Math 342 is our course on modern geometries. Our subject of study this year is finite geometry (but if you are interested in studying another subject, see below), choosen because of its beauty and utility (applications include coding theory). It's also a subject that is accesible to student groups of wide backgrounds, abilities, and interests:
- The subject has a short "on-ramp", so students with no 300-level experience will not feel so disadvantaged by their lack of experience with higher-level mathematics. [In fact, the sole prerequisite for Math 342 is linear algebra.] Because of the nature of the subject, Math 342 also a good course to learn and/or improve one's proof writing skills.
- The subject can be approached and appreciated with the help of tantalizing graphics, although one classical text in the subject has almost no pictures at all. Students who enjoy using their visual/spatial intelligence as an aid in appreciating mathematics will enjoy the course, as will those who would rather rely almost entirely on deductive and logical thinking.
The basic 36 lectures for the course were designed and written by Noelle Evans ('02) as part of her R.E. Lee Scholarship for the summer of 2001. [Math 342 affords a somewhat unique opportunity to take a class designed in concert with a W&L student.] Each lecture introduces the main objects and actions of the subject at hand, with a problem or two to work out. From there the student can choose to pursue the subject more deeply, or move on to the next subject.
Each student will be expected to pursue some of the subjects in depth (suitable to their own particular interests and talents), and to present some of their work to the class. Students will also present homework solutions in class, and there will be quizzes covering the basics.
Noelle Evans ('02)
Modern geometry is somewhat unique among undergraduate mathematics subjects in that there are over a dozen independent subjects that could be offered. To afford our math majors as much flexibility as possible, if there is a subject other than finite geometry that you would seriously rather study, I would be happy to talk to you about setting up an independent study course. Possible subjects include (with prerequisites in parenthesis):
1. Integral Geometry and Geometric Probability (linear algebra and multivariable calculus - a web site for this course is currently under construction, and was started by Ed Finley ('03))
2. Polyhedra (linear algebra)
3. Geometry of Singularities (multivariable calculus, big-time, along with linear algebra)
4. Algebraic Geometry (currently taking abstract algebra)
5. Differential Geometry (multivariable calculus, big-time, along with linear algebra)