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!