Princeton Lectures in Analysis: Difference between revisions

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{{Short description|Series of four mathematics textbooks}}{{italic title}}

{{Infobox book series

| name = ''Princeton Lectures in Analysis''

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The first author, [[Elias M. Stein]], was a [[mathematician]] who made significant research contributions to the field of [[mathematical analysis]]. Before 2000 he had authored or co-authored several influential advanced textbooks on analysis.<ref name=oconnor>{{cite web |first1=J. J. |last1=O'Connor|first2=E. F. |last2=Robertson |title=Elias Menachem Stein |date=Feb 2010 |publisher=[[University of St Andrews]] |url=http://www-history.mcs.st-and.ac.uk/Biographies/Stein.html |accessdate=Sep 16, 2014}}</ref>

Beginning in the spring of 2000, Stein taught a sequence of four intensive undergraduate courses in analysis at [[Princeton University]], where he was a mathematics professor. At the same time he collaborated with Rami Shakarchi, then a graduate student in Princeton's math department studying under [[Charles Fefferman]], to turn each of the courses into a textbook. Stein taught [[Fourier analysis]] in that first semester, and by the fall of 2000 the first manuscript was nearly finished. That fall Stein taught the course in [[complex analysis]] while he and Shakarchi worked on the corresponding manuscript. Paul Hagelstein, then a [[postdoctoral scholar]] in the Princeton math department, was a teaching assistant for this course. In spring 2001, when Stein moved on to the [[real analysis]] course, Hagelstein started the sequence anew, beginning with the Fourier analysis course. Hagelstein and his students used Stein and Shakarchi's drafts as texts, and they made suggestions to the authors as they prepared the manuscripts for publication.<ref name=fefferman>{{cite news |first1=Charles |last1=Fefferman |authorlink1=Charles Fefferman |first2=Robert |last2=Fefferman |authorlink2=Robert Fefferman |first3=Paul |last3=Hagelstein |first4=Nataša |last4=Pavlović |first5=Lillian |last5=Pierce|author5-link=Lillian Pierce |title=Princeton Lectures in Analysis by Elias M. Stein and Rami Shakarchi—a book review |journal=Notices of the [[American Mathematical Society|AMS]] |volume=59 |number=5 | date=May 2012 |pages=641–47 |url=httphttps://www.ams.org/notices/201205/rtx120500641p.pdf |accessdate=Sep 16, 2014}}</ref> The project received financial support from Princeton University and from the [[National Science Foundation]].<ref>Page ix of all four Stein & Shakarchi volumes.</ref>

Shakarchi earned his Ph.D. from Princeton in 2002<ref name=duren>{{cite news |first=Peter |last=Duran |authorlink=Peter Duren |title=Princeton Lectures in Analysis. By Elias M. Stein and Rami Shakarchi |journal=[[American Mathematical Monthly]] |volume=115 |number=9 | date=Nov 2008 |pages=863–66}}</ref> and moved to [[London]] to work in finance. Nonetheless he continued working on the books, even as his employer, [[Lehman Brothers]], [[Bankruptcy of Lehman Brothers|collapsed]] in 2008.<ref name=fefferman/> The first two volumes were published in 2003. The third followed in 2005, and the fourth in 2011. [[Princeton University Press]] published all four.<ref name=ss1/><ref name=ss2/><ref name=ss3/><ref name=ss4/>

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''Complex Analysis'' treats the standard topics of a course in complex variables as well as several applications to other areas of mathematics.<ref name=fefferman/><ref name=shiu/> The chapters cover the [[complex plane]], [[Cauchy's integral theorem]], [[meromorphic function]]s, connections to Fourier analysis, [[entire function]]s, the [[gamma function]], the [[Riemann zeta function]], [[conformal map]]s, [[elliptic function]]s, and [[theta function]]s.<ref name=ss2>Stein & Shakarchi, ''Complex Analysis''.</ref>

''Real Analysis'' begins with [[measure theory]], Lebesgue integration, and [[differentiation (mathematics)|differentiation]] in [[Euclidean space]]. It then covers [[Hilbert space]]s before returning to measure and integration in the context of [[Measure space|abstract measure spaces]]. It concludes with a chapter on [[Hausdorff measure]] and [[fractal]]s.<ref name=ss3>Stein & Shakarchi, ''Real Analysis''.</ref>

''Functional Analysis'' has chapters on several advanced topics in analysis: [[Lp space|L^''p'' spaces]], [[Distribution (mathematics)|distributions]], the [[Baire category theorem]], [[probability theory]] including [[Brownian motion]], [[several complex variables]], and [[oscillatory integral]]s.<ref name=ss4>Stein & Shakarchi, ''Functional Analysis''.</ref>

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[[Category:Series of mathematics books]]

[[Category:Princeton University Press books]]

[[Category:2003 non-fiction books]]

[[Category:2005 non-fiction books]]

[[Category:2011 non-fiction books]]

[[Category:Mathematics textbooks]]

[[Category:Books of lectures]]