Differential geometry can be viewed as the study of space and curvature. The course depends heavily upon calculus, it uses the tools of linear algebra, and it develops geometric insight. As such it is a good course for students who want to strengthen their understanding of the core mathematics curriculum.
Differential geometry is a crucial tool in modern physics.
Several more recent developments in physics, as Yang-Mills theory and string theory, involve differential geometry. The courses 120A and 120B deal with differential geometry in a special context, curves and surfaces in 3-space, which has a firm intuitive basis, and for which some remarkable and striking theorems are available. The course begins with curves in the plane and in 3-space, which already have some interesting geometric features. Curvature and torsion measure how curves bend and twist. There are some beautiful theorems that if a curve in 3-space forms a closed loop, it has to bend at least a certain amount, and if it forms a knot, it has to bend at least a larger certain amount.