Instructor: H. Knaust. Phone: 747-7002, email: helmut@math.utep.edu,
Office hours MW 11:30-12:20, T 2:30-3:30.

Meeting Time/Place: MR 4:30-5:50 in BH 130

Target Audience: Senior Undergraduate Math Majors, Graduate Students in Mathematics and Statistics, MAT Students.

Course Content: We will study the concept of a metric space. The rational numbers are dense in the set of real numbers: for every real number we can find a rational number arbitrarily close. If we want to consider the related question, whether and in what sense polynomials are dense in the set of continuous functions, we are naturally led to the general concept of distance between two mathematical objects. A set with a distance function is called a metric space. In the first part of the course, you will learn about basic properties a metric spaces might have such as compactness, completeness and connectedness.

As one of the most important examples of metric spaces we will then study the space of continuous functions with its notion of uniform convergence. One of the highlights of the course will be the proof of the Stone-Weierstraß-Theorem, which generalizes the result about polynomials mentioned above.

Prerequisite: Math 3341 (Introduction to Analysis), or equivalent. The prerequisite material can be found for instance in: Edward D. Gaughan, Introduction to Analysis, 5^th ed., Ch. 0-5.

Textbook: Jerrold E. Marsden & Michael J. Hoffman, Elementary Classical Analysis, 2^nd ed., W.H. Freeman and Co., New York.

In-class Presentations: The course participants will take center stage during class meetings. You will regularly give presentations of proofs of results in the textbook in class. Your presentations are the most important part of the course.

Homework: You will also be assigned written homework problems, which will be graded. Graduate students will be assigned some extra problems.

Tests: The midterm will take place on Monday, October 18. The final on Tuesday, December 13 at 4:00-6:40 is mandatory and comprehensive.