COURSE: MTH 015

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 students 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]