Introduction to Differential Geometry: MATH 4540
Spring 2025

Instructor:   Xiaodong Cao, Office:521 Malott.

E-mail: xiaodongcao at cornell.edu

Teaching Assistant: Mingjun Sun (Email: ms3732 at cornell.edu OH: 9-10 am or by appointment, 218 MLT)

Time and Place:  1:25 pm - 2:40 pm, Tuesday and Thursday, 203 MLT

Office Hour: 11-11:59 am Wednesday  or by appointment.

Text:  The following book is recommended:

• Differential Geometry and Applications, Richard Hamilton, Monique Chyba and Xiaodong Cao (notes will be provided)

Prerequisites: Calculus and Linear Algebra. The course will be self contained. But a little bit knowledge of Differential Equation and Topology will also help.

Midterm Exams:  The midterm exams are on March 6th (tentative)and April 17th (tentative).   Make-ups will not be given for the midterm exams. Students can only be excused from the midterms because of serious illness or a family emergency of comparable gravity. To be excused you will need a note from your doctor or dean.

Final Exam and Final Project: The final exam (take-home) and final project are both due on May 15th.

Homework: Homework will be assigned every two week and will be due on the date stated on the homework. The homework assignments will be announced in class. You must hand in the homework through Gradescope before 11:59pm on its due date. Late homework will NOT be accepted under any circumstances.

Grading: The course grade is apportioned as follows: Final exam 25%; the first midterm exam 25%; the second midterm 25%; homework grades 20%; final project 5%.

Academic honesty: It is the obligation of each student to understand the Cornell Code of Academic Integrity regarding academic honesty and to uphold these standards. This states, "A Cornell student's submission of work for academic credit indicates that the work s the student's own. All outside assistance should be acknowledged, and the student's academic position truthfully reported at all times." Students are encouraged to talk about the problems, but should write up the solutions individually. Students should acknowledge the assistance of any book, software, student or professor.

Copyright : Course materials posted on this website or distributed in class are intellectual property belonging to the author. Students are not permitted to buy or sell any course materials without the express permission of the instructor. Such unauthorized behavior constitutes academic misconduct.

Disabilities: Students with disabilities who will be taking this course and may need disability-related classroom accommodations are encouraged to make an appointment to see the instructor as soon as possible. Also, stop by the Office of Disability Services to register for support services.


 

Schedule of Lectures (Tentative! Updated 1/30)