MATH 532/736I

Modern Geometry  - Spring 2008
Professor Robert Sharpley
Meets: TuTh   2:00-3:15 in LeConte College 405

Instructor Information
 Office:   LeConte 313 D.
 Office Hours: 1:00-2:00 pm Tue, Thur

 Teaching Assistant: Anamaria Rusu
  Office Hours: Tue & Thur 10:00a.m.-2:00p.m.
   Location: LC 105
Course Announcements For Tuesday, Apr 8, 2008:
  • Test 3 is now scheduled for Thursday, Apr 17. We will review for the test on Tuesday, Apr 15.
Recent Course Announcements:
  • The following homework was due Tuesday, March 4.
    Page 29 (Cederberg): 3,4. # 8 [Extra Credit]
    For Problem 8, you may refer to the marked-up model or prove it using the results of this section.
    Two higher resolution pdf's for the Desargues' configuration may be found by clicking the two thumbnail images:
  • Course Notes on Finite Affine Geometries are now available HERE
    • These will be updated with Figures as guides for the proofs.

  • Click HERE for a description of the construction of the Parthanon, the use of geometry and second order corrections for optical illusions created by the human visual system in processing objects using perspective geometry.

  • Escher's Art incorporating Mathematics
    Euclidean Angels
    and Devils     		Hyperbolic Angels
    and Devils
    Sketch of Hyperbolic
    Upper Half Plane     		Lizards in Hyperbolic
    Upper Half Space

Course Topics

This course is a study of modern geometry as a logical system based upon postulates and undefined terms. Projective geometry, theorems of Desargues and Pappus, conics, transformation theory, affine geometry, Euclidean geometry, non-Euclidean geometries, and topology. Students will be expected to use Geometer's Sketchpad software (available in the computer labs) to prepare a portion of the assigned homeworks. Attendence is required and the exams will be over the lectures and homework.

Prerequisites

Math 241 or Math 250 (Math 241/250)

Lecture materials drawn from Primary References.

Primary References

  1. Gilbert Lecture Notes (230 pp, 1.3 MB)
  2. A Course in Modern Geometries by Judith N. Cederberg, Springer Undergraduate Texts in Mathematics, 2005. [ISBN-0387-98972-2].
  3. The Four Pillars of Geometry by John Stillwell, Springer Undergraduate Texts in Mathematics, 2005. [ISBN-13:978-0387-25530-9].

Course Grading

Assigned Homework (10%), Three Tests (20 % each) and Final Exam(30%).

Graduate students will be required to write a term paper on a topic negotiated with the instructor, and their coursework will be graded more rigorously.

Attendance

Classroom attendance is required according to official university 10% policy. Make-up tests are not normally given for missed examinations.

Important Course Dates

Homework Assignments & Other Course Materials

   Check this LINK for homework assignments and other course materials.

 

For further information, please contact sharpley@math.sc.edu
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This page maintained by Robert Sharpley (sharpley@math.sc.edu) and last updated January 13, 2008. 
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URL: http://www.math.sc.edu/~sharpley/math532