General information:

• Lectures: Tue, Th 11:00-12:15pm, room 380X


• Professor: Eleny Ionel, office 383K, ionel "at" math.stanford.edu,
  Office Hours: Tue and Th 1pm-2pm and by appointment.

• Textbook: Manfredo Do Carmo, Differential Geometry of Curves and Surfaces


• Course Description: This course provides an introduction to differential geometry, focusing mostly on the geometry of curves and surfaces in three-space with a view towards higher dimensional extensions (we do not plan to emphasize computational aspects of differential geometry). Topics covered in this class include: curves and surfaces, first fundamental form, parallel transport, curvature, geodesics, Gauss-Bonnet theorem, constant curvature surfaces and minimal surfaces.

  For more details see Course Outline and Homework Assignments

• Prerequisites: Familiarity with linear algebra and multivariable calculus (at the level of Math 50s series) will be assumed throughout the class; some previous exposure to mathematical reasoning is recommended for those considering taking this class.
• Grading Policy: homework 30%, midterm 30%, final exam 40%.
• Exam Schedule:
  Midterm: Th, Feb 7, in class;
  Final Exam: Mon, March 18th, 3:30pm-6:30pm.

• Homework: Weekly assignments will be posted on this website every Thursday and due the following Thursday in class; no late homework will be accepted under any circumstances. To accommodate exceptional situations such as a serious illness, your lowest homework score will be dropped.

Note: It is very important that you do all the homework since it is almost impossible to learn without working through many examples and problems. You are permitted and in fact strongly encouraged to discuss the homework problems with others in the class or your instructor, but you must write up your homework solution by yourself. In particular, you should understand well enough the solution to be able to reproduce it yourself, especially since similar problems and ideas are likely to appear in the exams.

Students are expected to take care in writing their assignments. For instance, assignments should be written neatly and contain clear, complete solutions; solutions sets which contain multiple pages should be stapled; and never forget to put your name on the top of your work.

• Stanford's Honor Code and Fundamental Standard;

• Statement from the Registrar concerning students with documented disabilities: "Students who may need an academic accommodation based on the impact of a disability must initiate the request with the Student Disability Resource Center (SDRC) located within the Office of Accessible Education (OAE). SDRC staff will evaluate the request with required documentation, recommend reasonable accommodations, and prepare an Accommodation Letter for faculty dated in the current quarter in which the request is being made. Students should contact the SDRC as soon as possible since timely notice is needed to coordinate accommodations. The OAE is located at 563 Salvatierra Walk (phone: 723-1066)."