Previous Weeks in Math 300 / Honors 213 class
Week 1: Monday, January 16
- 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
Other Notes:
- Office Hours begin next Monday
Week 2: Monday, January 23
- Topics
- Reading
- Greenberg: Chapter 2
- Devlin chapters 1 - 4
:
Monday:
Tuesday:
- No class - family illness
Wednesday:
- The parallel postulate - attempted proof
Friday:
- The problem with diagrams
- The power of diagrams
- Diagrams as heuristics for the search for a proof.
Other notes:
- Office Hours begin this week
Week 3: Monday, January 30
- Topics
- Logic and proof
- Axiomatic systems
- Reading
- Greenberg: Chapter 2, start chapter 3
- Devlin chapters 1 - 4
:
Monday:
- An introduction to logic: propositional logic and truth tables.
Tuesday:
- Forms of argument using the propositional calculus
Wednesday:
- RAA / ATC proofs
- Predicates
Friday:
- Predicate logic
- Rules for quantifiers
Other notes:
- Hour Exam #1 will be next Friday.
Week 4: Monday, February 6
- Topics
- Reading
- Greenberg: Chapter 3
- Devlin chapters 1 - 4
Monday:
- Discussion on the Devlin book
Tuesday:
- Back to chapter 2: Logic rules
Wednesday:
- Incidence Geometry
- Review for first hour exam
Friday:
Other notes:
Week 5: Monday, February 13
- Topics
- Incidence axioms
- Hilbert's axioms
- Reading
- Greenberg: Chapters 2, 3
- Devlin chapters 1 - 4
Monday:
Tuesday:
- Models
- Equivalence relations
Wednesday:
- Projective Plane
- Affine Plane
- Extending an affine plane to a projective plane
Friday:
Week 6: Monday, February 20
Monday:
- Consequences of the axioms of betweeness
Tuesday:
- Questions on the homework (mostly problems 9 and 10)
Wednesday:
Friday:
- No class or office hours - History of Science Conference
Other notes:
- Exam #2 will be next week (this was delayed 2/27/06 to Monday, March 6)
Week 7: Monday, February 27
Monday:
- Final discussion on axioms of betweeness
Tuesday:
Wednesday:
- Axioms of congruence
- Axioms of continuity
- Happy St. David's day!
Friday:
- Axioms of continuity
- Review for exam #2
Other notes:
- Exam #2 has been rescheduled for Monday, March 6
Week 8: Monday, March 6
- Topics
- Hilbert's axioms
- Neutral Geometry
- Reading
Monday:
- Exam #2 (rescheduled from Friday, March 3)
Tuesday:
Wednesday:
- Dedikind's Axiom
- Axioms of parallelism
- Exam #2 returned and discussed
Friday:
Other notes:
- Friday, March 10 is Mid-term (not an exam date for us)
Week 9: Monday, March 13
Spring Break! (no classes or office hours)
Exam #3 will be on Friday, March 31
Week 10: Monday, March 20
- Topics
- Hilbert's axioms
- Neutral Geometry
- Reading
Monday:
- Measure of angles and segments
Tuesday:
- Saccheri-Legendre theorem
Wednesday:
- Corollaries of the Saccheri-Legendre theorem
Friday:
- Equivalents of the parallel postulate
Other notes:
- Exam #3 will be next Friday
Week 11: Monday, March 27
- Topics
- Hilbert's axioms
- Neutral Geometry
- Reading
Monday:
- Geometry and topology
- Equivalents of the parallel postulate.
Tuesday:
Wednesday:
- Angle sum of a triangle (concluded)
- Review for exam #3
Friday:
Other notes:
Week 12: Monday, April 3
- Topics
- The emergence of non-Euclidean geometry
- Reading
- Greenberg: Chapters 5 - 6
Monday:
- History of the parallel postulate (chapter 5)
Tuesday:
- No class (family illness)
Wednesday:
Friday:
- History of the parallel postulate
Other notes:
- The fourth hour exam will be on Wednesday, April 26
- The final exam for this class is scheduled for Friday, May 12, at 8:00
AM.
Week 13: Monday, April 10
- Topics
- The emergence of non-Euclidean geometry
- Reading
Monday:
- The history of the parallel postulate
Tuesday:
- The discovery of non-Euclidean geometry (chapter 6).
- Introduction to hyperbolic geometry
Wednesday:
- Introduction to hyperbolic geometry.
Friday:
Other notes:
- The fourth hour exam will be on Wednesday, April 26
- The final exam for this class is scheduled for Friday, May 12, at 8:00
AM.
Week 14: Monday, April 17
Monday:
- On the nature of parallel lines in hyperbolic geometry
Tuesday:
- Guest lecturer: Martin Jackson
Wednesday:
Friday:
Other notes:
-
Over the next few weeks, I will not be able to be in my office as much
as I would like. Martin Jackson has kindly offered to include Math
300 / Honors 213 students in his office hours, which are posted
on his web page (click here).
- The fourth hour exam will be on Wednesday, April 26
- The final exam for this class is scheduled for Friday, May 12, at 8:00
AM.
Week 15: Monday, April 24
Topics
- Independence of the parallel postulate, and consequences
Reading
- Greenberg: Chapter 7 through page 243
- Poincaré
handout
Monday:
Tuesday:
- Return HW
- Review for exam #4
Wednesday:
Friday:
- The Metamathematical Theorem
- Tom Lehrer
Other notes:
-
Over the next few weeks, I will not be able to be in my office as much
as I would like. Martin Jackson has kindly offered to include Math
300 / Honors 213 students in his office hours, which are posted
on his web page (click here).
- The fourth hour exam will be on Wednesday, April 26
- The final exam for this class is scheduled for Friday, May 12, at 8:00
AM.
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