Spring 2023
Formal geometries and models. Topics selected from projective, affine, Euclidean, and non-Euclidean geometries.
Lectures: Tuesdays and Thursdays 11:30am -- 12:50pm in Physics P113
Office hours: Tuesdays 2 -- 3pm, Thursdays 1:30 -- 2:30pm, or by appointment
MLC: Wednesdays 5 -- 6pm on Zoom
Office: Math Tower 3-114
Textbook: Euclidean and Non-Euclidean Geometries Development and History (4th edition) by Marvin J. Greenberg
Syllabus: pdf
Grades: 30% homework + 70% midterms (two) and final, check the syllabus for details.
We will use Brightspace and Gradescope (entry code: XVK68Z)
Notes for MAT 200 on logic and methods of proofs, and on sets and functions.
Part I: Introduction, Euclid's axioms
Part II: Incidence geometry, Affine and projective geometry
Part III: Betweenness axioms, Congruence axioms, Continuity axioms
Part IV: Neutral geometry (AIA, EA, measurement), Equivalence of Euclid V, Saccheri and Lambert, Angle sum of a triangle
Part V: Real elliptic geometry, Hyperbolic geometry
Midterm 1, scheduled in class on March 2, 2023.
Practice Midterm 1 and solutions, and a list of axioms to be provided during the exams.
Midterm 2, scheduled in class on April 13, 2023.
Practice Midterm 2 and solutions, and a list of axioms and major results to be provided during the exams.
Take-Home Final, to be posted only on Brightspace on May 9, 2023. It is due on May 11, 2023, to be submitted to Gradescope.
Information on project, due May 13, 2023.
LaTeX resources: TeXShop (for MacOS), TeXstudio, and of course Overleaf (recommended -- easy to use, online)
Overleaf Intro to LaTeX
many templates on Overleaf for papers
Detexify: a tool to translate handwritten symbols to LaTeX codes
Some readings that might help choose a topic: Hilbert's axioms for solid geometry, straigntedge-and-compass constructions