CRN 14486
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Tiger gotta hunt. Bird gotta fly.
Man gotta sit and wonder why, why, why.
Tiger gotta sleep. Bird gotta land.
Man gotta tell himself he understand.
Kurt Vonnegut Jr.
Syllabus
- Topic. Introduction to Higher Mathematics.
- Time and Place. MW 13:30-14:50 in Bell 130
- Instructor. Helmut Knaust, Bell Hall 219, hknaust@utep.edu, 747-7002
- Office Hours. M 15:00-16:00, R 17:00-17:50, or by appointment.
- Textbook and materials. Mount Holyoke College. Laboratories in Mathematical Experimentation. A Bridge to Higher Mathematics. Springer-Verlag. Amazon lists the price at $49.95 (8/26). Bring the textbook to all class meetings. Also please bring a USB stick to all class meetings.
- Co-requisite. Calculus I (Math 1411).
- Course Description. An introduction to mathematical problem solving, experimentation, and proof writing, and the relationship among all three. The course will be built around a series of in-depth problems from a variety of areas of higher mathematics, especially those not encountered in pre-calculus and calculus courses.
- Course Objectives. This course is built on the proposition that you learn mathematics, and how to construct mathematical proofs, better when you formulate the questions and discover the answers yourself. Upon successful completion of the course, you will be able to investigate mathematical questions, big and small, both experimentally and theoretically. This is very different from courses like pre-calculus, calculus and differential equations, which are primarily focused on computations. Although there are computations in this course, they are a tool for discovering, and proving, more general mathematical truths.
- Laboratories. Class time will be devoted exclusively to labs. Each lab will start with a brief explanation of the question or problem to be explored. You will perform experiments (usually with a computer or programmable calculator) and gather data. The data will lead you to make your own conjectures, which you will then test and refine by further experimentation. Finally, when you are more certain of your conjectures, you will prove them carefully. (In practice, this process is rarely as straightforward and linear as outlined here. You will often revisit earlier steps as you carry out later steps.) You will work in small groups in class (as well as outside of class). There will also be whole-class discussions about your experimental and theoretical discoveries. After two weeks of work in class (and while you are starting the next lab), you will have a week to write up your discoveries, both experimental and theoretical, into a clearly-written report. (Grading criteria are below.) The reports are either written individually, or jointly by the members of your group. After each report is graded and returned to you, you will have approximately one more week to revise your report for a better grade, if you like.
- Grades. Each lab will be graded based on the following criteria: (1) Experimental design, (2) Organization and presentation of data, (3) Analysis of data, (4) Statement of conjectures, and most importantly (5) Mathematical analysis (including proofs) of conjectures (see p. xvii of the text). The final grade for each lab will be the average of the grades you receive on your initial report, and on your revision. If you do not turn in a revision, it will simply be the grade of your initial report. Your grade for the course will be the average of the final grades for each of the labs. Deadlines for the various assignments will be announced in class. A late submission of an assignment will result in a grade of zero.
- Mathematica. Some of the projects will use Mathematica. An introduction to this software can be found as follows: open the program, go to Help->Virtual Book->Introduction->Getting Started; alternatively watch the screencast video at http://url.wolfram.com/3.pPa0/. Mathematica is installed on many lab computers at UTEP. You can also access the program remotely from home; instructions can be found here: Remote access to Mathematica. A student version of the software is available at the UTEP Bookstore (Windows only) or at www.wolfram.com.
- Time Requirement. I expect that you spend an absolute minimum of six hours a week outside of class. 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 every class meeting. Students with four absences (excused or unexcused) will be dropped from the course with a grade of "F".
- Drop Policy. The class schedule lists Friday, October 29, 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".
- 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 cass@utep.edu, or visit their office located in UTEP Union East, Room 106. For additional information, please visit the CASS website at sa.utep.edu/cass.
- Academic Integrity. All students must abide by UTEP's academic integrity policies, see http://sa.utep.edu/studentlife/student-conduct-2/ for details.
Calendar
| Monday | Wednesday | ||
|---|---|---|---|
| August 27 | Syllabus, Farey sums | August 29 | Project 1 Day 1 |
| September 3 | (Labor Day) | September 5 | Project 1 Day 2 |
| September 10 | Project 1 Day 3 | September 12 | Project 1 Day 4 |
| September 17 | Project 1 due (individual) Project 2 Day 1 | September 19 | Project 2 Day 2 |
| September 24 | Project 2 Day 3 | September 26 | Project 2 Day 4 |
| October 1 | Project 2 due (team) Project 3 Day 1 | October 3 | Project 3 Day 2 |
| October 8 | Project 1 revision due Project 3 Day 3 | October 10 | Project 3 Day 4 |
| October 15 | Project 3 due (team) Project 4 Day 1 | October 17 | Project 4 Day 2 |
| October 22 | Project 2 revision due Project 4 Day 3 | October 24 | Project 4 Day 4 |
| October 29 | Project 4 due (team) Project 5 Day 1 | October 31 | Project 5 Day 2 |
| November 5 | Project 3 revision due Project 5 Day 3 | November 7 | Project 5 Day 4 |
| November 12 | Project 5 Day 5 | November 14 | Project 4 revision due (team) (Typesetting etc.) |
| November 19 | Project 5 due (team) Project 6 Day 1 | November 21 | Project 6 Day 2 |
| November 26 | Project 6 Day 3 | November 28 | Project 5 revision due (team) Project 6 Day 4 |
| December 3 | Project 6 Day 5 | December 5 | Project 6 due (individual) |
Materials
- Project 6 (Chapter 8): 6Padic.nb
- Project 5 (Chapter 14): 5QuadIter.nb | 501Compositions.nb | 502Repeller.nb
- Project 4 (Chapter 11): 4SeqSer.nb
- Project 3 (Chapter 9): 3Parametric.nb | 301CurveSalad.nb | 302Proof Without Words (302ooee.nb)
- Project 2 (Chapter 3): 2Euclid.nb | 201Comparison.nb
- Project 1 (Chapter 1): 1Iteration.nb | 101Intro.nb | 102Cobweb.nb
