MATH465

Solve problems and write proofs in Euclidean geometry based on axioms and basic theorems, and design geometric constructions utilizing straightedge and compass as well as the software Geometer's Sketchpad.

Read about the development of geometry and how this development is related to other fields of mathematics, and analyze the structures of axiomatic systems.

Solve problems in geometry analytically (utilizing Cartesian coordinates).

Propose and justify theorems in hyperbolic geometry, illustrate with models the geometric objects and their properties in hyperbolic geometry and elliptic geometry.

Reveal and use general properties of Euclidean plane transformations and special properties of Euclidean plane isometries and affine transformations using synthetic and algebraic methods. Solve geometric problems using transformations.