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The '''''Princeton Lectures in Analysis''''' is a series of four [[mathematics]] textbooks, each covering a different area of [[mathematical analysis]]. They were written by [[Elias M. Stein]] and Rami Shakarchi and published by [[Princeton University Press]] between 2003 and 2011. They are, in order, ''Fourier Analysis: An Introduction''; ''Complex Analysis''; ''Real Analysis: Measure Theory, Integration, and Hilbert Spaces''; and ''Funcional Analysis: Introduction to Further Topics in Analysis''.
Stein and Shakarchi wrote the books based on a sequence of intensive undergraduate courses Stein began teaching in the spring of 2000 at [[Princeton University]]. At the time Stein was a mathematics professor at Princeton and Shakarchi was a graduate student in mathematics. Though Shakarchi graduated in 2002, the collaboration continued until the final volume was published in 2011. The series emphasizes the unity among the branches of analysis and the applicability of analysis to other areas of mathematics.
The ''Princeton Lectures in Analysis'' has been identified as a well written and influential series of textbooks, suitable for advanced undergraduates and beginning graduate students in mathematics.
== History ==
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The first author, [[Elias M. Stein]], is a [[mathematician]] who has made significant research contributions to the field of [[mathematical analysis]]. Beofre 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 article |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 article |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.
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