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Survey of Geometry Homepage |
Farris |
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Math 101 #39385 |
Spring 2004 |
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Daly Science 203 |
TR 9:55-11:40 |
Links:
Scott Serano's animation of cube-slicing, Farris's Java applet for constructing frieze patterns.
Geometry is a vast field with a rich history and delightful vistas. Our course has two principal goals: working as a generalist, you will acquire a broad view of the whole of geometry, both as a historical subject and a living discipline; you also will carry out a specialized inquiry into a particular topic of your own choice, discovering something for yourself and presenting the results in written and oral form. Bring cheerful energy and vigorous enthusiasm and our course will be fun for all of us.
Source materials: Our course will follow the excellent text, The Geometric Viewpoint, a Survey of Geometries, by Thomas Q. Sibley. The order of our course may surprise you: we will begin each of the first four chapters in the first four class meetings. Homework problems and ideas for projects will be drawn from this text. A variety of software and electronic resources will help us see what’s going on: Geometer’s Sketchpad, is installed on laptops in our classroom, as well as in the O’Connor labs; it seems that everyday there are more websites devoted to illuminating some facet of geometry. A former student in this course created a page of links that is still posted. Choose Suzuki’s links from our course page.
Course requirements: I will assess your work in five categories, each worth 100 pts: your class presentation and overall participation, a notebook of well-written homework solutions, evaluated by your peers, one take-home exam, four quizzes, and a research project. Each of these is explained below.
Course calendar:
During the first two weeks of class, I will give presentations meant to introduce you to the broad themes of our course: Euclidean and noneuclidean geometries and transformation groups. I will demonstrate the software that you may want to use for your own class presentations.
4/6 Schedule of student presentations will be set by this date. I have plans for 8 half-hour presentations by student groups between 4/20 and 5/11, with 2 students per presentation. A list of presentation topics and dates will be available soon. Work with me in advance to plan handouts, software needs, transparencies. I will continue to offer class activities, cleaning up around the edges so that the student presentations can highlight the most interesting features of the chosen material.
4/13 Quiz I. The other quizzes will be 4/22, 5/11, and 5/27.
4/22 Your proposal for your research project is due. Work alone or with one other student to research a topic that interests you. Your presentation group may be different from your research group. I will provide a variety of choices that range from computer-intensive to low-tech reading and writing, from ancient history to modern unsolved problems, from physics to the fourth dimension. The ideal is for you to discover something for yourself. The results of your inquiry will be presented in two ways: a public presentation (see below) and a short written paper . Although you will work in a group with other students, you must write your own paper, and submit it to me electronically. Papers are subject to review by TurnItIn.com, a service that checks papers for originality.
4/29 Receive Take-home Midterm Exam, which will be due Monday 5/3 by 4 PM.
5/27 Notebook due. This should consist of five (such a small number!) well-written solutions selected from the "notebook problems" mentioned below. Each problem must have a Review Form attached, each one filled out by a different student in our class. Of course, this means you have to review problems for other people’s notebooks. The Review Form explains the rules. I also ask you to take two Journal questions (described below) and turn them into one-page "personal essays."
During the last three weeks of class, I will resume my role as principal presenter of material, leaving you free to work on the last stages of your research.
6/10 Instead of a final exam, we will produce a Geometry Festival, with student groups presenting the results of their research projects. Typically, you will have a story that would really take half an hour to tell, but you have to condense it to fit in 15 or 20 minutes. In the past, other students and professors have attended this event and found it entertaining. (The Festival runs 9:10-12:10.)
Homework: It can be enjoyable to listen to someone else talk about geometry, but the real test of your understanding is solving problems for yourself. Homework will come in four flavors: study problems, turn-in problems, notebook problems, and journal entries.
Study problems are assigned as exercises to help you digest the material. These will not be collected or graded, but you will have a chance to present your solutions in class (working toward a high score in participation). It would be reasonable for a study problem to have a reincarnation as an exam question. Turn-in problems are just that: Our grader will evaluate your work for correctness and effort.
Notebook problems merit careful written solutions, about a page in length. In order to end up with five satisfying solutions for your notebook, you should attempt all the notebook problems assigned.
Journal entries: A journal is a way to keep track of your own ideas, to gain perspective on them by reading them after some time has passed. When a journal entry is assigned, spend just ten minutes writing down your thoughts about that topic. What will this do for you? When the time comes to discuss this topic in class, you will have something on paper to remind you of what you think about it; and should this topic come up as an essay on an exam, you will have already written a draft. I ask you to write up two of your journal entries to add to your notebook.
Contact your professor! Office hours: MW 2:45-3:45 Tu/Th 1:15-2:15 in O’Connor 314, x4430. Email: ffarris@scu.edu. Web: math.scu.edu/~ffarris .
First homework assignment: Study: 1.1/ 1, 3, 6, 7ab; 1.2/1, 3, 6, 15
Turn-in: 1.1/ 5, 9, 10, 1.2/ 7, 9
Toward Your Notebook: Problems 1.2/ 4, 12; explain clearly how to construct a regular pentagon. Journal Without looking at your text, describe Euclid’s elements. How would you describe what was unique about Euclid’s achievement?