"Tiger gotta hunt. Bird gotta fly.
Man gotta sit and wonder why, why, why.
Tiger gotta sleep. Bird gotta land.
Man gotta tell himself he understand."
Kurt Vonnegut Jr.


Math 5370 (16676 and 19451) Fall 2005

M or T 17:00-19:50 in BELL 130

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

  • Office Hours. MTR 16:30-17:00, 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:
    • 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 the Fundamental Theorem of Calculus); and
    • Thoroughly understand the definitions of the basic concepts of Analysis such as convergence, continuity, differentiability and integration;
    • Continue to develop your ability to use the method of proof to establish these fundamental results.
    • 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.
    • Once you have devised a proof, be able to write it down in a clear, concise manner using correct English and mathematical grammar.
    • 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. Occasionally, you will have short writing assignments. These assignments will contribute 15% to your grade.

  • Tests. Two 80-minute exams will be given on the following dates:
    • Monday, September 26 (or Tuesday, September 27)
    • Monday, October 31 (or Tuesday, November 1)
    Each exam counts 15% of your grade.

  • Final Examination. The final exam on Monday, December 5 (or Tuesday, December 6), 17:00-19:45, is comprehensive and mandatory. It counts 25% 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 a problem/theorem grade of 0 for the day of the absence. Three absences (excused or unexcused) will lead to dismissal from the class with the grade of "F".

  • Information on the Web. This syllabus and ancillary material can be found on my homepage http://helmut.knaust.info.

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