MATH 701 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 my lecture notes and post chapters here as they become available:

Chapters 1 and 2

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 perhaps closest to Rudin's, but it will have a more geometric and modern flavor.

W. Rudin, Principles of Mathematical Analysis, 3rd ed., McGraw-Hill, 1976

C. Pugh, Real Mathematical Analysis, Springer, 2003

H. Royden and P. Fitzpatrick, Real Analysis, 4th ed., Pearson, 2010

G. Folland, Real Analysis: Modern Techniques and Their Applications, 2nd ed., Wiley, 1999

A. Kolmogorov and S. Fomin, Intoductory Real Analysis, Dover, 1975

Here are two further suggestions that aren't textbooks per se:

R. Boas, A Primer of Real Functions, 4th ed., MAA, 1997
A real gem! By all means read this little book if you haven't done so already in your undergraduate days. Full of insights and beautiful constructions.

B. Gelbaum and J. Olmsted, Counterexamples in Analysis, Dover, 2003
A key to mastering the topics in this course is the ability to produce examples/counterexamples. This book does a good job at covering classical (mostly one-variable) stuff. I suggest that you look at the table of contents, try to come up with your own examples, then compare with what the authors had in mind.

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