MATH 411 NON EUCLIDEAN GEOMETRY 09/06/01

Professor Joel Zeitlin Phone: 677-7796

Office: FOB 418 Office Hours: Tu W Th 1:30 – 2:30

Email: jzeitlin@csun.edu Web: http://www.csun.edu/~vcmth02q

REQUIRED TEXT: Marvin Greenberg, Euclidean and Non-Euclidean Geometries, Development and History, 3RD Edition, Freeman, 1993.

REQUIRED SUPPLEMENT: in bookstore

REQUIRED EQUIPMENT: Straight edge, compass, mathematical calculator, ... Computer ownership helpful but not required--available in campus labs. Geometer’s Sketchpad is reccommended.

OTHER SOURCES (not required)

Coxeter, Introduction to Geometry.

Beardon, The Geometry of Discrete Groups

Henderson, Experiencing Geometry in Euclidean, Spherical, & Hyperbolic Spaces, 2nd

Noronha, ….available in bookstore … new.

Rosenfeld, A History of Non-Euclidean Geometry.

Henderson web site: http://www.math.cornell.edu/~dwh/

http://www.math.yorku.ca/Who/Faculty/Whiteley/geometrysites.html/

GRADING:

• Total points from HW(& in class work) + quizzes+tests + final. I will rank the totals and use gaps (usually available) to separate grades.

• I do use + and - grades when I think it is appropriate.

• No late HW--enter quietly & hand in your work rather than waiting while answers are discussed--or mail or email it.

• Makeup tests & quizzes are practically impossible to do fairly. You can drop your lowest quiz. Talk to me ahead of time regarding any problems.

OBJECTIVES & CONTENT: To understand the elements of Non-Euclidean Geoemetry via axioms and examples --aided by constructions and transformations. We will proceed directly through Greenberg (which gives an axiomatic introduction) up to his introduction of models at least, with supplementary material to develop intuition inspired by Henderson.

In mathematics, ..., we find two tendencies present. On the one hand, the tendency toward abstraction seeks to crystallize the logical relations inherent in the maze of material that is being studied, and to correlate the material in a systematic and orderly manner. On the other hand, the tendency toward intuitive understanding fosters a more immediate grasp of the objects one studies, a live rapport with them, so to speak, which stresses the concrete meaning of their relations. David Hilbert, 1934.