University of Pittsburgh Math 1350 : Introduction to Differential Geometry : Fall 2014

Math 1350: Introduction to Differential Geometry

Mon, Wed, Fri 11:00 - 11:50pm -- 524 Thackeray Hall

Homework , Midterm 1 , Midterm 2 , Midterm 2 solutions , Final exam

Instructor. Dr. Marta Lewicka (office hours at 2pm on Fridays in Thackeray 408)
Grader. Kim Romanelli (office hours: Tue 11-12 and Th 10-12 in MAC center)
Textbook. A.N. Pressley, "Elementary Differential Geometry." Springer Undergraduate Mathematics Series, Springer; 2nd ed. 2010.

Other books:
1. M. Do Carmo, "Differential geometry of curves and surfaces." Prentice-Hall, Inc., Englewood Cliffs, N.J., 1976
2. S. Montiel: "Curves and surfaces." American Mathematical Society, 2005.
3. M. Spivak: "A Comprehensive Introduction to Differential Geometry." 3rd ed. Houston, Tex.: Publish or Perish, Inc., 1999.
Grades. Exam grading is curved. Grades will be based homework (30%), two midterms (15% + 15%) and the final exam (40%). There will be no make up midterm exams. If you miss the midterm exam for a *documented* medical reason, your grade on it will be the prorated grade of your final exam. Incompletes will almost never be given, and only for cases of extreme personal tragedy.
Homework. Homework will be assigned each Monday (starting in the second week of the semester), and it will be due the following Monday at the beginning of class. Late homework will not be accepted. The lowest homework grade will be dropped. The solution of each exercise will be evaluated in the scale 0-5 points, taking into account the correctness, clarity and neatness of presentation. You may collaborate and discuss the problems with each other but should write up solutions independently.
Core topics. This course is an introduction to differential geometry of curves and surfaces. It covers material related to:
1. Theory of curves in R^2 and R^3. Curvature, torsion, Frenet equations, four vertex theorem, isoperimetric inequality, Fenchel's theorem.
2. Theory of surfaces in R^3. First and second fundamental form, curvature, the Gauss Theorema Egregium, covariant derivative, the Gauss-Bonnet theorem, Euler characteristic, minimal surfaces, surfaces of constant curvature.

Calendar.

25 Aug (Mon): First Class
1 Sept (Mon): Labor Day -- no class
3 Oct (Fri): Midterm 1
13 Oct (Mon): Fall Break -- no class
14 Nov(Fri) : Midterm 2
26, 28 Nov (Wed, Fri): Thanksgiving Break -- no class
5 Dec (Fri): Last Class
Final Exam: 9 Dec, 2014, 12:00PM - 1:50PM, in Thack 524