare: utilizarea imaginilor color și a modelelor 3D transformă abstractizarea în intuiție vizuală, facilitând înțelegerea unor teme complexe precum funcțiile eliptice sau grupurile simple. Structura celor 25 de capitole ghidează cititorul de la Teorema lui Pitagora spre logica matematică și combinatorică, oferind o perspectivă unificată asupra curriculumului universitar. Mathematics and Its History completează perspectiva oferită de The History of Mathematics – A Brief Course 3e de R Cooke; în timp ce Cooke pune accent pe contribuțiile multiculturale globale, John Stillwell se concentrează pe coeziunea internă a ideilor matematice și pe modul în care acestea se întrepătrund. Față de lucrările sale anterioare, precum The Story of Proof, unde analiza evoluția demonstrației ca mecanism, volumul de față servește drept o sinteză a întregii matematici de licență, fiind ideal pentru un curs de tip capstone.

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Specificații

ISBN-13: 9781461426325
ISBN-10: 1461426324
Pagini: 684
Ilustrații: XXII, 662 p.
Dimensiuni: 155 x 235 x 37 mm
Greutate: 1.02 kg
Ediția:Third Edition 2010
Editura: Springer
Locul publicării:New York, NY, United States

Public țintă

Graduate

De ce să citești această carte

Recomandăm această carte studenților și profesorilor care caută o sinteză logică a matematicii universitare. Cititorul câștigă o înțelegere profundă a contextului în care au apărut teoriile moderne, beneficiind de o prezentare vizuală superioară. Este resursa ideală pentru a vedea cum algebra, geometria și analiza se unesc într-un singur corp de cunoștințe, fiind optimizată pentru studiu intensiv.

Despre autor

John Stillwell este un matematician și autor recunoscut pentru abilitatea de a sintetiza concepte complexe într-o formă accesibilă. Opera sa, publicată frecvent la edituri de prestigiu precum Springer, explorează adesea fundamentele disciplinei. În lucrări precum Yearning for the Impossible sau The Real Numbers, Stillwell a investigat tensiunea dintre intuiție și rigoarea matematică. Activitatea sa academică este marcată de un interes constant pentru istoria și filozofia matematicii, transformând evoluția ideilor într-un instrument pedagogic esențial pentru educația universitară modernă.

Cuprins

The Theorem of Pythagoras.- Greek Geometry.- Greek Number Theory.- Infinity in Greek Mathematics.- Number Theory in Asia.- Polynomial Equations.- Analytic Geometry.- Projective Geometry.- Calculus.- Infinite Series.- The Number Theory Revival.- Elliptic Functions.- Mechanics.- Complex Numbers in Algebra.- Complex Numbers and Curves.- Complex Numbers and Functions.- Differential Geometry.- Non-Euclidean Geometry.- Group Theory.- Hypercomplex Numbers.- Algebraic Number Theory.- Topology.- Simple Groups.- Sets, Logic, and Computation.- Combinatorics.

Recenzii

“Mathematics and Its History is an original, engaging and effective book, which I think would be enjoyed by students, lay readers with the right background, or indeed mathematicians themselves.” (Danny Yee, Danny Yee's Book Reviews, dannyreviews.com, March, 2019)
From the reviews of the third edition:

"The author’s goal for Mathematics and its History is to provide a “bird’s-eye view of undergraduate mathematics.” (p. vii) In that regard it succeeds admirably. ... 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. ... The author has done a wonderful job of tying together the dominant themes of undergraduate mathematics. ... While Stillwell does a wonderful job of tying together seemingly unrelated areas of mathematics, it is possible to read each chapter independently. I would recommend this fine book for anyone who has an interest in the history of mathematics. For those who teach mathematics, it provides lots of information which could easily be used to enrich an opening lecture in most any undergraduate course. It would be an ideal gift for a department’s outstanding major or for the math club president. Pick it up at your peril — it is hard to put down!"
(Richard Wilders, MAA Reviews)
“I appreciate and recommend Stillwell’s presentation of mathematics and history written in a lively style. The author’s concept (history mostly as the means of approaching mathematics) remains a matter of interest for both the mathematician and the historian … .” (Rüdiger Thiele, Zentralblatt MATH, Vol. 1207, 2011)
From the reviews 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 areintroduced 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)
"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)
"Since Stillwell treats many topics, most mathematicians will learn a lot from this book as well as they will find pleasant and rather clear expositions of custom materials. The book is accessible to students that have already experienced calculus, algebra and geometry and will give them a good account of how the different branches of mathematics interact."
(Denis Bonheure, Bulletin of the Belgian Society)

Notă biografică

John Stillwell is a professor of mathematics at the University of San Francisco. He is also an accomplished author, having published several books with Springer, including The Four Pillars of Geometry; Elements of Algebra; Numbers and Geometry; and many more.

Textul de pe ultima copertă

From the reviews 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)
"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 willbe enjoyed by the broad mathematical community."
(European Mathematical Society)
"Since Stillwell treats many topics, most mathematicians will learn a lot from this book as well as they will find pleasant and rather clear expositions of custom materials. The book is accessible to students that have already experienced calculus, algebra and geometry and will give them a good account of how the different branches of mathematics interact."
(Denis Bonheure, Bulletin of the Belgian Society)
This third edition includes new chapters on simple groups and combinatorics, and new sections on several topics, including the Poincare conjecture. The book has also been enriched by added exercises.

Caracteristici

New edition extensively revised and updated The author’s style and exposition are unique Features new exercises throughout the book Contains a new section on the Poincare conjecture Includes new chapters on simple groups and combinatorics