CRN 11247

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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: TR 12:00-13:20 in LART 102.
  • Instructor: Dr. Helmut Knaust, Bell Hall 219, tel. 747-7002, e-mail:
  • Office Hours: I will offer frequent 30-minute office hour slots on Blackboard Collaborate Ultra. Check available times here, then send me an email message to reserve a spot one day in advance.
  • Teaching Assistant: Mr. E. Agyei-Kodie. Office hours: T 9:00-11:00, R 9:00-11:00 & 15:00-17:00 in MARCS.
  • Textbook: Stephen Abbott: Understanding Analysis, Springer-Vlg., 2nd edition, 2nd printing.
  • 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 results involving these definitions and concepts.
    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: R September 23, T October 26 and T November 23. 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 during the final period Tuesday, December 7 at 13:00-15:45. This project accounts for 25% of your grade.
  • Homework. I will regularly assign written homework. The homework will be checked, but will not contribute to your grade.
  • Graduate Credit. If you take this undergraduate course for graduate credit, you will complete an additional homework set. This assignment is due on Thursday, December 2, and will be graded for an additional 15% of your grade. (Since your possible score therefore increases to 115%, I will divide your total class score by a factor of 1.15 to get to a 100% scale.)
  • 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 29, 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.
  • CoVid-19 Precaution. Please stay home if you have been diagnosed with COVID-19 or are experiencing COVID-19 symptoms. If you are feeling unwell, please let me know as soon as possible, so that we can work on appropriate accommodations. If you have tested positive for COVID-19, you are encouraged to report your results to, so that the Dean of Students Office can provide you with support and help with communication with your professors. The Student Health Center is equipped to provide COVID-19 testing. The Center for Disease Control and Prevention recommends that people in areas of substantial or high COVID-19 transmission wear face masks when indoors in groups of people. The best way that Miners can take care of Miners is to get the vaccine. If you still need the vaccine, it is widely available in the El Paso area, and will be available at no charge on campus during the first week of classes. For more information about the current rates, testing, and vaccinations, please visit
  • Academic Integrity. All students must abide by UTEP's academic integrity policies. For detailed information visit the Office of Student Conduct and Conflict Resolution (OSCCR) website. Academic Integrity is a commitment to fundamental values. From these values flow principles of behavior that enable academic communities to translate ideals into action.” Specifically, these values are defined as follows:
    • Honesty: advances the quest for truth and knowledge by requiring intellectual and personal honesty in learning, teaching, research, and service.
    • Trust: fosters a climate of mutual trust, encourages the free exchange of ideas, and enables all to reach their highest potential.
    • Fairness: establishes clear standards, practices, and procedures and expects fairness in the interaction of students, faculty, and administrators.
    • Respect: recognizes the participatory nature of the learning process and honors and respects a wide range of opinions and ideas.
    • Responsibility: upholds personal responsibility and depends upon action in the face of wrongdoing.
  • Military Service. If you are a military student with the potential of being called to military service and/or training during the course of the semester, you are encouraged to contact the instructor as soon as possible.
  • Counseling Center. You are encouraged to go to Counseling and Psychological Services (202 Union West) for personal assistance as you work through personal concerns. Confidential counseling services are offered in English or in Spanish.
  • Disabilities. If you have a disability and need special accommodation, please contact the Center for Accommodations and Support Services (CASS). The Center aspires to provide students accommodations and support services to help them pursue their academic, graduation, and career goals. Phone 747-5148. E-mail:

Final Projects



Virtual office hours for Test 3 | Polya's How to Solve It | Checking proofs, and Greek letters | How to Write Mathematics, by Martin Erickson


September 9

Video 1

Video 2

Video 3

Personal tools