- Be familiar with all topics covered in the reader, and in
*Mathematics Through the Eyes of Faith*. - Reader: Pages 1–46 (up to Section 3.3).
- Assigned readings from
*Mathematics Through the Eyes of Faith*. - Be familiar with all topics discussed in the lectures.
- The different types of proof, and what distinguishes them from one another.
- The proof that if
*x*^{2}is even then*x*is even. - The Pythagoreans: their philosophy and proof that √2 is irrational.
- Converting a repeating decimal to a fraction and vice versa.
- The components of an axiomatic system.
- Be able to give reasons for basic Euclidean geometric theorems.
- The theory behind the computation of the Earth’s circumference.
- The various propositions from Euclid, especially Propositions I.5, I.6, I.29, and I.47.
- Be prepared to perform simple geometric or other mathematical arguments. For example, you may be asked to supply reasons for steps in a proof, or to complete the second half of a proof that Euclid gives (that is similar but not identical to the first half). See especially Proposition I:15, Proposition I.16, Proposition I.17, and Proposition I.20.