Advanced geometry presents a formal and fundamental development of Euclidean geometry with an emphasis on valid arguments. Non-Euclidean geometry will also be investigated. The course begins with a thorough review of geometry and continues with a selection of more advanced topics including the nine-point circle, Ceva's Theorem, Euler line, and Menelaus' Theorem.
- Understand the basic rules of logic, including the roles of axioms or assumptions
- Appreciate the role of mathematical proof in formal reasoning
- Proficiently construct logical arguments and rigorous proofs
- Present mathematical arguments, in both written and oral form, clearly and precisely to an audience of peers and faculty.