MAT 362 - Differential Geometry of Surfaces (Spring 2021)

MAT 362: Differential Geometry of Surfaces

Spring 2021 (online synchronous)

E-mail: rlastname at scgp dot stonybrook dot edu

Class Hours: Tu/Th 11:30am-12:50pm

Office Hours: Tu 2-3pm, Th 10-11am

MLC Office Hours: Tu 4-5pm

Textbooks

1. Main Reference: T. Shifrin, Differential Geometry: A First Course in Curves and Surfaces, available online.

2. M. P. do Carmo, Differential Geometry of Curves and Surfaces.

Course Description

In this course we will develop the basic theory of differential geometry of curves and surfaces. Main

topics of study will consist of geodesics, parallel transport, curvature, isometries, the Gauss map and

the Gauss-Bonnet theorem. Time permitting we will also discuss special topics and applications, e.g.

Relativity.

Grading Policy

Grades will be calculated as follows:

30% Homeworks

30% Midterm

40% Final Exam

Homeworks

Homework sets will be assigned biweekly and posted on Blackboard. Students must upload their solutions

in the Assignments section of Blackboard before 11:59 pm EST of the due date - late homework will not

be accepted. For a given homework assignment, a random subset of problems will be chosen for grading.

You are expected to complete all assigned problems since you will not know which ones are to be graded.

Homework solutions will be graded not only for correctness but also for clarity, conciseness and rigor (in

the mathematical sense). You are allowed to work with other students on the homework sets, but you

must write your own solutions.

Examinations

Both the Midterm and Final will be take-home exams and will be posted on Blackboard one week before

the due dates. You are allowed to consult any reference you like for these exams, but you are not allowed

to discuss the problems (digitally or in-person) with anyone. You will be required to sign a statement that

you have followed these rules. Cheating or any other form of academic misconduct will not be tolerated.

The Midterm will be due on March 30, 2021 and the Final will be due on May 18, 2021. Solutions

must be uploaded to Blackboard before the end of the day on the due date. There will be no makeup

examinations.