MATH 240C: Real Analysis
Spring 2019
Instructor:
Jacob Sterbenz
Links
240C
Home
Syllabus
Meetings
Schedule
Homework
Qual
Notes
240ABC Syllabus
- Detailed
Syllabus of material in Folland covered prior to the qual. Please note that while the
qualifying exam will not cover every topic on this list, one should have a good familiarity
with this material prior to attempting the exam.
Resources and References
The following will also be used as HW sets this
quarter:
Here are some additional resources:
- Terry Tao's course notes from a similar analysis qual class at UCLA:
- 245A:
Basic
measure and integration.
- 245B:
Point-set
topology and functional analysis.
- 245C:
Includes
Fourier transform, Sobolev spaces, and interpolation.
- Useful texts:
- "Real
Analysis:
Modern Techniques and Their Applications", G.B. Folland.
- This is the primary reference for 240ABC as well as
the real analysis qualifying exam.
- "Analysis",
E.
Lieb and M. Loss.
- This is a secondary reference for 240ABC.
The chapters on rearrangements and the HLS inequality will not
be on the qual, although these ideas often come up in practice. Overall
this text is recommended for those students who plan to go on reading
research articles in analysis and PDE.
- "Real
Analysis:
Measure Theory, Integration, and Hilbert Spaces", E. Stein
and R. Shakarchi.
- This is perhaps the best reference for an introduction
to Lebesgue measure on Rn. There is also a good coverage of other
material including abstract measure theory and differentiation, and the
spectral theorem for compact operators on a Hilbert space.
- "Real
Analysis
(3d edition)" H. Royden.
- A classic introduction to real variables, especially
one dimensional Lebesgue measure. The first few chapters are often used
as an undergraduate text these days.
- "Real
and
Complex Analysis" W. Rudin.
- Another classic text on real analysis. Notable for its
unified treatment of basic ideas in measure and integration, functional, Fourier,
and complex analysis.
- "An
Introduction to Measure Theory" T. Tao.
- Includes much of the material from Tao's blog site for
UCLA 245A, which is similar to our 240A.
- "An
Epsilon
of Room, I: Real Analysis" T. Tao.
- Includes much of the material from Tao's blog site for
UCLA 245ABC, similar to our 240ABC.
- "Integration
and
Modern Analysis" J. Benedetto and W. Czaja.
- A very good introduction to a wide range of topics in
measure theory. Includes an excellent supply of exercises and
historical material.