SYLLABUS FOR MATHEMATICS 147A WINTER 2015

TuTh 2:00-3:15 Girvetz 2115

Instructor: John Douglas Moore Office: SH 6714 Office hours: TuTh 3:30, W 1 and by appointment. Telephone: 893-3688 email: moore@math.ucsb.edu

TEXT: Andrew Pressley, Elementary Differential Geometry, Springer, 2001.

TENTATIVE FORMULA FOR GRADES: Final exam, March 17, 4-7pm (45%), one midterm, Thursday, February 5 (25%), class participation, in class quizzes and homework (30%). The instructor reserves the right to change these percentages.

PLEASE NOTE: MATHEMATICS 147B WILL NOT BE OFFERED SPRING 2015.

(If you would like a reading course, or a special project, based on topics often covered in Math 147B, please see the instructor.)

TENTATIVE LIST OF TOPICS TO BE DISCUSSED:

1. Curvature of plane curves, curvature and torsion of space curves (Chapters 1-3 in the text by Pressley).

2. Definition of surfaces (Chapter 4) and first fundamental form (Chapter 5).

3. Second fundamental form, principal curvatures, Gaussian curvature and mean curvature (Chapters 6 and 7).

4. Geodesics (Chapter 8).

5. Gaussian Curvature is Intrinsic (Chapter 10).

6. Additional topics as time permits.