Princeton Lectures in Analysis: Difference between revisions

Revision as of 04:35, 18 September 2014

Revision as of 23:05, 21 September 2014

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== History ==

[[File:Elias Stein.jpeg|thumb|Elias M. Stein]]

The first author, [[Elias M. Stein]], is a [[mathematician]] who has 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. |last2=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 articlenews |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 |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 |month=May |year=2012 |pages=641–47 |url=http://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 articlenews |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 |month=Nov |year=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/>

== Contents ==

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== Reception ==

The books "received rave reviews indicating they are all outstanding works written with remarkable clarity and care."<ref name=oconnor/> Reviews praised the exposition,<ref name=fefferman/><ref name=duren/><ref name=ziemer/> identified the books as accessible and informative for advanced undergraduates or graduate math students,<ref name=fefferman/><ref name=duren/><ref name=gouvea>{{cite web |first=Fernando Q. |last=Gouvêa |url=http://www.maa.org/publications/maa-reviews/fourier-analysis-an-introduction |title=Fourier Analysis: An Introduction |publisher=[[Mathematical Association of America]] |date=Apr. 1, 2003 |accessdate=Sep. 16, 2014}}</ref><ref name=shiu>{{cite articlenews |first=P. |last=Shiu |title=Complex Analysis, by Elias M. Stein and Rami Shakarchi |journal=The Mathematical Gazette |volume=88 |number=512 |month=Jul |year=2004 |pages=369–70}}</ref> and predicted they would grow in influence as they became standard references for graduate courses.<ref name=fefferman/><ref name=duren/><ref name=schilling>{{cite articlenews |first=René L. |last=Schilling |title=Real Analysis: Measure Theory, Integration and Hilbert Spaces, by Elias M. Stein and Rami Shakarchi |journal=The Mathematical Gazette |volume=91 |number=520 |month=Mar |year=2007 |page=172}}</ref> William Ziemer wrote that the third book omitted material he expected to see in an introductory graduate text but nonetheless recommended it as a reference.<ref name=ziemer>{{cite articlenews |first=William P. |last=Ziemer |title=Real Analysis: Measure Theory, Integration and Hilbert Spaces. By E. Stein and M. Shakarchi |journal=SIAM Review |volume=48 |number=2 |month=Jun |year=2006 |pages=435–36}}</ref>

[[Peter Duren]] compared Stein and Shakarchi's attempt at a unified treatment favorably with [[Walter Rudin]]'s textbook ''Real and Complex Analysis'', which Duren calls too terse. On the other hand, Duren noted that this sometimes comes at the expense of topics that reside naturally within only one branch. He mentioned in particular geometric aspects of complex analysis covered in [[Lars Ahlfors]]'s textbook but noted that Stein and Shakarchi also treat some topics Ahlfors skips.<ref name=duren/>