Math 499w-02  -  Senior Seminar - Spring 2011, Prof. Mark Janeba
Meetings Text
TTh 2:30-4:00 p.m.
Ford  222
As has become customary for the mathematics senior seminar, we will
be writing our own text, based on an outline provided by the instructor. 

The Nature of This Course

The senior seminar is the capstone course for the mathematics major at Willamette.  As such, one of its purposes is to bring together things learned throughout your mathematical coursework.  While this will inevitably involve specific content or facts you have learned in prior courses, our primary focus in the seminar is to increase and polish the student's ability to reason mathematically, and to enhance the student's ability to reason independently.  Consequently, the specific content of any iteration of the seminar is seen primarily as a vehicle - something to reason about. 

In this edition of the seminar, our topic is Linear Fractional Transformations or Möbius Transformations, also known as bilinear maps.  Topics include a brief introduction to complex arithmetic and geometric interpretations thereof, the Riemann Sphere or one-point compactification of the complex plane and its geometric relationship with the complex plane, the geometry of linear fractional transformations on the plane and on the sphere, and the relationship of linear fractional transformations with the Poincaré disk or half-plane models of hyperbolic geometry.

Being a seminar, this course will involve virtually no lecturing by the instructor.  Rather, most class sessions will consist of student presentations of assigned problems or other material.  As instructor, I will provide an outline of the course content that has a great many carefully-chosen and explicit gaps in its reasoning.  Students will work out how to fill those gaps and present their findings in class.  Early in the semester, the gaps will be very specific and students will be assigned specific work to prepare in small groups for presentation in class.  Later in the semester the gaps will get larger, and students will need to develop more autonomy in their thinking.  If things go well, we will come to work on the material more collectively, with each student bringing to class the progress they have made on the problems at hand, and the class as a whole working through to solutions.

For each class session, two students will be assigned as scribes to record (independently) what the class accomplishes and to write up (collaboratively) the results using TeX / LaTeX.  By the end of the course, we will have produced a small book or monograph on the subject of Linear Fractional Transformations, with the entire class as authors.

As the presentation assignments become less rigid, we will have a few quizzes (four to six total).  Some will be announced in advance, some will not.  These will test basic concepts previously covered, to encourage students to keep current with the course, and assess how well they are doing so.  Likewise after the first few weeks I will be requiring students to keep a journal of their work for the class, to be collected periodically, so that I can get a clear picture of the amount and quality of work you are putting into the material.

In light of the forgoing, we have the following Course Goals:
At the completion of this course, the successful student will have demonstrated these abilities:


In-class presentations
Write-ups of class results (When assigned as scribes)
Quizzes and journals

Once we get beyond the assignment of specific problems to specific students, your presentations will be evaluated both for their quality and quantity.  Strong but infrequent contributions may be evaluated less generously than frequent contributions of moderate quality.  Regular and steady engagement with the subject is an absolute requirement.  After the first few weeks, when specific material is no longer assigned to specific students, voluntary class participation will be the only way to earn your presentation grade.  Therefore, to be successful, students must make every effort to come to every class prepared to discuss the material chosen for the day.  Students will receive feedback on a regular basis so that there are no surprises in this regard. 

Departmental Colloquium Attendance Requirement: As is the case with all 400-level mathematics courses at Willamette, students in this class are required to attend four of the semester's departmental colloquia.  The purpose of this requirement is to instill an appreciation of the breadth and variety of mathematical topics, techniques, people and (academic) programs.  If scheduling conflicts make colloquium attendance impossible, alternative short written assignments will be made.  If a student anticipates needing this alternative for more than one colloquium session, they should contact the instructor well in advance so that suitable assignments can be prepared.  Failure to complete this requirement will result in a modest grade penalty for the course.

Accommodations for students with disabilities: Accomodations required by students with disabilities will be provided upon reasonable advance notice and verification of requirement/eligibility from the Office of Disability Services (Bishop Wellness Center).  If you forsee needing an accomodation, it is probably best to inquire at the Office of Disability Services at the start of the semester.

Policy on
in-class distractions and cell phones: It is important to respect the concentration and attention of your fellow students in the class, especially in a seminar setting.  Class time is limited, precious, and the tuition is quite expensive per minute.  Arriving late for class is severely frowned upon.  Electronic devices not required for the course must be turned off during class time.  If your cell phone rings during regular class time, you will be required to bring cookies or other treats for the entire class at the next class meeting. 

Academic Honesty Expectations
Quizzes are to be taken with books and notes closed (except as noted on the quiz paper), completely on your own. Unannounced or "pop" quizzes will probably allow you to use your notes (at the instructor's discretion).  A calculator may be allowed, depending on quiz content, but palmtop computers, PDAs, laptop computers, cell phones, Blackberries, and especially any equipment that communicates wirelessly will not be allowed in quizzes and exams.

For all other coursework, you may (and should) discuss the problem, methods of approach, examples you have found, and even the solution(s), with anyone. Because this class is intended as an experience of the process of doing mathematics rather than a content-focussed course, the use of outside written sources (including internet sources) is discouraged except as noted in specific assignments.  In any case, any sources you use must be acknowledged explicitly in your work.

Plagiarism is the copying or paraphrasing of any work from another source without proper written acknowledgement.  All group members are responsible for knowing all the sources their group's members used in completing an assignment.

In keeping with college policy, plagiarism will be reported to the dean (see student handbook). Systematic or organized plagiarism will result in course failure. If you are uncertain about some aspect of the academic honesty policy, it is your responsibility to get clarification from the instructor. 

Last Modified January 16, 2011.
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