18.994 | Fall 2004 | Undergraduate

Seminar in Geometry

Lecture Notes

Professor’s instructions on preparing lectures for class (PDF)

The lecture notes were prepared by the Instructor Dr. Emma Carberry and the students: Kai Fung, David Glasser, Michael Nagle, Nizam Ordulu. The full set of lecture notes are available as a single file (PDF) or mapped to the lectures in the table below.

lec # TOPICS
1 Introduction (PDF)
2 A Review on Differentiation (PDF)
3 Inverse Function Theorem (PDF)
4 Implicit Function Theorem (PDF)
5 First Fundamental Form (PDF)
6 Curves (PDF)
7 Gauss Map I: Background and Definition (PDF)
8 Gauss Map II: Geometric Interpretation (PDF)
9 Gauss Map III: Local Coordinates (PDF)
10 Introduction to Minimal Surfaces I (PDF)
11 Introduction to Minimal Surfaces II (PDF)
12 Review on Complex Analysis I (PDF)
13 Review on Complex Analysis II (PDF)
14 Isothermal Parameters (PDF)
15 Bernstein’s Theorem (PDF)
16 Manifolds and Geodesics I (PDF)

Manifolds and Geodesics II (PDF)


Complete Minimal Surfaces I (PDF)


Complete Minimal Surfaces II (PDF)

20 Weierstrass-Enneper Representations (PDF)
21 Gauss Maps and Minimal Surfaces (PDF)

Course Info

As Taught In
Fall 2004
Learning Resource Types
Lecture Notes
Projects with Examples
Problem Sets