Syllabus

Instructor

Dr. Helmut Knaust, Bell Hall 124, tel. 747-7002, e-mail: helmut@math.utep.edu

Office Hours

M 16:00-16:45, after class, or by appointment.

Textbook

There is no textbook. Class notes will be provided by the instructor.

Prerequisites

The course requires a certain level of mathematical maturity that you should have gained by, for instance, having thoroughly and successfully grappled with the concept of infinity in your Calculus II course (which is the formal prerequisite for this course) and/or in Dr. Guthrie's summer course.

Course Objectives

Real Analysis is "Calculus with Proofs". You should expect (and I will expect) that you make considerable progress in the following areas:

1. Become familiar with the fundamental results of "Analysis on the Real Line" (highlights of the course include the Intermediate Value Theorem, the Mean Value Theorem, and possibly the Fundamental Theorem of Calculus);

2. Thoroughly understand the definitions of the basic concepts of Analysis such as convergence, continuity, differentiability and integration;

3. Continue to develop your ability to use the method of proof to establish these fundamental results.

4. Be able to recognize a rigorous proof when you read one. Conversely, be able to pick out the weak spot(s) in a less rigorous argument. Be able to fill in details in a sketchy proof.

5. Once you have devised a proof, be able to write it down in a clear, concise manner using correct English and mathematical grammar.

6. Be able to present and defend a proof to a group of your peers.

In-class Activities and Presentations

Mathematics is not a spectator sport. Therefore I do not give lectures. I will call on students to give presentations of exercises in the class notes. I will also regularly ask for volunteers to present solutions to tasks at the blackboard. Your presentations are the most important part of the course. Your chances of passing the course without spending a significant amount of time on preparing in-class demonstrations are zero: Your in-class work, evaluated for both quality and quantity, will account for 30% of your grade.

Writing Assignments

Every week you are required to turn in written solutions to three tasks or exercises of your choice. Unsolved problems are worth 0, 1 or 2 points; problems which have been presented in class are worth 0 or 1 points. Each problem will count only once. I do not accept late work. These assignments will contribute 20% to your grade.

Tests

Two 80-minute exams will be given on the following dates:

• Monday, September 25

• Monday, October 30

Each exam counts 15% of your grade.

Final Examination

The final exam on Monday, December 4, at 17:00-19:45, is comprehensive and mandatory. It counts 20% of your grade.

Time Requirement

I expect that you spend an absolute minimum of six hours a week outside of class on reading the textbook, preparing for the next class, reviewing your class notes, and completing assignments. Not surprisingly, it has been my experience that there is a strong correlation between class grade and study time.

Attendance

Due to the course structure, attendance is mandatory. An unexcused absence will result in an exercise/task grade of 0 for the day of the absence. Three absences (excused or unexcused) will lead to dismissal from the class with a grade of "F".

Information on the Web

This syllabus and ancillary material can also be found on my homepage http://www.math.utep.edu/Faculty/helmut.