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Viewing: MA 518 : Geometry of Curves and Surfaces

Last approved: Thu, 02 Jun 2016 15:29:55 GMT

Last edit: Thu, 02 Jun 2016 15:29:48 GMT

Catalog Pages referencing this course
Change Type
Major
MA (Mathematics)
518
013816
Dual-Level Course
No
Cross-listed Course
No
Geometry of Curves and Surfaces
Geometry Curves and Surfaces
College of Sciences
Mathematics (17MA)
Term Offering
Spring Only
Offered Every Year
Spring 2017
Previously taught as Special Topics?
No
 
Course Delivery
Face-to-Face (On Campus)

Grading Method
Graded/Audit
3
16
Contact Hours
(Per Week)
Component TypeContact Hours
Lecture3.0
Course Attribute(s)


If your course includes any of the following competencies, check all that apply.
University Competencies

Course Is Repeatable for Credit
No
 
 
Andrew Cooper
Teaching Assistant Professor
Assoc

Open when course_delivery = campus OR course_delivery = blended OR course_delivery = flip
Enrollment ComponentPer SemesterPer SectionMultiple Sections?Comments
Lecture1717NoNone
Open when course_delivery = distance OR course_delivery = online OR course_delivery = remote
Prerequisite: MA 242 and MA 405
Is the course required or an elective for a Curriculum?
No
Geometry of curves and surfaces in space; Arclength, torsion, and curvature of curves; Tangent spaces, shape operators, and curvatures of surfaces; metrics, covariant derivatives, geodesics, and holonomy. Applications in the physical sciences and/or projects using computer algebra.

1) The course title has been changed from "A First Course in Differential Geometry" to "Geometry of Curves and Surfaces" to more accurately reflect the existing course content. 


2) The semester of the offering has been changed from Fall to Spring (annually).


No

Is this a GEP Course?
GEP Categories

Humanities Open when gep_category = HUM
Each course in the Humanities category of the General Education Program will provide instruction and guidance that help students to:
 
 

 
 

 
 

 
 

 
 

 
 

Mathematical Sciences Open when gep_category = MATH
Each course in the Mathematial Sciences category of the General Education Program will provide instruction and guidance that help students to:
 
 

 
 

 
 

 
 

Natural Sciences Open when gep_category = NATSCI
Each course in the Natural Sciences category of the General Education Program will provide instruction and guidance that help students to:
 
 

 
 

 
 

 
 

Social Sciences Open when gep_category = SOCSCI
Each course in the Social Sciences category of the General Education Program will provide instruction and guidance that help students to:
 
 

 
 

 
 

 
 

 
 

 
 

Interdisciplinary Perspectives Open when gep_category = INTERDISC
Each course in the Interdisciplinary Perspectives category of the General Education Program will provide instruction and guidance that help students to:
 
 

 
 

 
 

 
 

 
 

 
 

 
 

 
 

Visual & Performing Arts Open when gep_category = VPA
Each course in the Visual and Performing Arts category of the General Education Program will provide instruction and guidance that help students to:
 
 

 
 

 
 

 
 

 
 

 
 

Health and Exercise Studies Open when gep_category = HES
Each course in the Health and Exercise Studies category of the General Education Program will provide instruction and guidance that help students to:
 
 

 
 

 
 

 
 

 
&
 

 
 

 
 

 
 

Global Knowledge Open when gep_category = GLOBAL
Each course in the Global Knowledge category of the General Education Program will provide instruction and guidance that help students to achieve objective #1 plus at least one of objectives 2, 3, and 4:
 
 

 
 

 
Please complete at least 1 of the following student objectives.
 

 
 

 
 

 
 

 
 

 
 

US Diversity Open when gep_category = USDIV
Each course in the US Diversity category of the General Education Program will provide instruction and guidance that help students to achieve at least 2 of the following objectives:
Please complete at least 2 of the following student objectives.
 
 

 
 

 
 

 
 

 
 

 
 

 
 

 
 

Requisites and Scheduling
 
a. If seats are restricted, describe the restrictions being applied.
 

 
b. Is this restriction listed in the course catalog description for the course?
 

 
List all course pre-requisites, co-requisites, and restrictive statements (ex: Jr standing; Chemistry majors only). If none, state none.
 

 
List any discipline specific background or skills that a student is expected to have prior to taking this course. If none, state none. (ex: ability to analyze historical text; prepare a lesson plan)
 

Additional Information
Complete the following 3 questions or attach a syllabus that includes this information. If a 400-level or dual level course, a syllabus is required.
 
Title and author of any required text or publications.
 

 
Major topics to be covered and required readings including laboratory and studio topics.
 

 
List any required field trips, out of class activities, and/or guest speakers.
 

College(s)Contact NameStatement Summary
College of SciencesDavid E AspnesThis course revision looks fine to Physics.
College of EngineeringMikhail DevetsikiotisECE sees nothing objectionable in these course revisions from their point of view.
No new resources are required due to this course revision. The current version of this course is taught by graduate faculty in our department as part of their regular teaching load.

The objective of this course is to introduce students to the main concepts of differential geometry by studying geometry of curves and surfaces embedded in three dimensional spaces. 


Student Learning Outcomes

A student who successfully completes this course will be able to:


1. Compute geometric invariants of curves and surfaces: length, curvature, torsion, first and second fundamental forms, mean curvature, Gauss curvature.


2. Distinguish between intrinsic and extrinsic invariants of curves and surfaces.


3. Compute covariant derivatives and holonomy.


4. Draw inferences about the global shape of a curve or surface given information about its curvature.


5. Explain physical phenomena in geometric terms. 


Evaluation MethodWeighting/Points for EachDetails
Test50Two tests are given during the semester and, combined, they are worth 50% of the final grade
Final Exam30The final exam is worth 30% of the final grade.
Homework20Homework, given bi-weekly, is worth 20% of the final grade.
TopicTime Devoted to Each TopicActivity
Geometry of curves3 weeksLectures
Introduction to surfaces2 weeksLectures
The Gauss map2 weeksLectures
Minimal surfaces2 weeksLectures
Intrinsic geometry of surfaces3 weeksLectures
Global differential geometry2 weeksLectures
Review and applications1 weekLectures
mlnosbis 4/15/2016: No overlapping courses. Consultation notes listed above.

ghodge 4/15/2016 Ready for ABGS reviewers.

ABGS Reviewer Comments:
-No Issues.
Key: 3504