Syllabus/achievement requirements

This course consists of two (at times interrelated) parts:

Part I: Measure and integration

Part II: Linear operators, mostly on Hilbert spaces

Literature

• Tom L. Lindstr?m, Spaces ¡ª An introduction to Real Analysis, Pure and Applied Undergraduate Texts, vol. 29, American Mathematical Society, Providence, RI, 2017. Errata can be found here.
• Erik B¨¦dos, Notes on Elementary Linear Analysis. The notes can be downloaded here. 

The curriculum will consist of Chapter 7 and Chapter 8 (except sections 8.6¨C8.8) in Spaces plus the notes on linear analysis.

Alternative literature

It can often be helpful to look at other presentations of the curriculum. For the first part of the course, I recommend the following texts.

• Terence Tao, An introduction to measure theory, Graduate Studies in Mathematics, vol. 126, American Mathematical Society, Providence, RI, 2011.

• John N. McDonald and Neil A. Weiss, A course in real analysis, Academic Press, Inc., San Diego, CA, 1999.

Note that the material is organized differently than in Spaces, so a side-by-side comparison might prove difficult. My advice is to at least take a look at Section 2.1 on Problem solving techniques in Tao.

For the second part of the course, the following texts may be helpful and/or interesting.

• Barbara D. MacCluer, Elementary functional analysis, Graduate Texts in Mathematics, vol. 253, Springer, New York, 2009.

• Nicholas Young, An introduction to Hilbert space, Cambridge Mathematical Textbooks, Cambridge University Press, Cambridge, 1988.