CRN 10631

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Syllabus for Math 3341

"Contrariwise," continued Tweedledee, "if it was so, it might be; and if it were so, it would be; but as it isn't, it ain't. That's logic."
Lewis Carroll

  • Time and Place: TR 12:00-13:20 in LART 202.
  • Instructor: Dr. Helmut Knaust, Bell Hall 124, tel. 747-7002, e-mail:
  • Office Hours: TR 13:30-15:00, or by appointment
  • Textbook: There is no textbook. Class notes will be provided by the instructor.
  • 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 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, and hopefully the Mean Value Theorem and 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.
  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. Therefore I do not give lectures. I will call on students to give presentations of exercises in the class notes. I will also regularly ask for volunteers to present solutions to tasks at the blackboard. Your presentations are the most important part of the course. Your chances of passing the course without spending a significant amount of time on preparing problems to present in class are zero: Your in-class work, evaluated for both quality and quantity, will account for 30% of your grade.
  • Tests: Two exams will be given on the following Thursdays: October 5 and November 16. Each exam counts 20% of your grade. You may not leave the classroom during tests or during the final.
  • Final Examination: The final exam on Tuesday, December 12, 13:00-15:45, is comprehensive and mandatory. It counts 30% of your grade.
  • Graduate Credit: If you take this undergraduate course for graduate credit, you will write up solutions to some additional problems. Please let me know at the beginning of the semester!
  • Time Requirement: I expect that you spend an absolute minimum of at least six hours outside of class on reviewing your own notes and preparing problems for the next class. 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. Six absences (excused or unexcused) will lead to dismissal from the class with a grade of "F".
  • Drop Policy. The class schedule lists Friday, November 3, 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.
  • 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:


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