Math 5378: Differential Geometry - Spring 2024

Course Details

• Class Meetings:
  • Time: 02:30 PM - 03:20 PM, MWF
  • Location: Vincent Hall 2
• Instructor:
  • Name: Erkao Bao
  • Office: Vincent Hall 356
  • Email: my last name at umn dot edu
• Course Management:
  • Platform: Canvas
  • All class announcements and assignments will be posted on canvas.
• Instructor Office Hours:
  • 1:30-2:30pm Wed
  • 11:10 - 12:10pm Fri
  • by appointment
• Textbook:
  • Title: “Differential Geometry of Curves and Surfaces” by Do Caromo
  • Errata: List compiled by Bjorn Poonen

Course Objectives

To familiarize students with the foundational principles of differential geometry with emphasis on curves and surfaces in space. The curriculum includes:

• Basic theory of curves
• Frenet formulas
• Basic theory of surfaces
• Curvature
• Parallel transport
• Geodesics
• Gauss-Bonnet theorem

Detailed Weekly Course Topics Breakdown

Prerequisites

• Multivariable calculus (Math 2263 or equivalent)
• Linear algebra
• Differential equations (Math 2243 or equivalent)

Academic Support

1. Participate in study groups.
2. Utilize the SMART Learning Commons for free tutoring across Twin Cities Campuses.
3. Attend instructor’s office hours (refer to ‘Course Details’ for timing).

Assessments

Homework

• Frequency: Weekly on Canvas
• Submission: Via Canvas
• Evaluation: A few problems from each problem set will be selected for grading. Your lowest problem set score will be dropped from your final grade.

In class midterm Exam 1

• Duration: 50 mins
• Date & Time: Feb 23, Friday, 02:30 PM - 03:20 PM
• Location: in class

In class midterm Exam 2

• Duration: 50 mins
• Date & Time: Apr 3, Wednesday, 02:30 PM - 03:20 PM
• Location: in class

Final Exam

• Duration: 2 hours
• Time: Friday 5/3/2024 - 8:00a.m.-10:00a.m.
• Location: Vincent 2

Make-up Exams

• No make-up exams or quizzes will be given.
• Missing a midterm is permitted only for the most compelling reasons.
• In extraordinary situations, obtain permission from the lecturer (not your TA!) to miss an exam in advance; otherwise, a score of 0 will be awarded.
• If excused from a midterm, the course grade will be determined by giving extra weight to the final exam.
• In extremely exceptional situations, students missing the final exam will fail the course.

Grading Policy

• Homework: 40%
• Each Midterm: 15%
• Final Exam: 30%

Calculator Policy

• Calculators are not required and will not be permitted during exams.

Drops/Withdrawals

• Important dates and deadlines