Geometry

Math 342 - Spring 2006

Syllabus and assignments

 

 

 

 

 

 

office hours

 

 

 

Instructor: Dr. C. Edward Sandifer

Office: Higgins 219 C

Office Phone: (203) 837-9362

eMail:  SandiferE (at) WCSU.edu

 

Office hours:  click here: office hours

 

Meets:  Higgins 110 TuTh 8:00 - 9:15

 

Book list: Roads to Geometry, 3rd Edition, by Edward C. Wallace and Stephen F. West, Pearson/Prentice Hall, ISBN 0-13-041396-8

 

Final Exam -Tuesday, May 16 at 11:00 am

 

 

Course description from the catalog

 

MAT 342 Topics in Geometry 3 SH
The central theme of the course is the study of many different geometries, rather than a single geometry. The focus will be on those geometries that have been developed since 1800 with references back to the geometry of Euclid. Prerequisite: MAT 242 or permission of the instructor. Spring semester.

 

Expect to cover: Almost all of chapters 1, 2 and 3 of the textbook, and parts of chapters 4 and 6.  See additional details at the bottom of this page

 

Expected course requirements:

 

  1. Two or three hour exams (100 points each)

  2. Final exam, during exams week (200 points)

  3. Project.  Find a theorem first proved by one of the geometers on the list below.  Prepare a presentation (poster and short talk).  You may want to coordinate this with your Math History project, if you are taking that course this semester  (50 points)

  4. Homework, from book.  See list below (10 to 20 points per assignment)

  5. Other homework: involving Lenart Spheres.  Details to follow

  6. On Line quizzes, using WebCT - (5 to 20 points each)

 

Grading:

The worth of an assignment is exactly proportional to the number of points on the assignment.  

Corollaries:

  1. The final exam is worth the same as two hour exams

  2. The project is worth half as much as an hour exam

  3. An hour exam is worth five to ten times as much as an hour exam

Honesty:

  1. Do not represent someone else's work as your own.  

  2. Do not do anything with regard to this course that you would be ashamed to admit to the Instructor.

Within these parameters, I want to encourage a culture of community learning, where people help each other learn and support each other's dreams, ambitions and success.

 

 

Hit Counter   since January 30, 2006

 

Homework assignments from the Book.  Due dates will be announced in class, and posted on the course home page.

 

1.    Ch 1.3       p 24            5,6,7,8,30

2.    Ch 2.6       p 71            6, 10, 11

3.    Ch 3.2       p 88            6, 7, 8, 10

4.    Ch 3.3       p 94            1, 10

5.    Ch 3.4       p 101           2

6.    Ch 3.5       p 106           1

7.    Ch 3.6       p 115           2, 3, 4, 5, 6, 14, 15, 16

 

List of modern (since 1600) geometers (in alphabetical order)

 

  1. Beltrami

  2. Birkhoff, G. D.

  3. Bolyai

  4. Coxeter, HSM

  5. Desargues

  6. Descartes (1596-1650)

  7. Euler (1707-1783)

  8. Fano, Gino (1871-1952)

  9. Fermat (1605-1665)

  10. Gauss (1777-1855)

  11. Gergonne

  12. Heath , Sir Thomas Little, FRS (1861-1940)

  13. Hilbert

  14. Klein

  15. L’Huilier

  16. Lagrange

  17. Lambert

  18. LeGendre

  19. Lobachevsky

  20. Pascal

  21. Pasch

  22. Poincaré

  23. Poncelet (1788-1867)

  24. Riemann

  25. Saccheri

  26. Steiner

  27. van Schooten

 

Nobody’s heard of my young friend

Tom Hull

Folding Flat theorem

Pictures and short biographies of many of these at

http://www-groups.dcs.st-and.ac.uk/~history/

Expect to cover

Expect to cover:

Chapter 1 – Axiomatic Systems

1.1              Historical Background

1.2              Axiomatic Systems

1.3              Finite Geometries

1.4              Axioms for incidence geometry

Chapter 2 – Axiom Sets

2.2              Euclidean Geometry

2.3              Modern Euclidean Geometries

2.4              Hilbert’s Axioms

2.5              SMSG Postulates

Chapter 3 – Neutral Geometry

3.1 – 3.7

Chapter 4 – Euclidean Geometry

4.2

4.5

4.8

Chapter 6 – Non-Euclidean Geometry

6.2 – 6.4

This makes 20 sections