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Organization, Regulations, and Courses 2025-26


MATH 42 Differential Geometry I

As the Greek roots of the word suggest, geometry has its origins in our natural and practical need to measure the world around us. Over the millennia, geometry has evolved to encompass the general study of the measurable properties of "space." Consequently, any problem that involves a notion of "space" and "measurement" has the potential to be "geometrized"; i.e., turned into a statement about geometry. A prime example of this is the geometrization of gravity in Einstein's general theory of relativity. With applications across STEM, this course will serve as an introduction to differential geometry, which applies ideas from linear algebra and multivariable calculus to the exploration of geometry. Topics might include: vector fields & integral curves; covariant differentiation, parallel transport & geodesics; (Gaussian) curvature and Gauss’ Theorema Egregium; the Gauss-Bonnet Theorem; Isometries & Riemannian metrics.

Prerequisite

Math 13 and MATH 22 or MATH 24

Degree Requirement Attributes

Dist:QDS

The Timetable of Class Meetings contains the most up-to-date information about a course. It includes not only the meeting time and instructor, but also its official distributive and/or world culture designation. This information supersedes any information you may see elsewhere, to include what may appear in this ORC/Catalog or on a department/program website. Note that course attributes may change term to term therefore those in effect are those (only) during the term in which you enroll in the course.