Is differential geometry pure math?

Question

Is this course pure math? Is it college math or graduate level math? Do physics and engineering majors need this course? What's the name of the textbook for this course that MIT uses?

Answer 1

Differential geometry has been invented as a pure branch of mathematics (I don't like to say just "math", it sounds disrespectfully to me and I am advising to use the complete word "mathematics" when it come to this langiage of science). It has been interoduced by George Rihman as a tensor analysis on curved manifoldsin the midst of 19 century despite its foundations have been developed by Fridrikh Gauss who hasn't published his works at that time. It became a mathematical foundation for general relativity in 1916. Basics of differential geometry are taught as a part of undergraduate program in Calculus course. But this is a simplest part of it, designed for physicists and engineers More serious part of differential geometry (tensor geometry) is stuidied by those who wants to be specialized in general relativity, as well as by professional mathematicians.

Answer 2

In the college I attended, it was is offered as an undergraduate course. This subject has a wide range of applications and yes, physics and engineering are included. I can't tell though whether it is required, but it would probably be good for you to eventually take. I checked though a list of courses offered at MIT and found that they have a course "Introduction to Lie Groups", which currently uses the book called "Differential Geometry, Lie groups and Symmetric Spaces" by Sigurdur Helgason who is an MIT professor.