MT 881: Real Analysis
Time/Location: MW 11-11:50, Gasson Hall 208
Instructor: John Baldwin
Office: 545 Maloney Hall
Office Hours: By appointment
Syllabus: For a .pdf copy of the syllabus, click here.
This is a first-year graduate course in Real Analysis. Topics include measure theory, integration, differentiation of measures, Fourier transforms, Banach spaces (in particular $L^p$ spaces), Hilbert spaces.
An undergraduate course in analysis is highly recommended (two semesters are preferred), at the level of BC's Analysis I and Analysis II.
The text for this course is Real Analysis for Graduate Students (2nd edition), by Richard Bass. Fortunately, it's available for free. It is a bit dry, but very clear. I'll try and provide plenty of motivation. For outside sources of motivation, see Stein and Shakarchi's book Real Analysis: Measure Theory, Integration, and Hilbert Spaces. Another good source is Folland's Real Analysis: Modern Techniques and Their Applications.
There will be regular HW assignments, every two weeks, and a final exam at the end. HW and the final will count equally for your grade.