This course is designed to be a "bridging course" between undergraduate analysis and graduate real analysis. The course will cover some topological notions on the real line, continuous functions, the Riemann integral, measure theory and the Lebesgue integral. If time permits, topics in Fourier series will also be discussed. This course is suitable for students who are not quite ready for Math 607 (Real Variables) or who would rather see a concrete construction of measure and integration (as opposed to the more abstract approach taken in Math 607).
The required textbook is The Way of Analysis by Robert Strichartz , published by Jones and Bartlett, 1995. We will cover chapters 3, 4, 6, 14 and (if time permits) 12.
The prerequisite for this course is Math 409 (Advanced Calculus I) or its equivalent. The essential background you need is familiarity with the kind of analytic reasoning used in "epsilon-delta proofs".
The course meets Tuesday and Thursday, 9:35-10:50am in BLOC 624. Office Hours are Monday thru Thursday 1:30-2:30pm. in BLOC 623. If those times are inconvenient, you can set up an appointment by e-mailing me (boggess@math.tamu.edu) or by calling 845-3261.
Course grades will be determined by homework (25%); an in-class presentation (10%); a take-home midterm exam (30%) and an in-class final exam (35%). You may collaborate with other students on the homework. No collaboration is allowed on the take-home mid-term and the final exam. Books and notes are allowed on the mid-term. No books or notes are allowed on the final exam.