CRN 26712

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  • Course: Math 5370 (Topics in Advanced Calculus)
  • Time and Place. TR 18:30-19:50 in BELL 130A.
  • Instructor: Dr. Helmut Knaust, Bell Hall 219, tel. 747-7002, e-mail:
  • Office hours: T 15:00-16:20, R 14:00-15:00, 30 minutes before class, after class, or by appointment.
  • Textbook: There is no textbook. Class notes will be provided by the instructor.
  • Prerequisites: The course requires knowledge of Analysis on the Real Line. Thus the prerequisite is Math 3341 or equivalent.
  • Course Content: We will study the construction of the real numbers, sequences and series of functions, uniform convergence, and transcendental functions. If time permits, we will investigate the beginnings of Complex Analysis.
  • Course Objectives: You should expect (and I will expect) that you make considerable progress in the following areas:
  1. Become familiar with fundamental results of mathematical analysis and how they relate to the precalculus and calculus topics taught in the high school curriculum;
  2. Thoroughly understand the basic concepts in Analysis such as the set of real numbers, convergence, continuity, differentiation and integration;
  3. Continue to develop your ability to use the method of proof to establish theoretical results.
  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. 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. I will not lecture. Your presentations are the essential 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 40% of your grade. See Ground Rules below for details.
  • Tests: Three exams will be given during the semester, on Tuesdays, February 20 and April 3, and Thursday, May 3. The last exam is comprehensive. Each exam counts 20% of your grade.
  • Time Requirement: I expect that you spend an absolute minimum of nine hours a week outside of class on preparing in-class presentations and reviewing your class notes. 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. Five absences (excused or unexcused) will lead to dismissal from the class with a grade of "F".
  • Ground Rules:
    • The notes distributed in class contain “exercises" and “tasks". Students will solve these problems at home and then present the solutions in class. The instructor will call on students at random to present “exercises"; he will call on volunteers to present solutions to the “tasks".
    • When in the audience, students are expected to be actively engaged in the presentation. This means checking to see if every step of the presentation is clear and convincing, and speaking up when it is not. When there are gaps in the reasoning, the students in class will work together to fill the gaps.
    • The instructor serves as a moderator. His major contribution in class will consist of asking guiding and probing questions. He will also occasionally give short presentations to put topics into a wider context, or to briefly talk about additional concepts not dealt with in the notes.
    • Students may use only the class notes and their own notes taken during the semester; they are not allowed to consult other books or materials (with the exception of the material listed at the bottom). Students must not talk about assignments to anyone other than class participants and the instructor. Students are encouraged to collaborate with other class participants; if they do, they must acknowledge other students’ contributions during their presentation. Exemptions from these restrictions require prior approval by the instructor.
    • The instructor is an important resource. He expects frequent visits from all students in class during his office hours – many more visits than in a “normal" class. Among other things, students probably will want to come to the instructor’s office to ask questions about concepts and assigned problems, they will probably occasionally want to show the instructor their work before presenting it in class, and they probably will have times when they just want to talk about the frustrations they may experience.
    • It is of paramount importance that we all agree to create a class atmosphere that is supportive and non-threatening to all participants. Disparaging remarks will be tolerated neither from students nor from the instructor.
  • Drop Policy. The class schedule lists Thursday, March 29, as the last day to drop with an automatic "W". The College of Science will not approve any drop requests after that date.
  • 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. Please note that you may not leave the classroom during a test.
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