Elias M Stein Rami Shakarchi Real Analysis Reviews
 The covers of the four volumes of the Princeton Lectures in Assay | |
| |
| Author | Elias M. Stein, Rami Shakarchi |
|---|---|
| Country | United States |
| Language | English |
| Subject area | Mathematics |
| Publisher | Princeton University Printing |
| Published | 2003, 2003, 2005, 2011 |
| No. of books | 4 |
The Princeton Lectures in Analysis is a series of 4 mathematics textbooks, each covering a dissimilar area of mathematical analysis. They were written by Elias M. Stein and Rami Shakarchi and published past Princeton Academy Printing between 2003 and 2011. They are, in order, Fourier Analysis: An Introduction; Circuitous Assay; Existent Analysis: Measure Theory, Integration, and Hilbert Spaces; and Functional Assay: Introduction to Further Topics in Analysis.
Stein and Shakarchi wrote the books based on a sequence of intensive undergraduate courses Stein began pedagogy in the spring of 2000 at Princeton Academy. 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 connected until the final book was published in 2011. The series emphasizes the unity among the branches of analysis and the applicability of assay to other areas of mathematics.
The Princeton Lectures in Analysis has been identified every bit a well written and influential series of textbooks, suitable for advanced undergraduates and beginning graduate students in mathematics.
History [edit]
The first author, Elias Thou. 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.[one]
Showtime 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 nether Charles Fefferman, to turn each of the courses into a textbook. Stein taught Fourier analysis in that first semester, and past the fall of 2000 the first manuscript was almost finished. That autumn Stein taught the grade 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 banana for this course. In jump 2001, when Stein moved on to the real analysis grade, Hagelstein started the sequence anew, beginning with the Fourier assay course. Hagelstein and his students used Stein and Shakarchi'south drafts every bit texts, and they made suggestions to the authors as they prepared the manuscripts for publication.[ii] The project received fiscal support from Princeton Academy and from the National Science Foundation.[3]
Shakarchi earned his Ph.D. from Princeton in 2002[4] and moved to London to work in finance. Nonetheless he connected working on the books, fifty-fifty as his employer, Lehman Brothers, collapsed in 2008.[2] The commencement two volumes were published in 2003. The tertiary followed in 2005, and the fourth in 2011. Princeton University Press published all 4.[v] [six] [7] [8]
Contents [edit]
The volumes are dissever into seven to ten capacity each. Each chapter begins with an epigraph providing context for the fabric and ends with a listing of challenges for the reader, separate into Exercises, which range in difficulty, and more difficult Issues. Throughout the authors emphasize the unity among the branches of analysis, often referencing one co-operative within some other branch'due south volume. They also provide applications of the theory to other fields of mathematics, particularly fractional differential equations and number theory.[ii] [iv]
Fourier Assay covers the discrete, continuous, and finite Fourier transforms and their properties, including inversion. It besides presents applications to partial differential equations, Dirichlet's theorem on arithmetic progressions, and other topics.[5] Because Lebesgue integration is not introduced until the third book, the authors use Riemann integration in this volume.[4] They begin with Fourier analysis because of its cardinal role within the historical development and contemporary practice of analysis.[9]
Complex Analysis treats the standard topics of a grade in circuitous variables equally well as several applications to other areas of mathematics.[2] [x] The capacity cover the complex aeroplane, Cauchy's integral theorem, meromorphic functions, connections to Fourier analysis, entire functions, the gamma function, the Riemann zeta function, conformal maps, elliptic functions, and theta functions.[6]
Real Analysis begins with measure theory, Lebesgue integration, and differentiation in Euclidean space. Information technology and so covers Hilbert spaces before returning to measure out and integration in the context of abstruse measure spaces. It concludes with a chapter on Hausdorff measure out and fractals.[vii]
Functional Assay has chapters on several avant-garde topics in analysis: L p spaces, distributions, the Baire category theorem, probability theory including Brownian motion, several circuitous variables, and oscillatory integrals.[8]
Reception [edit]
The books "received rave reviews indicating they are all outstanding works written with remarkable clarity and care."[1] Reviews praised the exposition,[2] [iv] [11] identified the books as accessible and informative for advanced undergraduates or graduate math students,[2] [4] [nine] [10] and predicted they would abound in influence equally they became standard references for graduate courses.[2] [four] [12] William Ziemer wrote that the third book omitted material he expected to run across in an introductory graduate text but nonetheless recommended it as a reference.[11]
Peter Duren compared Stein and Shakarchi's attempt at a unified treatment favorably with Walter Rudin's textbook Existent 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 co-operative. He mentioned in item geometric aspects of complex assay covered in Lars Ahlfors'due south textbook but noted that Stein and Shakarchi also treat some topics Ahlfors skips.[4]
List of books [edit]
- Stein, Elias Grand.; Shakarchi, Rami (2003). Fourier Analysis: An Introduction. Princeton University Press. ISBN069111384X.
