Fourier (and more generally harmonic) analysis grew out of the study of Fourier series and is one of the most active and beautiful areas of mathematics. It's modern applications touch on areas as pure as group theory and as applied as wavelets (the basis of the JPEG 2000 compression scheme), signal processing, and quantum mechanics.
This course will be a fantastic follow-up to real analysis (but this course has a decidedly less epsilon-delta feel to it). It will be especially helpful for anyone going on to graduate school in mathematics or physics (we'll do a lot with the Fourier integral transform, an indispensable tool in applied math and physics, but one which few Rose students ever see.)
A few topics we'll consider:
The actual course work will consist of homework assignments every 1 to 2 weeks, and a couple of take-home exams. The textbook will be "Fourier Analysis and Its Applications" by Gerald Folland. Folland is a first-class expositor, and this is really an excellent book. Go check it out on Amazon .