Syllabus for Math 356 (Jan. 2007)

 

Text:  Cederberg, A Course in Modern Geometries, 2nd Ed.

Matrices on TI Calculators        Topic Bibliography

Day

Morning

Afternoon

Assignments

Tu. 2

1.1-1.2 Intro. to Axiom Systems

Exploration 1: Intro. to Cabri & Video?

1. Read 1.1-1.3;
1.2: 1,2*,3*,4,5,7,8

We. 3

1.3 Finite Projective Planes

2.1-2.2 Euclid's Geometry, Exploration 2: Hyperbolic Geometry

2. Read 2.1-2.4
1.3: 4-6,8,15*,16, Exp. 2

 

Th. 4

2.3-2.4 Hyperbolic Axiom, Sensed Parallels

Proof writing in Geometry and Presentation Conferences

3. Read 2.5-2.6; 2.2: 1, 2*, 3a (use Cabri); 2.4: 5*,6

 

Fr. 5

2.5-2.6  Asy. Triangle, Saccheri Quadrilaterals

Problem Session: Come prepared to present any problem assigned so far.

 4. Read 2.7-2.8;
2.5: 2,3*,6; 2.6: 1*,2,4,7,8 

 

 

 

 

 

Mo. 8

2.7-2.8 Triangle Area, Ultraparallels

2.9 Elliptic Geometry 

5. Read 2.9-3.2;
2.7: 1,2,4,7; 2.8: 4*,5*,6; 

 

Tu. 9

2.10, 3.1-3.2 Intro. to Symmetry

3.3-3.4 More Symmetry

6. Read 3.5-3.6
Exp. 3, 3.3: 9,11-15,16*,17*

 

We.10

3.5-3.6 Analytic Model

Problem Session

7. Read 3.7
3.5: 1,5,6,14*,16
3.6: 1,3*

 

Th.11

3.7 Isometries

1st Take-Home Exam

Exam 1  

Fr. 12

Office Hours

Exam 1 Due 

8. Read 3.8
3.7: 1*,3,5,6,8*

 

 

 

 

Mo.15

3.8 Direct Isometries

Presentations: (1) Early Geometry, (2) Development of Non-Euclidean Geometry

9. Read 3.9; 3.8: 1,2,3,5*,7,13, 15*,16,18,21

 

Tu.16

3.9 Indirect Isometries

Presentation: (3) Paper Folding Geometry

10. Read 3.14; 3.9: 1,2a,5,8*,9,11*(a&b),13

 

We.17

3.14 3-D Isometries 

Presentations: (4) Symmetry in Culture, (5) Frieze & Wall Patterns, Plane Tilings

11. Read 3.12-13


              

Th.18

3.12-3.13 Similarities & Affinities

Problem Session

 

12. Read 5.1; 3.12: 2,7,12*
3.13: 3,5,7,8,11*

 

Fr.19

5.1 Intro. to Chaos

Presentation: (6) Dimension Four & More plus Demo of Cabri 3-D by Richard Allen

13. Read 5.2; 5.1: 9-12


  

 

 

 

 

Mo.22

5.2 New Geometry

Presentation: (7) Fractals in Culture

14. Read 5.3-5.4; 5.2: 1-5, 19, 21*

 

Tu. 23

5.3-5.4 Dimension, IFS

Olafractal Exploration

15. Read 5.5-5.6
5.3: 13*, 15*, 16, 18, 20,  26-28a, 30, 31

 

We.24

5.5 Fractals 

 Problem Session

16. 5.4: 3,4,5,16,17  

 

Th.25

Catch-up & Review

2nd Take-Home Exam 

Exam 2  

 

Fr.26

Office Hours

Exam 2 Due

           

Sa.27

10:30-12:30: In-class Essay Exam

 


   

 

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