MATH 540 Modern Geometries (Graduate)

A review of the basic techniques of straight edge and compass construction, including constructions requiring propositions from Book III of Euclid’s Elements (ca. 300 BC), gives students an intuitive foundation necessary for the approaches that follow. First is an overview of the nature of postulates and propositions in Euclid, which are radically different from their modern counterparts. From there, the bulk of the course is devoted to geometry based in Hilbert’s axioms (1899), where the theory of plane geometry is built with an eye toward understanding the dilemma of Euclid’s parallel postulate. The historical development leading from Euclid to hyperbolic and elliptic geometry is then situated in this mathematical context.

Prerequisites: Calculus I, II, and linear algebra, and an introductory course on mathematical proofs.

Related Offerings:

MATH 510 Applied Statistical Methods (3 credit hrs.) (Summer 2025)
MATH 520 Number Theory (3 credit hrs.) (Summer 2024)
MATH 530 Abstract Algebra (4 credit hrs.) (Fall 2023)
MATH 540 Modern Geometries (4 credit hrs.) (Winter/Spring 2024 & Winter/Spring 2025)
MATH 550 Mathematical Analysis (4 credit hrs.) (Fall 2024)

University of Indianapolis

Semester: Full Winter/Spring 2024

Instructor: Jeff Oaks

Credit Hours: 4 Graduate

Date: 1/16/24 – 5/4/24

Location: Online Asynchronous

Teacher Level: Grades 9-12

Graduate Certificate Available: No

Master’s Completion Option: Yes

MATH 540 Syllabus

Master of Arts in Curriculum & Instruction