Differential Geometry: Definitions and Pictures
                Nic Ford
              May – June 2019
                                                                                                                                                                                              The foundations of the field have changed a lot since its
                                                                                                                                                                                              beginnings in the 19th century, but modern mathematicians have
                                                                                                                                                                                              built out a beautiful set of tools for doing calculus in
                                                                                                                                                                                              non-Euclidean geometries.
                                                                                                                                                                                              We’ll be discussing how these work and give some examples of how
                                                                                                                                                                                              to use them to do geometry.
 What is it?
   Differential geometry is about using tools from multivariable
   calculus and linear algebra to study the geometry of curved shapes
   and spaces.
                                                                                                                                                                                              We’ll be discussing how these work and give some examples of how
                                                                                                                                                                                              to use them to do geometry.
 What is it?
   Differential geometry is about using tools from multivariable
   calculus and linear algebra to study the geometry of curved shapes
   and spaces.
   The foundations of the field have changed a lot since its
   beginnings in the 19th century, but modern mathematicians have
   built out a beautiful set of tools for doing calculus in
   non-Euclidean geometries.
 What is it?
   Differential geometry is about using tools from multivariable
   calculus and linear algebra to study the geometry of curved shapes
   and spaces.
   The foundations of the field have changed a lot since its
   beginnings in the 19th century, but modern mathematicians have
   built out a beautiful set of tools for doing calculus in
   non-Euclidean geometries.
   We’ll be discussing how these work and give some examples of how
   to use them to do geometry.