# MATH 561: Differential Geometry.

INSTRUCTOR: Ruifang Song.
office: 411 Van Vleck
e-mail: rsong AT math DOT wisc DOT edu
office hours: To be anounced.

TEXTBOOK:

Differential Geometry of curves and surfaces, Manfredo P. do Carmo.
CLASS SCHEDULE: (Jan 21, 2014-May 9, 2014)
MATH 561: 13:00-14:15 TR.

• There will be weekly homework assignments due on Thursdays at the beginning of class. There will be one in-class midterm on March 13 and one final exam. The final grade will be roughly 35% for each exam, and 30% for homework.
Syllabus and tentative week-by-week schedule

HOMEWORK: Homework will be assigned about weekly.

• Homework 1 (due on Jan 30): section 1.2: 1, 2, 3; section 1.3: 1, 5, 6; section 1.4: 5, 13; section 1.5: 1, 4
• Homework 2 (due on Feb 6): section 1.5: 12, 13; section 1.6: 3; section 1.7: 3
• Homework 3 (due on Feb 13): section 2.2: 1, 7ab, 8, 11, 17ac; section 2.3: 2, 6, 15a
• Homework 4 (due on Feb 27): section 2.4: 2, 3, 7; section 2.5: 1a, 5, 7, 9; section 2.6: 1, 3, 5
• Homework 5 (due on Mar 6): section 3.2: 5, 9(a), 13, 17
• Homework 6 (due on Mar 13): section 3.2 #8(b); section 3.3: #5 (Note: If there is a star in front of a problem, that means you can find hints in the back of the book)
• Homework 7 (due on Mar 27): section 3.5 #12 (Hint: Given a compact surface S, take a sphere enclosing S and tangent to S at some point p. Show that the Gaussian curvature of S at p is bigger than or equal to the Gaussian curvature of the sphere at p.), 13, 14
• Homework 8 (due on April 3): 4.2: #2, 4, 10, 14; 4.3: #1
• Homework 9 (due on April 10): section 4.4: #4, 15(a)
• Homework 10 (due on April 17)4.4: #5, 11, 22 (Hint: Use the result in problem 15)