CRN 15606

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Syllabus (Under Construction)

  • Course: Math 5370 (Topics in Advanced Calculus)
  • Time and Place.
  • Instructor: Dr. Helmut Knaust, Bell Hall 219, e-mail:
  • Office hours: , 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, and as time permits: p-adic numbers, sequences and series of functions, uniform convergence, and/or transcendental functions.
  • 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.
  • Discussion Board. You will post solutions, questions, corrections, comments and improvements online, on BlackBoard's Discussion Board. Start by reading the announcements on the board.
  • In-class Activities: Mathematics is not a spectator sport. I will not lecture. You will prove the statements given to you in handouts and post your findings on the BlackBoard Discussion Board. Your chances of passing the course without spending a significant amount of time on working on these problems are zero: Your contributions to the Cyberboard, evaluated for both quality and quantity, will account for 40% of your grade. See Ground Rules below for details.
  • Tests and Final: Two tests will be given during the semester, on Mondays March 6 and April 24. The final on Thursday, May 11, 19:00-21:45, is comprehensive. Each of the three exams 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.
  • Drop Policy. The class schedule lists Thursday, March 30, as the last day to drop with an automatic "W". After the deadline, I may only be able to drop you from the course with a grade of "F".
  • 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 by 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 747-948. E-mail:

    • The notes distributed in class contains numerous “tasks". You should try to prove as many of the tasks as you can for yourself. (On the Discussion Board you can only get credit for at most two problems per week.)
    • You are also expected to be actively engaged in the discussions on the Discussion Board. This means challenging the presenter to see if every step of the presentation is clear and convincing, and insisting when it is not. When there are gaps in the reasoning, you may help to fill the gaps.
    • The instructor serves as a moderator. His major contribution will consist of posting guiding and probing questions. He may also occasionally give short video 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 notes listed in the Materials section below 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 on the other hand are encouraged to collaborate with other class participants; if they do, they must acknowledge other students’ contributions during their posts on the Cyberboard. Exemptions from these restrictions require prior approval by the instructor.
    • The instructor is an important resource. The office hours are usually well attended by students – much more so than in a “normal" class. Among other things, students probably will want to ask questions about concepts, assigned problems or their posts on the board, they will probably occasionally want to show the instructor their work before posting it, 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 oral or written remarks will be tolerated neither from students nor from the instructor.


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