mth405 | undergraduate

Modern Geometry

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This course explores geometry from heuristic, axiomatic, and computational angles. Students examine ancient results, Euclid, non-Euclidean geometry via the Poincaré disk, and transformational geometry.

This undergraduate-level course is 5 weeks This course is available to take individually or To enroll, speak with an Enrollment Representative.

Course details:

Credits: 3
Duration: 5 weeks

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    Transformations and Constructions

    • Develop proofs for isometries.
    • Analyze the compositions of transformations.
    • Perform basic constructions with straight-edge and compass.

    Hyperbolic Geometry and Geometric Models

    • Prove simple theorems of hyperbolic geometry.
    • Construct objects in the Poincaré Disk.
    • Perform calculations in the Poincaré Disk.

    Axiomatic Systems and Incedence and Plane Geometries

    • Solve elementary geometry problems.
    • Demonstrate properties of components of axiomatic systems.

    Neutral and Euclidean Geometries

    • Prove elementary theorems in neutral geometry.
    • Prove theorems in Euclidean Geometry.
    • Develop proofs related to Euclid’s Playfair Postulate.

    Area and Circles

    • Develop geometric proofs for area.
    • Demonstrate relationships between circles and other geometric shapes.
    Tuition for individual courses varies. For more information, please call or chat live with an Enrollment Representative.

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    Teacher Rate: For some courses, special tuition rates are available for current, certified P-12 teachers and administrators. Please speak with an Enrollment Representative today for more details.

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    While widely available, not all programs are available in all locations or in both online and on-campus formats. Please check with a University Enrollment Representative.

    Transferability of credit is at the discretion of the receiving institution. It is the student’s responsibility to confirm whether or not credits earned at University of Phoenix will be accepted by another institution of the student’s choice.