18.994 | Fall 2004 | Undergraduate

Seminar in Geometry


Course Meeting Times

Lectures: 2 sessions / week, 1.5 hours / session

Format and Description

In this course, students take turns in giving lectures. For the most part, the lectures are based on Robert Osserman’s classic book A Survey of Minimal Surfaces, and Michael Spivak’s Calculus on Manifolds, Manfredo Do Carmo’s Curves and Surfaces.  Lars Ahlfors’ Complex Analysis will also be referred to at various points. Note that Do Carmo treats only surfaces in R3; many things are easy to generalise; some things do not generalise or it is difficult to see how they do. Spivak refers to ‘Calculus on Manifolds’; Spivak 3 and 4 refer to volumes of his ‘Differential Geometry’ series.


Osserman, Robert. A Survey of Minimal Surfaces. Dover Phoenix Editions. New York: Dover Publications, May 1, 2002. ISBN: 0486495140.

Spivak, Michael. Calculus on Manifolds: A Modern Approach to Classical Theorems of Advanced Calculus. New York: Westview Press, June 1, 1965. ISBN: 0805390219.

Do Carmo, Manfredo. Differential Geometry of Curves and Surfaces. Englewood Cliffs, N. J.: Prentice Hall, February 1, 1976. ISBN: 0132125897.

Ahlfors, Lars. Complex Analysis. 3rd ed. New York: McGraw-Hill Science/Engineering/Math, January 1, 1979. ISBN: 0070006571.

Students may wish to consult additional material when preparing lectures. Osserman’s book has a long list of references, which he refers to throughout the text.

For general information about reading mathematics, students should consult the article “How to Read Mathematics” by Shai Simonson and Fernando Gouveau. It is published on the web, and talks about the language of mathematics, and how best to approach it.


Homework assignments are handed out each Wednesday, and are due the following Wednesday. The lowest homework grade can be dropped. No late homework is accepted.

Students may work together on homework assignments, in fact they are encouraged to do so. However, they must write up their homework assignment by themselves.

Course Info

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