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Apr 25, 2024
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MATH 5110 - College Geometry
An axiomatic approach to Euclidean geometry. A core batch of theorems of Euclidean geometry are proven, and interesting geometric problems are solved using the axioms and theorems. Additional concepts and techniques – such as similarity, transformations, coordinate systems, vectors, matrix representations of transformations, complex numbers, and symmetry – are introduced as ways of simplifying the proofs of theorems or the solutions of geometric problems. Hyperbolic geometry is introduced from an axiomatic standpoint, primarily to illustrate the independence of the Parallel Postulate. Computers are used to produce dynamic drawings to illustrate theorems and problems.
Requisites:
Credit Hours: 3
Repeat/Retake Information: May not be retaken.
Lecture/Lab Hours: 3.0 lecture
Grades: Eligible Grades: A-F,WP,WF,WN,FN,AU,I
Learning Outcomes:
- Demonstrate the dependence of some of the axioms commonly included in axiom sets for high school math books.
- Demonstrate the independence of the Parallel Postulate using examples from Euclidean and Hyperbolic Geometry.
- Incorporate methods of similarity, transformations, coordinates, vectors, matrices, complex numbers, and symmetry to simplify proofs or solve geometric problems.
- Prove a core batch of the standard theorems of Neutral, Euclidean, and Hyperbolic Geometry using deductive, axiom-based proofs.
- Solve geometric problems using the axioms and theorems of Euclidean Geometry.
- Use computer programs to produce dynamic drawings to illustrate geometric theorems and problems.
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