MATH 527, "Principles of Analysis", is a required course for first-year graduate students in the Program in Applied Mathematics. Its aim is to provide the theoretical analysis background needed for subsequent work. MATH 583, "Methods of Applied Mathematics", also required, covers methods of applied mathematics.

Some of the term papers written by my first-year students in these courses: (PDF)

Tyler McMillen (1997-8): Storing images with fractal image compression
Dmitry Kondrashov (1997-8): Geometric theory of crystal growth
Jeanine Smallwood (1997-8): Euler Euler everywhere (calculus of variations)
Sheree LeVarge (2002-3): Theory of semigroups
Matt Beauregard (2002-3): Global Attractors for Infinite-Dimensional Systems...
Suz Tolwinski (2006-7): Hilbert Transform, Empirical Mode Decomposition, and Data Analysis

A handout: Permanently unfinished notes on "Some geometry in high-dimensional spaces", (Starting point of Math 527a, Fall 2002)

Math 527 Text:   my notes on Principles of Analysis (419 pages)

The file is compressed in djvu format. The (freeware) djvu browser can be obtained from Lizardtech.com. I wrote the notes during 1988-1991, in Plain TeX with primitive macros (120MB hard drive); figures were scotch-taped onto the master. It would be a major effort to make revisions. For this reason, there are many mistakes---mathematical and typographical---that have not been corrected. Ivan Shalaev, a student in Math 527 in 2004-5, undertook to scan the manuscript; moreover, he fixed a number of errors with a photo editing program. I am very grateful for his interest and effort.