Math 561 - The Differential Geometry of Curves and Surfaces

• Some lecture notes on Curves based on the first chapter of do Carmo's textbook.
• Solutions to some problems from the first chapter of the do Carmo's textbook.
• More solutions to problems from the first chapter of the do Carmo's textbook.
• Some lecture notes on surfaces base on the second chapter of do Carmo's textbook.
• Solutions to some problems from the second chapter of do Carmo's textbook.
• An elementary proof that stereographic projection is conformal and another copy of this document.
• An online book on differential geometry which I like better than the Do Carmo textbook. In this book there is a careful statement of the Inverse and Implicit Function Theorems on page 3 and a proof that the three definitions of a regular surface are equivalent on page 6.
• Some lecture notes on the Gauss map based on the third chapter of do Carmo's textbook.
• Some lecture notes on manifolds and maps that I used whenever I taught Math 761. They are too advanced for 561 but they do contain complete proofs of the Inverse and Implicit Function Theorems and the Existence and Uniqueness Theorem for Ordinary Differential Equations.