Pre-announcement

MAT 494 Computer algebra and geometry

Line number 69255

CANCELED (due to low enrollment & extreme faculty shortage)

Spring 2004, MWF 12:40-1:30 p.m. in ECG 320

Please contact the instructor a.s.a.p. if you might at all be interested in this class.

This class uses the computer algebra system (CAS) MAPLE to study core concepts of classical differential geometry of curves and surfaces (in the plane and in 3-space).

Regarding computer algebra, this class is at an intermediate level with an applied, problem-solving oriented focus. This means that the use of CAS is at a considerably higher level than is typical for first and second year classes such as single and multi-variable calculus (MAT 270, MAT 271, MAT 272), linear algebra (MAT 342), and the first course in differential equations (MAT 274) which typically employ only simple one/few-line-commands.
On the other hand this class is not an advanced course that studies the theory of CAS per se as offered e.g. by the Symbolic Computation Group at the University of Waterloo or the Symbolic Computation Group at Florida State University. or the newly instituted Doctoral program in symbolic computataion at RISC-Linz.
Theoretical CAS concepts and features will be addressed on an as-need-basis, i.e., when they are important for advanced scientific applications.

This class teaches the intermediate level use of CAS in context -- i.e., it develops increasingly more advanced uses of CAS to study a specific subject. We have chosen to focus on core concepts of classical differential geometry, because this subject

is intrinsically beautiful,
is easily accessible to anyone who has a good background in multi-variable calculus (MAT 272),
is predestined to be studied using CAS as most sample calculations easily get out of hand when attempted with paper and pencil only -- yet most calculations are easily performed by a machine e.g. involving repeated differentiation and other algebraic operations),
is very useful for a variety of applications (e.g. nonlinear geometric control, manufacturing -- get Mark Henderson's course numbers - computer-aided-graphic-design -- get Gerald Farin's course numbers -)

Prerequisites:
Formally a C or better in Multi-variable Calculus MAT 272 is required. Informally the level of mathematical maturity expected is such that students feel at ease with writing simple proofs and working in somewhat abstract settings. This level is typically reached upon successful completion of Advanced Calculus (MAT 371), or even Mathematical Structures (MAT 300). But neither of these is a formal prerequisite. Another good indicator for being ready is successful completion of Intermediate Linear Algebra (MAT 342) and having enjoyed the theoretical one-third of that course.
No prior experience of using CAS is required. However, some prior experience of using MAPLE (or MATHEMATICA) in 1^st and 2^nd year calculus, linear algebra, ifferential equations is desirable. Mandatory is basic computer literacy as indicated by routine use of WINDOWS and/or LINUX/UNIX applications. Highly desirable is the successful completion of an introductory course to programming such as CSE 100 (C++, JAVA, C, PASCAL, ...) .

Class format:
The class is expected to meet in a fully mediated classroom such as ECG 320 in which all students have access to a computer. The class will be project-driven and students are generally expected to work together in teams. Rather than relying on traditional in-class paper-and-pencil exams, assessment will generally be based on in-class participation and out-of-class projects that are typically completed in teams.

Targeted audience:
Advanced undergraduate students and graduate students in mathematics, the biological and physical sciences, and engineering. Basically anyone who needs to perform nontrivial symbolic calculations in course-work, thesis-work, or in the work-place.
If appropriate, late-in-the-course projects might substitute topics of students' interest (e.g. partial differential equations) for the default concentration on differential geometry.

Further information:
Visit the WWW-site of a related spring 1998 class, and the collection of commented MAPLE worksheets (cauuion: many of these are very old and outdated...).

The class will be cancelled if too few students register for the class by early December. Thus, please contact the instructor as soon as possible if you may at all be interested in this class in spring 2004. The best way to ensure that the class will run is to find a few like-minded students and talk them into taking this class together. The more committed and the larger this group is, the easier it is to ask for modifications of the course content.....