Math 3903-001

Geometry

Fall 2009

PREREQUISITES: Successful completion of Calculus II,  interest in mathematics, willingness to work

Meetings

MWF 11:00-11:50 am D219

FINAL EXAM:  Wed., December 14, 2009, 10 am-11:50 am

Updated 18 November 2009

NOTES UPDATED 11/18/09

From previous incarnations of this course:  Some Candidate Problems for the Final Exam

SOME LINKS

Stereographic Projection Video

Proclus on the Parallel Postulate

Pictures of Surfaces

Poincare Disk

Escher-like Take on the Poincare Disk

(Note:  This is not Escher’s work, but is inspired by Escher’s work.  The Escher heirs do not take it kindly if you copy Escher’s work without permission so ask before you copy his work to your website.)

Heath’s translation of The Elements

Online, interactive copy of The Elements

Downloadable copy of Hilbert’s Foundations of Geometry

GeoGebra

KSEG

Real Projective Plane

Other Links!

 

INSTRUCTOR:  Dr. M. Dillon

OFFICE: D231
OFFICE HOURS: MWF: 12:50 pm -1:50 pm; M 3:15 pm- 4:15 pm, F 1:50 pm- 2:50 pm; also by appointment
PHONE: 678 915 4977
EMAIL: mdillon@spsu.edu

TEXT:  Notes online.  These will be updated throughout the course. Most recent installment:  pp 70-94

OTHER REFERENCES (if you are building a geometry library):   Coxeter, H.S.M, “Introduction to Geometry,”  Second Edition, John Wiley and Sons, Inc.,  New York, 1989.

 

Euclid, “The Thirteen Books of The Elements,” Vol. 1, 2 (Books I-IX), Translated with introduction and commentary by Sir Thomas L. Heath, Second Edition, Dover Publications, Inc., New York, 1956.

 

Fishback, W. T., “Projective and Euclidean Geometry,” Second Edition, John Wiley and Sons, Inc., New York, 1969.

 

Greenberg, M. J., “Euclidean and Non-Euclidean Geometries:  Development and History,” Fourth Edition, W. H. Freeman and Co., New York, 2008.  (for the history of the controversy surrounding the parallel postulate)

 

Hilbert, David, “Foundations of Geometry,”  Second English Edition, Translated by Leo Unger, Revised and Enlarged by Dr. Paul Bernays, Open Court, LaSalle, Illinois, 1999.

 

Joyce, David, “Euclid’s Elements,” complete text (Heath translation) with commentary (Joyce’s) and Java applets.  http://aleph0.clarku.edu/~djoyce/java/elements/elements.html

 

Loustau, John and Meighan Dillon, “Linear Geometry with Computer Graphics,” Marcel Dekker, Inc., New York, 1991.

 

Walker, Robert J., “Algebraic Curves,” Springer-Verlag, Berlin, 1978.

 

LEARNING OUTCOMES: The following are minimal expectations for students in this course. 

  1. Students should be able to state Euclid’s Postulates.
  2. Students should be able to explain the role of the Parallel Postulate in the development of geometry from classical to modern times.
  3. Students should be able to define the Projective Plane.
  4. Students should be able to prove theorems up to modern standards of rigor.

ATTENDANCE POLICY:  Class attendance is required for this course.

STUDENTS WITH DISABILITIES:  Students with disabilities who believe that they may need accommodations in this class are encouraged to contact the counselor working with disabilities at (678) 915 7226 as soon as possible to better insure that such accommodations are implemented in a timely fashion.

GRADING:  There will be homework assigned in class as we go, three in-class tests, and a comprehensive final exam.  

 

TESTS: The tests are scheduled tentatively for Friday, September 25, Friday, October 23, and Monday, November 23.  Tests occur approximately once a month; exact dates are subject to change. Each test is worth 100 points.   

 

FINAL EXAM:  It will be comprehensive and will include material not yet treated on tests. The final exam is worth 200 points.  

 

COURSE GRADE:  Your grade in the course will be based on 600 points distributed as follows:

 

Three tests

300 points

Homework

100 points

Final exam

200 points

 

To avoid disappointment, count on being graded according to the usual scale, that is, 540-600=A, 480-539=B, 420-479=C, 360-419=D, below 360=F.

 

Academic Dishonesty:  There is a zero tolerance policy on cheating in this course.  This policy includes copying homework problem solutions from anybody or anything, including but not limited to the internet, solutions manuals, computer programs, friends, help session tutors, or other professors. 

 

If you cheat on a test or on homework, even once, I will have you removed from the class and you will get an F in the course.  NO EXCEPTIONS.

 

RECORDING DEVICES:  The use of any and all electronic recording devices during class meetings of this course is expressly forbidden.  Electronic recording devices include, but are not limited to, cell phones, tape recorders, and video cameras.   Under certain circumstances, students with special needs may request permission of the instructor to record classes.  Permission granted under these circumstances will be strictly limited and all details will be in writing.  

 

WITHDRAW DATE:  Tuesday, October 13 is the last day to withdraw with a grade of "W".

 

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