MAT 362: Differential Geometry of Surfaces

Spring 2022

Department of Mathematics
Stony Brook University

Course Description: The foundation of differential geometry is the concept of curvature. The course will focus on understanding this and related concepts very clearly, both geometrically and computationally, for the case of curves and surfaces in Euclidean space. For this, you will need a solid background in multivariable calculus and linear algebra. We also hope to give some idea of how curvature is understood in higher dimensions; this is the basis of Riemannian geometry and General Relativity.

Textbook: Differential Geometry of Curves and Surfaces, by Manfredo P. do Carmo, Dover Publications, Second Edition, 2016.

Prerequisite: MAT 205 (Calculus III) and MAT 210 (Linear Algebra).

Instructor: Marcus Khuri, Math Tower 3-122. Office Hours: Tuesday and Thursday from 1:00-2:30pm via zoom. Email:

Course Assistant: Mohamad Rabah, Math Tower S-240A, Office Hours: Wednesday 3-4pm via zoom; Monday 3-4pm and Wednesday 2-3pm (in MLC). Email:

Class schedule: Tuesday and Thursday, 9:45-11:05am, Physics P130

Homework: Homework is a fundamental part of this course, and you will have to work hard on the assigned problems in order to succeed. Assignments will be posted on the course website at the beginning of each week, and will be due on Wednesday of the following week at 3pm. A box or envelop will be placed outside the office of the course assistant, where you may turn in your homework. Late homework will not be accepted. Homework will account for 40% of the total grade.

Homework 1 (Due 2/2) - §1.2: 2, 4; §1.3: 6, 10; §1.4: 5, 10, 11a.

Homework 2 (Due 2/9) - §1.5: 6, 10;

Homework 3 (Due 2/16) - §1.6: 1, 3; §1.7: 1, 2; §2.2: 1, 3, 7a, 7b, 16;

Homework 4 (Due 2/23) - §2.3: 1, 2, 4, 5; §2.4: 3, 8, 15, 18;

Homework 5 (Due 3/2) - §2.5: 1a, 5, 6, 14; §2.6: 1, 3, 5a;

Homework 6 (Due 3/23) - §3.2: 2, 3, 4, 5, 8; Study for Midterm;

Homework 7 (Due 3/30) - §3.3: 1, 3, 5, 16;

Homework 8 (Due 4/13) - §3.4: 7, 8, 9; §4.2: 1a, 1b, 4, 18;

Homework 9 (Due 4/27) - §4.3: 1, 3, 6, 9; §4.4: 2, 4, 5;

Homework 10 (Due 5/4) - §4.4: 8, 10, 13, 18, 23;

Homework 11 (Due 5/11) - §4.5: 1, 2, 3, 4a, 5;

Exams: There will be an in class midterm on Thursday, March 10, and in class final exam presentations. Each exam will respectively account for 25% and 35% of the total grade.

Help: The Math Learning Center (MLC) is located in Math Tower S-235, and offers free help to any student requesting it. It also provides a locale for students wishing to form study groups. The MLC is open 9am-7pm Monday through Friday. A list of graduate students available for hire as private tutors is maintained by the Undergraduate Mathematics Office, Math Tower P-143.

Disability Support Services (DSS)
If you have a physical, psychological, medical, or learning disability that may impact your course work, please contact the Student Accessibility Support Center, Stony Brook Union Suite 107, (631) 632-6748, or at They will determine with you what accommodations are necessary and appropriate. All information and documentation is confidential. Students who require assistance during emergency evacuation are encouraged to discuss their needs with their professors and the Student Accessibility Support Center. For procedures and information go to the following website: and search Fire Safety and Evacuation and Disabilities.

Academic Integrity
Each student must pursue his or her academic goals honestly and be personally accountable for all submitted work. Representing another person's work as your own is always wrong. Faculty is required to report any suspected instances of academic dishonesty to the Academic Judiciary. Faculty in the Health Sciences Center (School of Health Technology & Management, Nursing, Social Welfare, Dental Medicine) and School of Medicine are required to follow their school-specific procedures. For more comprehensive information on academic integrity, including categories of academic dishonesty please refer to the academic judiciary website at

Critical Incident Management
Stony Brook University expects students to respect the rights, privileges, and property of other people. Faculty are required to report to the Office of Student Conduct and Community Standards any disruptive behavior that interrupts their ability to teach, compromises the safety of the learning environment, or inhibits students' ability to learn. Until/unless the latest COVID guidance is explicitly amended by SBU, during Spring 2022 ``disruptive behavior" will include refusal to wear a mask during classes. For the latest COVID guidance, please refer to: