Instructor: Michael McCourt,
Adjunct Faculty, Department of Applied Mathematics, IIT.
Email:
mccomic@mcs.anl.gov (or mccomic@iit.edu) Web Page: math.iit.edu/~mccomic/420 Office Hours and Location: MW 11-12, E1 105d
Course Contents:
This course is meant to cover various aspects of geometry, using proofs and relevant software
to study how geometric constructs exist and interact. We will consider the extension from
Euclidean geometry to non-Euclidean geometry, and we will discuss ideas from differential
geometry as used to solve problems.
A partial list of topics in this class includes:
Euclidean space and axioms
Straight lines and polygons
Designing and completing proofs
Geomtric constructions
Fractal geometries
Manifold parameterization
Curvature and torsion
Non-Euclidean geometries
Topics will be added and removed as time permits, and subject to the interests of the class.
This class will focus more on breadth than on depth, by trying to mention many topics and
connect them to applications outside of mathematics.
Enrollment:
This course can be used by mathematics
education certification option students for their master's degree mathematics requirement,
for the regular master's degree in mathematics education mathematics requirement, and endorsement
for middle school mathematics teaching in the State of Illinois.
Otherwise, this course is treated as a MATH elective.
Textbooks: Alexander Givental, Kiselev's Geometry: Book I. Planimetry,
Sumizdat Publishing, ISBN: 0-9779852-0-2.
Alexander Givental, Kiselev's Geometry: Book 2. Stereometry,
Sumizdat Publishing, ISBN: 978-0-9779852-1-0.
Material will also be drawn from other sources as needed.
Prerequisites: Math 251 and Math 332 or permission of instructor
Grading:
Class Participation: 30%, Homework: 50%, Class Presentations 20%