Mathematics: Anyl in Several Real Vars I

Properties of the real numbers, basic topology of metric spaces, infinite sequences and series, continuity. Prerequisites: MATH 2468 or MATH 2551 or C- or better in MATH 2055; MATH 2248; MATH 2522 or MATH 2544.

Prereqs enforced by the system: (MATH 2055 or 2468 or 2551) and MATH 2248 and (MATH 2522 or 2544); Open to Degree and PACE students

The text for the class will be 'Mathematical Analysis' (second edition) by Tom Apostol. We will cover significant portions of chapters 1-4, 8. If time permits we'll go back and do some of 5. This material includes: basic properties of the real numbers, basic set theory, metric (Euclidean) topology in R^n, general metric space topology, sequences and convergence in R^n and metric spaces, continuity and its consequences, infinite series. Chapter 5 gives a rigorous intro to the theory of the derivative.

Read the assignments, come to class, do the homework, take the exams. Come to office hours or otherwise contact me if you have questions.

The grade will be based on a weighted average of scores from homework, a midterm, and the final exam: 60% homework, 15% midterm, 25% final. From past experience, I expect that there will be between 5 and 7 large homework sets, which the students should begin as soon as they are passed out.