Differential Geometry of Curves and Surfaces
MATH 390 Spring 2018
Course Information

Lectures: Hashinger 127, MWF 10:00-10:50am

Instructor: Dr. Mihaela B. Vajiac

Office: VN 102

Office hours: Announced on Webpage.

Webpage: http://www1.chapman.edu/~mbvajiac
Moodle Webpage: http://mathv.chapman.edu/moodle

Credits: 3

Text: Differential Geometry of Curves and Surfaces by Manfredo do Carmo, ISBN 978-0486806990 We will cover most of the concepts in the book and unlock the beauty of curves and surfaces.
Other helpful books: Elementary Differential Geometry by A.N. Pressley, and
Elementary Differential Geometry revised second edition, by Barrett O'Neill.

Homework: Homework, mostly from the text, will be assigned in class, usually on Fridays and will be due in class one week later. (An exception is the first homework, assigned today and due on Monday, Feb 5th). Homework will also be posted on the Web.

Collaboration: You are encouraged to work together on homework and to learn from each other. However, the paper you eventually turn in should represent your own understanding -- you should be able to justify every sentence. There is a fine line between collaborative learning and turning in another's work.

Exams: There will be one midterm take-home exam, announced in class one week before it is given. The midterm exam will include presentations of individual or group projects, the on-going and changing list to be announced every two weeks or so. The final exam will contain a written and an individual presentation component.

Grading Policy: Midterm 30%, the homework counts 30%, and the final exam counts 30%, class participation 10%.

Proofs: Mathematics is about proving things as much as it is about calculating things. The first homework is given mainly to see how well you understand the art of proof. If you have trouble with proofs, we can work on it, but there is no avoiding the concept of proof in (honest) mathematics.

Help: Office hours are there for a reason. Please come. You are not only doing yourself a favor, but also giving me valuable feedback. The more questions you ask, the better my next lecture will be.


Course Learning Outcomes:
1. Students will understand and apply theorems related to curves and surfaces embedded in the Euclidean Space.
2. Sudents will understand and apply results of tensor Calculus and the language of differential forms.
3. Students will prove basic results in Differential Geometry of Curves and Surfaces, as embedded in the Euclidean Space as well as abstract manifolds of dimensions 1 and 2.
4. Students will be able to write solutions to problems and extend theoretical proofs to examples.

Program Learning Outcomes:
1. Graduates will be able to communicate mathematical ideas orally and in writing.
2. Graduates will be able to read university level mathematical texts.
3. Graduates will be able to prove basic results in mathematics.
4. Graduates will be able to read professional literature in mathematics.

Fun: We'll have loads of fun, that's a promise!

Disabilities: Any student in this course who has a disability that may prevent him or her from fully demonstrating his or her abilities should contact me personally as soon as possible so we can discuss accommodations necessary to ensure full participation and facilitate your educational opportunity.

Academic Integrity: Students are assumed to be familiar with the Academic Integrity Code. Any violations of this code will be strictly dealt with in accordance with this code.

Disclaimer: The information in this syllabus is subject to change in the event of extenuating circumstances.

Mihaela Vajiac
Dept Math/CS/Phys
Chapman University. Last modified: Feb 2 10:42:46 PDT 2016