COURSE: MTH 519

COURSE TITLE: Introduction to Differential Geometry

CREDITS and HOURS: 4 credits, 4 hours.

DESCRIPTION: This is an introduction to differential geometry. The course
addresses curves and surfaces in two and three dimensional Euclidean spaces using
the techniques of differential and integral calculus and linear algebra. Topics
will be selected from Frenet-Serret frames, intrinsic and extrinsic properties
of surfaces, Gaussian and mean curvature, geodesics, minimal surfaces, and the
Gauss-Bonnet theorem.

PRE-REQUISITES: (MTH 233 and MTH 330)

or (MTH 233, MTH 334 and MTH 338)

CO-REQUISITES: None

RESTRICTIONS: None

DESIGNATION: Mathematics

ROLE IN CURRICULUM: Elective for mathematics major

LEARNING GOALS and ASSESSMENT:

Objective |
Assessment Plan |

The student will be
able to show whether or not a subset of the Euclidean space is a submanifold. |
When the class is being assessed, the exams will include
embedded questions to assess whether the students have sufficiently mastered
the topic-specific learning goals. |

The student will be
able to compute the first and second fundamental form of a surface. |
Same |

The student will be
able to compute the Gaussian curvature of a surface. |
Same |

When assessment activities are done, the results will be
summarized in memorandum form and filed with the department chairperson for
record keeping purposes.

Information obtained from assessment will be used to assess
and self-reflect on the success of the course and to make any necessary changes
to improve teaching and learning effectiveness.

RATIONALE: In this
course we will use the student’s knowledge of calculus and linear algebra to
study the geometry of curves or surfaces. It allows students to develop their
skills by working on mathematical objects that can be visualized in three
dimension Euclidean spaces. It is an opportunity to learn how practical
questions, like making a geographical map of the earth, can be studied by
developing mathematical tools. It is a natural continuation of the calculus
courses and linear algebra, and provides mathematical notions that are
essential for students who plan to join a graduate program.

COMMENTS: None

CONSULTATION:
None

Log
of changes [For departmental use]