Elements of Geometry
General
Prefix
MATH
Course Number
465
Course Level
Undergraduate
Department/Unit(s)
College/School
College of Science and Engineering
Description
Axiomatic systems, foundations of Euclidean geometry, plane Euclidean geometry, and non-Euclidean and transformational geometries.
Prerequisites
Credits
Min
3
Max
3
Repeatable
No
Goals and Diversity
MN Goal Course
No
Cultural Diversity
No
Learning Outcomes
Outcome
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.
Outcome
Read about the development of geometry and how this development is related to other fields of mathematics, and analyze the structures of axiomatic systems.
Outcome
Solve problems in geometry analytically (utilizing Cartesian coordinates).
Outcome
Propose and justify theorems in hyperbolic geometry, illustrate with models the geometric objects and their properties in hyperbolic geometry and elliptic geometry.
Outcome
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.
Dependencies
Courses
MATH465
is a
prerequisite
for:
Programs
MATH465
is a
completion requirement
for: