CRN 15606

Syllabus

• Course: Math 5370 (Topics in Advanced Calculus)

• Time and Place. TR 18:30-19:50, BELL 130A

• Instructor: Dr. Helmut Knaust, Bell Hall 219, e-mail: hknaust@utep.edu

• Office hours: TR 12:00-13:00, 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, 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. Thoroughly understand the basic concepts in Analysis such as the set of real numbers, convergence, continuity, differentiation and integration;
2. Continue to develop your ability to use the method of proof to establish theoretical results.
3. 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.
4. Be able to present and defend a proof to a group of your peers.

• In-class Activities: 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 and Final: Two tests will be given during the semester, on the following days: Tuesday, October 8 and Thursday, November 14. The final on Thursday, December 12, 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 Friday, November 1, 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".

• Attendance. You are strongly encouraged to attend class every day.

• Academic Integrity. All students must abide by UTEP's academic integrity policies. For detailed information visit the Office of Community Standards (OCS) website. Academic Integrity is a commitment to fundamental values. 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, please 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. Phone: 747-5302.

• 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: cass@utep.edu.

• Ground Rules:
  • The notes distributed in class contain numerous “tasks". Students will solve these problems at home. The instructor will then call on volunteers to present solutions to the “tasks" in class.
  • 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.

Materials

• Chapter 4
• A Primer on Equivalence Relations
• Chapter 2-3
• Chapter 1
• Proof Types (P. Kirby)