MATH 702 Texts and References
There is no adopted textbook for this course. Lectures will be based on the material that I believe are essential and useful for you to know. Such selection can't be found in a single textbook. I will try to write up useful notes when appropriate and post them here.
At the same time, there are several good analysis textbooks at this level that you can use for self-study, and to gain different perspectives on each particular topic. Here is a partial list, roughly in the order of my personal taste.
Our presentation is closest to Rudin's, but it will differ in several places.
- W. Rudin, Real and Complex Analysis, 3rd ed., McGraw-Hill, 1986
- E. Stein and R. Shakarchi, Real Analysis: Measure Theory, Integration, and Hilbert Spaces, Princeton University Press, 2005
- H. Royden and P. Fitzpatrick, Real Analysis, 4th ed., Pearson, 2010
- G. Folland, Real Analysis: Modern Techniques and Their Applications, 2nd ed., Wiley, 1999
Here are further suggestions for supplementary reading:
- J. Oxtoby, Measure and Category, 2nd ed., Springer, 1997
(A masterfully written little book with great insights on parallels and differences between measure theory and category in the topological sense of Baire.)
- T. Tao, An Introduction to Measure Theory and An Epsilon of Room 1: Real Analysis, American Mathematical Society, 2010 and 2011.
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Math 702