MAT 362: Differential Geometry of Surfaces

Spring 2018

Department of Mathematics
SUNY at Stony Brook

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'll 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, Prentice-Hall, 1976.

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

Instructor: Marcus Khuri, Math Tower 3-122. Office Hours: Tuesdays and Thursdays from 2:30-4:00pm. Email: khuri@math.sunysb.edu

Course Assistant: Erik Gallegos Banos, Math Tower 3-106, Office Hours: Tu 3-5pm; Tu 5-6pm (in MLC). Email: erik.gallegosbanos@stonybrook.edu

Class schedule: TuTh 1:00pm-2:20pm, Earth & Space 181

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 1/31) - §1.2: 2, 4; §1.3: 6, 10; §1.4: 5, 10, 11a; §1.5: 6, 10;

Homework 2 (Due 2/7) - §2.2: 1, 3, 7a, 7b, 16; §2.3: 1, 2, 4, 5;

Homework 3 (Due 2/14) - §2.4: 3, 8, 15, 18; §2.5: 1a, 5, 6, 14;

Homework 4 (Due 2/21) - §2.6: 1, 3, 5a; §3.2: 2, 3, 4, 5, 8;

Homework 5 (Due 2/28) - §3.3: 1, 4, 5a, 5b, 5c, 15, 18, 20;

Midterm Examination in class on 3/1 -- it covers sections 1.1-1.5, 2.1-2.6, 3.1-3.3.

Homework 6 (Due 3/21) - §3.4: 4, 7a, 7b, 10a, 10b; §4.2: 1a, 1b, 4, 18;

Homework 7 (Due 3/28) - §4.3: 1, 3, 6, 9; §4.4: 4, 5, 7a, 7b;

Homework 8 (Due 4/4) - §4.5: 1, 2, 3, 4a, 5;

Homework 9 (Due 4/11) - §4.6: 1, 3, 5, 6, 9, 14a, 14b;

Homework 10 (Due 4/18) - §4.7: 1, 2, 4, 5; §5.2: 2, 3;

Homework 11 (Due 4/25) - §5.3: 2, 6, 7; §5.4: 1, 2, 4;

Homework 12 (Due 5/9) - §5.5: 3, 4, 5; §5.6: 1, 2, 4;

Exams: There will be an in class midterm on Thursday, March 1, and an in class final on Thursday, May 3. 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 Disability Support Services, ECC (Educational Communications Center) Building, room 128, (631) 632-6748. They will determine with you what accommodations, if any, 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 Disability Support Services. For procedures and information go to the following website: http://www.stonybrook.edu/ehs/fire/disabilities

 
Academic Integrity
Representing another person's work as your own is always wrong. Faculty are 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 http://www.stonybrook.edu/commcms/academic_integrity/index.html

 
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 Judicial Affairs any disruptive behavior that interrupts their ability to teach, compromises the safety of the learning environment, or inhibits students' ability to learn. Faculty in the HSC Schools and the School of Medicine are required to follow their school-specific procedures.