Honors 213
Fourth Hour Exam Review
Disclaimer: I have attempted to be comprehensive in the
following, but important items may have been omitted by mistake. If
you see such an omission, please let me know, but you are responsible
for all of the lecture material to date.
The fourth hour exam for Honors 213 will be held on Monday, April
24, and will cover chapters 4 through 6 together with a brief
introduction of materials from the Poincaré and Klein models
and our discussion of the approach taken in the "metamathematical
theorem". The paper from Trudeau's book should also be reviewed, but
the Penrose paper will not apply until the final. The Weeks paper
will not be covered on this exam.
- Theorems, Definitions, and Names:
- Know definitions of terms that have been a part of the
discussion in chapters 4 - 6.
- Know the statements and proofs of theorems that have been a
part of chapters 4 - 6 and which we have covered (either in
homework or in class).
- Know who did what (chapters 5 and 6). I will not ask for
exact dates, but be able to place in century and country.
- Proofs
- As before, be able to construct proofs for fairly
straightforward statements. Be able to justify the steps in a
proof. A review of homework problems together with a review of
the steps undertaken in the proofs of theoems would be the best
review for this part.
- Philosophical musings
- What is the approach taken to prove that hyperbolic
geometry is consistent? What does it mean for a formal system
to be consistent? What would happen if someone actually found a
proof of Hilbert's parallel postulate/axiom?
Please let me know if there are any questions. Many thanks!