- Stein, Elias M.; Shakarchi, Rami (2003). Complex Analysis. Princeton Academy Press. ISBN0691113858.
- Stein, Elias M.; Shakarchi, Rami (2005). Existent Assay: Measure Theory, Integration, and Hilbert Spaces. Princeton Academy Press. ISBN0691113866.
- Stein, Elias M.; Shakarchi, Rami (2011). Functional Analysis: Introduction to Further Topics in Assay. Princeton University Printing. ISBN9780691113876.
References [edit]
- ^ a b O'Connor, J. J.; Robertson, Due east. F. (Feb 2010). "Elias Menachem Stein". Academy of St Andrews. Retrieved Sep 16, 2014.
- ^ a b c d eastward f g Fefferman, Charles; Fefferman, Robert; Hagelstein, Paul; Pavlović, Nataša; Pierce, Lillian (May 2012). "Princeton Lectures in Analysis by Elias M. Stein and Rami Shakarchi—a book review" (PDF). Notices of the AMS. Vol. 59, no. 5. pp. 641–47. Retrieved Sep 16, 2014.
- ^ Page ix of all four Stein & Shakarchi volumes.
- ^ a b c d east f g Duran, Peter (Nov 2008). "Princeton Lectures in Analysis. By Elias M. Stein and Rami Shakarchi". American Mathematical Monthly. Vol. 115, no. ix. pp. 863–66.
- ^ a b Stein & Shakarchi, Fourier Analysis.
- ^ a b Stein & Shakarchi, Circuitous Analysis.
- ^ a b Stein & Shakarchi, Real Analysis.
- ^ a b Stein & Shakarchi, Functional Analysis.
- ^ a b Gouvêa, Fernando Q. (Apr i, 2003). "Fourier Assay: An Introduction". Mathematical Association of America. Retrieved Sep 16, 2014.
- ^ a b Shiu, P. (Jul 2004). "Circuitous Analysis, by Elias Yard. Stein and Rami Shakarchi". The Mathematical Gazette. Vol. 88, no. 512. pp. 369–70.
- ^ a b Ziemer, William P. (Jun 2006). "Real Assay: Mensurate Theory, Integration and Hilbert Spaces. By Eastward. Stein and M. Shakarchi". SIAM Review. Vol. 48, no. two. pp. 435–36.
- ^ Schilling, René 50. (Mar 2007). "Existent Analysis: Measure Theory, Integration and Hilbert Spaces, past Elias M. Stein and Rami Shakarchi". The Mathematical Gazette. Vol. 91, no. 520. p. 172.
External links [edit]
- Book I at Princeton Academy Printing
- Book Two at Princeton Academy Press
- Book III at Princeton University Press
- Book IV at Princeton University Press
Source: https://en.wikipedia.org/wiki/Princeton_Lectures_in_Analysis
0 Response to "Elias M Stein Rami Shakarchi Real Analysis Reviews"
Post a Comment