MATH 255

Course description

: Math-255: Differential Geometry

This course builds on MTH 164 to describe calculus on curves, and surfaces. It provides useful tools for theoretical physics (in particular relativity theory) and the theory of hydrodynamics. It is also a useful basis for computer graphics. How can you show that NO flat map of the earth can EVER preserve all distances? Take this course… ask about Gauss curvature.

Instructor

: Surena Hozoori

Email: shozoori at ur.rochester.edu

Office: Hylan 1017

Lectures: MW 10:25am-11:40am

Lecture location: Hylan 303

Office hours: M 3:30pm-4:30pm, W 12pm-1pm

Textbook

Main source : Differential Geometry Curves-Surfaces-Manifolds, Wolfgang Kühnel, 3rd edition.

Secondary source : Differential Geometry of Curves and Surfaces, Manfredo P. Do Carmo, 2nd edition.

For further references, I can recommend seeing the following textbooks. We will not directly use these during this semester. However, they might be useful as additional sources you can consult for better understanding of the material, and each contain helpful exercises. Disclaimer: You should be aware that the topics included in each, as well as the terminology, notation, etc can be quite different. While I am more or less familiar with some of these textbook, I have not necessarily gone through carefully myself and gathered this list after doing some online research. So you should look into them with caution and curiosity! Anyways, they seem nice additional references to me.

(1) A Comprehensive Introduction to Differential Geometry, Michael Spivak. This (5 volume series) is a very well-known and comprehensive of the topics included in the course and beyond. It can serve more like the encyclopedia of geometry. The U of R library seems to have it.

(2) Differential Geometry: A First Course in Curves and Surfaces, Theodore Shifrin. Relatively concise and modern treatment of the curves and surfaces. You can download it here.

(3) Elementary Differential Geometry, Barrett O’Neill. A very nice book. Slightly different approach than our main textbooks. Digital/hard copy access through the library.

(4) Differential Geometry of Curves and Surfaces, T. F. Banchoff and S. T. Lovett. A fairly comprehensive reference. Digital access through the library.

(5) What is differential geometry?: curves and surfaces, A. Petrunin and S. Barrera. A nice set of lecture notes available at this link.

(6) Elementary Topics in Differential Geometry, J. A. Thorpe. A nice reference for surfaces. You can download a copy through the library.

Exams and Grading

For exam times and further info, see the see the Exams and Grading page.

Your grade for the course will be based on your performance on exams and homework assignments:

• Homework - 40%
• Midterm Exams - 15% each
• Comprehensive Final Exam - 30%

You will NOT be permitted calculators or other electronic devices (smart phones, smart watches, etc) on any exams. You will NOT be permitted books, notes, or “cheat sheets” on any exams. There will not be any make up exams offered in the course and in the case of a justified absence a portion of the final exam will replace the missing score.

The following is a rough indication of how your course grade will be assigned and exact grade cutoffs will be determined at the end of the semester:

Incomplete “I” grades are almost never given. The only justification is a documented serious medical problem or a genuine personal/family emergency. Falling behind in this course or problems with workload on other courses are not acceptable reasons.

Homework

We will have weekly/bi-weekly HW assignments during the semester, which means an assignment for almost every week (see /schedule). Each assignment typically contains 5 problems and the lowest HW scores will be dropped. The HW assignments are due Fridays 11:59pm.

Disability Support

The University of Rochester respects and welcomes students of all backgrounds and abilities. In the event you encounter any barrier(s) to full participation in this course due to the impact of disability, please contact the Office of Disability Resources. The access coordinators in the Office of Disability Resources can meet with you to discuss the barriers you are experiencing and explain the eligibility process for establishing academic accommodations. You can reach the Office of Disability Resources at: (585) 275-3424; Taylor Hall. Or, visit Disability Resources.

Please note that to be granted alternate testing accommodations, you (the student) must fill out forms with Disability Resources at least seven days before each and every exam. These forms are not sent automatically. Instructors are not responsible for requesting alternative testing accommodations at Disability Resources or making accommodations on their own.

Academic Integrity Statement

All assignments and activities associated with this course must be performed in accordance with the University of Rochester’s Academic Honesty Policy. More information is available at: www.rochester.edu/college/honesty.

Math Dept policy on unauthorized online resources: Any usage whatsoever of online solution sets or paid online resources (chegg.com or similar) is considered an academic honesty violation and will be reported to the Board on Academic Honesty. In particular, any assignment found to contain content which originated from such sources is subject to a minimum penalty of zero on the assignment and a full letter grade reduction at the end of the semester (e.g. a B would be reduced to a C). Depending on the circumstances, this may apply even if the unauthorized content was obtained through indirect means (through a friend for instance) and/or the student is seemingly unaware that the content originated from such sources. If you have any questions about whether resources are acceptable, please check with your instructor.

College Credit-Hour Policy

This course follows the College credit hour policy for four-credit courses. This course meets 3 academic hours per week.