CRN 23666

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"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 17:00-18:20 in UGLC 216
  • Instructor. Helmut Knaust, Bell Hall 219,, 747-7002
  • Office Hours. TR 16:00-16:50, or by appointment.
  • Principles8.jpg
    Textbook. D. Smith, M. Eggen, R. St. Andre. A Transition to Advanced Mathematics, 8th edition. Brooks/Cole.
  • Prerequisites. The course requires a certain level of mathematical maturity that you should have gained by, for instance, having thoroughly and successfully grappled with the concept of infinity in your Calculus II course (which is the formal prerequisite for this course).
  • Course Objectives. This is a Foundations course. This means that hardly any prior knowledge is required. The class prepares you "do" mathematics on your own and enables you take more advanced classes or read rigorous mathematical textbooks. You should expect (and I will expect) that you make considerable progress in the following areas:
  1. Make sense of an abstract definition by analyzing it carefully and constructing examples.
  2. Make sense of a mathematical statement and be able to bring to bear a variety of strategies for constructing its proof.
  3. Be able to recognize a rigorous proof when you read 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. Once you have devised a proof, be able to write it down in a clear, concise manner using correct English and mathematical grammar.
  5. Be able to present and defend a proof to a group of your peers.
  • Class Participation and Activities. Daily homework exercises will be presented by volunteers during the following class period. There may also be some in-class activities. Your participation will contribute 15% towards your grade.
  • Homework. I will also regularly assign written homework. The homework will be graded (or presented by student volunteers) but will not contribute to your grade.
  • Tests. Exams will be given on the following days: Tuesday, February 19, Thursday, March 26 28, and Thursday, April 23 25. Each exam counts 20% of your grade. You may not leave the classroom during tests or the final.
  • Final Examination. The final exam on Tuesday, May 14, 16:00-18:45, is comprehensive and mandatory. It counts 25% of your grade.
  • Time Requirement. I expect that you spend an absolute minimum of six hours a week outside of class on reading the textbook, preparing for the next class, reviewing your class notes, and completing assignments. Not surprisingly, it has been my experience that there is a strong correlation between class grade and study time.
  • Attendance. You are strongly encouraged to attend class.
  • Drop Policy. The class schedule lists Friday, April 5, 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".
  • 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:

Homework (in-class)

  • Open Problems: 3.2: 1dfh,4c,6ae,15ab; 3.3: 3ac,4c,8; 3.5: 1e,2a,5,8,10a,11b,13bde,16a; 4.1: 3df,18b

  • 5/7 4.2: 1c,10,15; 4.3: 1dfh,2dfh,10ab,11
  • 4/30 4.1: 3bdf,6b,8,18ab
  • 4/16 3.5: 1be,2a,5,8,10a,11b,13bde,16a
  • 4/11 3.3: 3ac,4c,8,9d
  • 4/2 3.1: 2,3d,6f,7afh,11ab; 3.2: 1dfh,2bc,4c,6ace,15ab
  • 3/12 2.5: 5c,6bc,8a
  • 3/7 2.4: 4k,5o,6dh
  • 2/28 2.3: 1cn,3b,7b,10b,11b,17b,18c
  • 2/26 2.1: 4a-d,5c-f,16a; 2.2: 9cf,12a,12b-c,15b16a
  • 2/12 1.6: 1bf, 2a,4f,5a,7
  • 2/5 1.4: 5cfi,6d,7dl,9d; 1.5: 4d,5a,10
  • 1/29 1.3: 1cdef,5,6bc,8hk
  • 1/24 1.2: 1bce,3ac,5bd,7ad,16bi
  • 1/22 1.1: 1bg,2ce,3hl,6abc,8b

Written Homework

Homework 7, due 5/9 | Homework 6, due 4/18 | Homework 5, due 4/11 | Homework 4, due 3/26 | Homework 3, due 3/12 | Homework 2, due 2/14 | Homework 1, due 2/7 2/12


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