CRN 11982

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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.

  • Time: MW 15:00-16:20 in LART 304.
  • Instructor: Dr. Helmut Knaust, Bell Hall 219, tel. 747-7002, e-mail:
  • Office Hours: MW 14:00-15:00, F 13:00-14:00 or by appointment.
  • Teaching Assistant: Pawel Masior, office hours M 12:00-13:00, W 12:00-12:30 in BELL 306.
  • Textbook: Stephen Abbott: Understanding Analysis, Springer-Vlg. The book is available at Amazon for $36.80 (8/19/2014).
  • Prerequisites: The course requires a certain level of mathematical maturity that you have gained by having thoroughly and successfully grappled with the concept of infinity in MATH 1312 as well as with the basics of logic and proofs in MATH 3325.
  • 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, differentiation and integration;
  3. Continue to develop your ability to use the method of proof to establish these fundamental results.
    Modified Dirichlet function
  4. Be able to recognize a rigorous proof when you read or see 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. Improve your ability to communicate Mathematics verbally.
  • Tests: Three exams will be given on the following days: September 24, October 22 and November 26. Each exam counts 25% of your grade. The third exam is comprehensive.
  • Final Project: Student groups will complete a final project and present the results in class and in a written report at the end of the semester (Wednesday, December 3, during class time & Monday, December 8, 13:00-15:45). This project accounts for 25% of your grade.
  • Homework. I will regularly assign written homework. The homework will be graded, but will not contribute to your grade.
  • Time Requirement. I expect that you spend an absolute minimum of six hours a week outside of class on working on the homework assignments, reading the textbook, and preparing for the next class. Many of you will need to spend more time than the minimum mentioned above. Not surprisingly, it has been my experience that there is a strong correlation between class grade and study time.
  • Drop Policy. The class schedule lists Friday, October 31, as the last day to drop with an automatic "W". After the deadline, I can only drop you from the course with a grade of "F". The College of Science has recently adopted the following policy: If students have attempted a course three times without passing (a drop counts as an attempt), they may not take the course a fourth time at UTEP.
  • Students with Disabilities. If you have a disability and need classroom accommodations, please contact The Center for Accommodations and Support Services (CASS) at 747-5148, or by email to, or visit their office located in UTEP Union East, Room 106. For additional information, please visit the CASS website at
  • Academic Integrity. All students must abide by UTEP's academic integrity policies, see for details.

Final Projects



Homework layout | Polya's How to Solve It | Checking proofs, and Greek letters | How to Write Mathematics, by Martin Erickson.

Mathematica notebooks: Alternating Harmonic Series I | Alternating Harmonic Series II

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