Previous Weeks in Math 300 class
Week 1: Monday, January 15
- Topics
- Introduction to the course
- Some history
- Reading
Monday:
- Martin Luther King, Jr. Birthday. No classes or office hours
Tuesday:
- Introduction to the course
Wednesday:
- Some history
- The axiomatic method
Friday:
- Euclid's first four postulates (we covered EP1 - EP3)
Other Notes:
- Office Hours begin next Monday
Week 2: Monday, January 22
Monday:
- EP4
- EP 5: The parallel postulate
- Attempts to prove the parallel postulate
- No office hours today (departmental meeting)
Tuesday:
Wednesday:
- Quantifiers and the predicate logic
Friday:
- No class - instructor ill
Other notes:
- Office Hours begin this week
Week 3: Monday, January 29
:
Monday:
- Theorems and Proofs
- Rules of the game
Tuesday:
- Rules of the game
- Axioms for incidence geometry
Wednesday:
- Incidence geometry and models
- Isomorphisms of models
Friday:
- Interpretations and models
- Projective and affine planes
Other notes:
Week 4: Monday, February 5
Monday:
- Affine and projective planes
- The problems with Euclid
Tuesday:
- Affine and projective planes
- The problems with Euclid
Wednesday:
Friday:
- Ruler and compass constructions
Other notes:
- Hour Exam #1 is next week
Week 5: Monday, February 12
Monday:
Tuesday:
- Axioms of betweeness: plane separation and line separation
Wednesday:
- Discussion on homework assignment
- Review for exam #1
Friday:
Other notes:
Week 6: Monday, February 19
Monday:
- Axioms of betweeness: line separation
Tuesday:
Wednesday:
Friday:
Other notes:
Week 7: Monday, February 26
Monday:
Tuesday:
- Assignment #5 assigned (due next Friday)
- Axioms of congruence
- Axioms of continuity
Wednesday:
- Dedekind's axiom
- Hilbert's parallel axiom
Friday:
- No class or office hours (History of Science Conference)
Other Notes
- No class or office hours Thursday and Friday (Columbia History of Science
conference.
-
Please note that the last day to withdraw with an automatic 'W' is
Monday, February 26. The rules for withdrawing from a class have
changed. Please review the revised policy on course withdrawals in the
Student Handbook
Week 8: Monday, March 5
Monday:
- Homework returned - notes
Tuesday:
Wednesday:
Friday:
- The measure of angles and segments
Other Notes
- Mid-term is Friday, March 9 (not an exam date for us)
- Next week is Spring Break! (no classes or office hours)
-
Hour exam #2 will be Friday following Spring Break
Week 9: Monday, March 12
Spring Break! (no classes or office hours)
Other Notes
-
Hour exam #2 will be Friday following Spring Break
Week 10: Monday, March 19
- Topics
- Neutral geometry
- The origins of non-Euclidean geometry
- Reading
Monday:
- Angle sums and the Saccheri-Legendre theorem
Tuesday:
- The Saccheri-Legendre theorem
- Quadrilaterals
- Equivalents of the parallel postulate (initial discussion)
- Assignment of group exercises
Wednesday:
- Equivalents of the parallel postulate
- Review for second hour exam
Friday:
Other Notes
Week 11: Monday, March 26
- Topics
- The origins of non-Euclidean geometry
- Reading
Monday:
- Equivalents of the parallel postulate: Rectangles
- History of the parallel postulate
Tuesday:
- Group exercise presentations
Wednesday:
- Group exercise presentations
- History of the parallel postulate
Friday:
Other Notes
Week 12: Monday, April 2
- Topics
- History of the parallel postulate
- Discovery of non-Euclidean geometry
- Reading
Monday:
- History of the parallel postulate
Tuesday:
- Discovery of non-Euclidean geometry
Wednesday:
- Discovery of non-Euclidean geometry
- Hyperbolic geometry
- Hyperbolic geometry: Angle sums and similar triangles
Friday:
- Hyperbolic geometry: Classifications of parallels
- Parallels that admit a common perpendicular
Other Notes
-
Hour Exam #3 Friday, April 27. Please note that this is in the last
full week of classes.
-
Last day of class Wednesday May 2
Week 13: Monday, April 9
Monday:
- Parallels that admit a common perpendicular
Tuesday:
- Asymptotic rays
- Classification of parallels
Wednesday:
- Classification of parallels
- Consistency of hyperbolic geometry - the Klein model
Friday:
- Working day on straight-edge and compass constructions.
Other Notes
-
Hour Exam #3 Friday, April 27. Please note that this is in the last
full week of classes.
-
Wednesday, May 2, is the last day of classes. No class work can
be accepted past 5:00 on that date.
Week 14: Monday, April 16
- Topics
- Independence of the Parallel postulate
- Reading
Monday:
- Consistency of hyperbolic geometry - the Klein model
- The Poincaré model(s)
Tuesday:
- Problem Presentation Session
Wednesday:
Friday:
Other Notes
-
Hour Exam #3 Friday, April 27 (next week). Please note that this is in the last
full week of classes.
-
Wednesday, May 2, is the last day of classes. No class work can
be accepted past 5:00 on that date.
Week 15: Monday, April 23
- Topics
- Reading
- Greenberg: Chapters 7, 8
- Please read The Three Crises in Mathematics: Logicism,
Intuitionism and Formalism Mathematics Magazine, Vol. 52, No. 4. (Sep.,
1979), pp. 207-216.
Stable URL:
Stable URL (From JSTORE)
Monday:
Tuesday:
Wednesday:
- Inversions
- Review for exam #3
Friday:
Other Notes
-
Hour Exam #3 Friday, April 27. Please note that this is in the last
full week of classes.
-
Wednesday, May 2, is the last day of classes. No class work can
be accepted past 5:00 on that date.
Week 16: Monday, April 30
- Topics
- Reading
- Greenberg: Chapter 8
- Please read The Three Crises in Mathematics: Logicism,
Intuitionism and Formalism Mathematics Magazine, Vol. 52, No. 4. (Sep.,
1979), pp. 207-216.
Stable URL:
Stable URL (From JSTORE)
- Please also read the Poincaré handout
Monday:
- Final discussion on hyperbolic geometry
Tuesday:
- Foundations (Chapter 8, Poincaré)
- Exam returned and discussed
Wednesday:
- Foundations (Ernst Snapper)
- Wrap-up and review for final exam
Friday:
- Reading Period (no classes - office hours as announced)
Other Notes
-
Wednesday, May 2, is the last day of classes. No class work can
be accepted past 5:00 on that date.
-
The final exam for Math 300 is scheduled for Friday, May 11, 8:00 -
10:00 AM. It will be a two hour, in-class, comprehensive final.
University regulations require that all students in this class take the
final at this time.
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