Differential Geometry of Curves and Surfaces

MATH 4230/5230 Fall 2026

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Course information

Instructor

Sebastian Casalaina-Martin

Class meetings

Monday, Wednesday, Friday, 11:15 AM - 12:05 PM

Classroom

Engineering Center, ECCR 151

Office hours

M 12:15 - 1:15 PM, T 1:15 PM - 3:15 PM; office MATH 266 (in the main office). Reserve an appointment through the link on canvas.

CU Boulder Academic Calendar
CU Boulder Final Exam Schedules
Canvas

Course description

Introduces the modern differential geometry of plane curves, space curves, and surfaces in three-dimensional space. Topics include the Frenet frame; curvature and torsion for space curves; Gaussian and mean curvature for surfaces; the Gauss and Codazzi equations; geodesics; and the Gauss–Bonnet theorem.

Department-enforced prerequisites: (MATH 2400 or APPM 2350), (MATH 2001 or MATH 2002), and (MATH 2130, MATH 3130, MATH 2135, or MATH 3135), all with a minimum grade of C−.

Textbook

1. Kristopher Tapp, Differential Geometry of Curves and Surfaces, Undergraduate Texts in Mathematics, Springer, 2016.

Available for free from the Springer website link above (use VPN if you are off campus)

Homework and preparation

Read the listed sections before class. After every class, complete the assigned exercises on the Homework and Syllabus page.

Assessment

Homework 5%, Daily Quizzes 5%, Weekly Quizzes 10%, Midterm I 25%, Midterm II 25%, Final 30%.

The lowest two Homework scores will be dropped, the lowest five Daily Quiz scores will be dropped, and the lowest two Weekly Quizzes will be dropped.