Math 572 Foundations of Geometry
Fall 2007
MWF 8:30 am

Course syllabus

Alignment of course material with standards

Monday, August 20: Introduction

Wednesday, August 22: What is a proof?

Friday, August 24: More on proofs and definitions

Monday, August 27: Definitions for geometry
       Choose groups and meeting times

Wednesday, August 29: Definitions, common notions, and axioms for Euclidean geometry

Friday, August 31: Proofs from Unit I

Monday, September 3: NO CLASS - Labor Day

Wednesday, September 5: Proofs from Unit II

Friday, September 7: End of proofs from Unit II; start of student proofs - III.1 and beginning of III.2

*** Reminders:  II.6 is to be done after III.2 (and is therefore YOUR responsibility!)
    Also, you do NOT need to prove III.5, but you may use these results from now on.

Monday, September 10: III.2, II.6

Wednesday, September 12: III.3, III.4

***Reminders: For III.6 and III.7, you should prove the converse statement.
    For III.8 and III.9, you just need to state the converse, not prove it.
    You don't need to do anything with IV.1 and IV.2 (just Postulate 5 and the definition of parallel)
    In Unit IV, make note of when you use Postulate 5.

Friday, September 14: III.6, start of III.7

Monday, September 17: III.7-III.9

Wednesday, September 19: IV.3, IV.4, start of IV.5

*** We are skipping V.9, V.11, V.12, and V.13.

Friday, September 21: IV.5, IV.6

*** IV.14 is to be written up individually and turned in next Friday, rather than presented in class.

Monday, September 24: IV.7, IV.8, most of IV.9

*** V.1 and V.2 are just definitions, so there will not be presentations for them.

Wednesday, September 26: IV.9 finish, V.3

Friday, September 28: V.5-V.8

Monday, October 1: NO CLASS

Wednesday, October 3: V.9-V.10

*** Skip V.14.  VI.1, VI.3, VI.8, and VI.11-13 are all definitions.  Skip VI.10 and VI.14.
*** VI.5 is to be written up individually and turned in on Wednesday, October 10.

Friday, October 5: V.11

Monday, October 8: V.12-13

*** VII.1 is a definition, and you can skip VII.10-11.

Wednesday, October 10: V.15, start of VI.2

Friday, October 12: VI.2, VI.4, VI.6

Monday, October 15: VI.7, VI.9, start of VII.2

Wednesday, October 17: VII.2-VII.4

Friday, October19: VII.5-VII.6

Monday, October 22: VII.7-VII.8, start of VII.9

Wednesday, October 24: VII.9, VIII.1-VIII.2

*** IX.1 is a definition, and you can skip IX.2, IX.3, and IX.5.

Friday, October 26: second half of V.15 and IX.4  (We'll go back to finishing Unit VIII on Monday.)

Monday, October 29: VIII.3-VIII.4, IX.7

Wednesday, October 31: IX.9-IX.11

Friday, November 2: IX.16,  IX.19, IX.20

**Monday, November 5: Midterm exam
    You may bring your list of theorems and any notes you have written on them but no additional pages.
    Sample exam

Wednesday, November 7: Introduction to Geometer's Sketchpad

Friday, November 9: Discussion of Sketchpad exercises and the role of conjectures in mathematics

Monday, November 12: More Geometer's Sketchpad (meet in the computer lab, Cardwell 41)

Wednesday, November 14: Continuing exercises from Monday (meet in the computer lab)
    ** Graded midterms due

Friday, November 16: More on conjectures
    List of conjectures and one proof from Sketchpad exercises due

Monday, November 19: Using Sketchpad for transformations

Monday, November 26: Non-euclidean geometry and the Poincare half-plane model

Wednesday, November 28: Rigid motions in hyperbolic geometry

Friday, November 30: Distances in hyperbolic geometry
    Proof of Ceva's theorem due

Monday, December 3: Postulates 2-4 in hyperbolic geometry

Wednesday, December 5: Wrap-up of hyperbolic geometry
    Hyperbolic geometry module
    (This is just to help you see how things work - you do not need to submit answers to the problems.)

Friday, December 7: Review
    Hyperbolic geometry problems due

Tuesday, December 11: Final exam
    You many bring your list of theorems as well as one additional sheet of notes.
    Sample Final
    (You may ignore #3, which covers material we have not done.)

You may also wish to watch the following:
Youtube video on Mobius tranformations

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Last modified: 7 December 2007