I would say the two volume series Analysis I and Analysis II by Terence Tao is an excellent introduction to real analysis, having learnt from those books myself. I have not gone through Spivak or Rudin in detail; I know Rudin is concise and cover. Abbott, Elementary Classical Analysis by J. E. Marsden and M. J. Hoﬀman, and Elements of Real Analysis by D. A. Sprecher. A list of analysis texts is provided at the end of the book. Although A Problem Book in Real Analysis is intended mainly for undergraduate mathematics. You do not need to buy a book for this course, but the following may be useful for background reading. If you do buy something, the starred books are recommended [1] Functional Analysis, W. Rudin, McGraw{Hill (). This book is thorough, sophisticated and demanding. [2] Functional Analysis, F. Riesz and B. Sz.-Nagy, Dover (). This is a File Size: KB. The purpose of this book is to complement the existing literature in introductory real and functional analysis at the graduate level with a variety of conceptual problems (1, in total), ranging from easily accessible to thought provoking, mixing the practical and the theoretical aspects of the subject.

: Real and Functional Analysis (Graduate Texts in Mathematics) (v. ) () by Lang, Serge and a great selection of similar New, Used and Collectible Books available now at great prices/5(19). This book works great as a reference (after having learned Real & Complex Analysis), but is a pain in the ass to learn it from. If you are looking for a good first text on Measure theory, I would recommend Eli Stein's book on Measure Theory or Folland's Real Analysis Everything contained in the book is useful, though - there are no throwaway theorems or rehashed proofs of earlier material/5. Analysis, Real and Complex Analysis, and Functional Analysis, whose widespread use is illustrated by the fact that they have been translated into a total of 13 languages. He wrote the first of these while he was a C.L.E. Moore Instructor at M.I.T., just two years after receiving his . Topics in Real and Functional Analysis by Gerald Teschl. Publisher: Universitaet Wien Number of pages: Description: This manuscript provides a brief introduction to Real and (linear and nonlinear) Functional Analysis.

The real numbers. In real analysis we need to deal with possibly wild functions on R and fairly general subsets of R, and as a result a rm ground-ing in basic set theory is helpful. We begin with the de nition of the real numbers. There are at least 4 di erent reasonable approaches. The axiomatic approach. As advocated by Hilbert, the real File Size: KB.