Detailed Schedule -- Geometry Through History

MATH 392, section 3 -- Spring 2016, Prof. Little

This is a tentative, evolving schedule. If necessary, some topics may be added, deleted, or rearranged during the course of the semester. Any major changes will be announced in class and here. The notation [M] refers to our main course text, McCleary, Geometry from a Differentiable Viewpoint.

Date Class Topic Readings/Assignments
1/27 Course Introduction -- Euclid's Elements [M], Chapter 2
1/29 Proposition I, 47 -- a taste of the power of Euclid [M], Chapter 2
2/1 Deductive Structure of Euclid, Elements, Book I [M], Chapter 2
2/3 Euclid's theory of parallels [M], Chapter 3
2/5 Angle sum in a triangle, similar triangles [M], Chapter 3
2/8 Girolamo Saccheri, S.J. and his results on parallels [M], Chapter 3
2/10 Spherical geometry [M], Chapter 1
2/12 Spherical trigonometry and the spherical Pythagorean theorem [M], Chapter 1
2/15 Gauss and parallels [M], Chapter 4
2/17 The hyperbolic plane [M], Chapter 4
2/19 Quiz 1 -- More on the hypberbolic plane [M], Chapter 4
2/22 Hyperbolic space, the horosphere [M], Chapter 4
2/24 Bolyai-Lobachevsky theorem [M], Chapter 4
2/26 The hyperbolic Pythagorean theorem [M], Chapter 4
2/29 Descartes and coordinate geometry readings on course homepage
3/2 More on coordinate geometry readings on course homepage
3/4 Spare day readings on course homepage
3/7,9,11 Spring Break -- no class
3/14 Curvature of plane curves [M], Chapter 5
3/16 Curves in space, Frenet-Serret [M], Chapter 6
3/18 Midterm Exam
3/21 More on curves in space [M], Chapter 6
3/23 Surfaces, ``review from MATH 241'' [M], Chapter 7 -- Notify me of Final Project choices
3/25,28 Easter Break -- no class
3/30 Surfaces, tangent planes [M], Chapter 7
4/1 Surfaces, lengths, angles, first fundamental form [M], Chapter 7
4/4 Curvature for surfaces [M], Chapter 8
4/6 Gaussian and mean curvature [M], Chapter 8
4/8 Metric equivalence of surfaces [M], Chapter 9
4/11 Gauss's Theorema Egregium [M], Chapter 9
4/13 Geodesics on a surface [M], Chapter 10
4/15 Quiz 2 -- More on geodesics [M], Chapter 10
4/18 Geodesics, concluded [M], Chapter 10 -- Final Project Bibliographies due
4/20 Riemann's Habilitationsvortrag [M], appendix
4/22 ``Abstract'' surfaces [M], Chapter 13
4/25 ``Abstract surfaces,'' continued [M], Chapter 13
4/27 Models of the hyperbolic plane [M], Chapter 13
4/29 Final project presentations
5/2 Final project presentations
5/4 Final project presentations
5/6 Final project presentations
5/9 Semester wrap-up Final Project Papers due
There will be no final exam for this course. The final project will effectively replace a final.

Last modified: March 9, 2016