differential geometry, branch of mathematics that studies the geometry of curves, surfaces, and manifolds (the higher-dimensional analogs of surfaces).
In structural geology, differential geometry is used to analyze and describe geologic structures. In computer vision, differential geometry is used to analyze shapes. In image processing, differential geometry is used to process and analyse data on non-flat surfaces.
To start learning differential geometry, you just need to know some calculus. The geometry of curves and surfaces embedded in 3-space is rich as an introduction, and you can get started if you're comfortable with first-year calculus.
Abstract: Normally, mathematical research has been divided into “pure” and “applied,” and only within the past decade has this distinction become blurred. However, differential geometry is one area of mathematics that has not made this distinction and has consistently played a vital role in both general areas.Dec 31, 1987
So you should definitely take a real analysis course and a topology course (if possible, in parallell) before diving into differential geometry. espen's post reminded me to point out that you also need to know a very good amount of theoretical linear algebra before delving into the theory of differentiable manifolds.Nov 17, 2013
Gaspard MongeGaspard Monge (1746–1818) is considered the father of differential geometry.
Not particularly harder or easier than any other mathematical subject.
Differential Equations (Math 326), Numerical Analysis (Math 345), Probability and Statistics Math 360 and 361 (or 341 if you don't have time for both) are important. Numerical Analysis 2 (Math 346) and Linear Algebra 2 (Math 333) are highly recommended as well for all applied mathematicians.