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Viewing: MA 555 : Introduction to Manifold Theory

Last approved: Sat, 27 Aug 2016 08:01:03 GMT

Last edit: Sat, 27 Aug 2016 08:01:03 GMT

Catalog Pages referencing this course
Change Type
Major
MA (Mathematics)
555
013839
Dual-Level Course
No
Cross-listed Course
No
Introduction to Manifold Theory
Introduction Manifold Theory
College of Sciences
Mathematics (17MA)
Term Offering
Fall Only
Offered Every Year
Fall 2016
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
 
 
Irina Kogan
Associate Professor
Full

Open when course_delivery = campus OR course_delivery = blended OR course_delivery = flip
Enrollment ComponentPer SemesterPer SectionMultiple Sections?Comments
Lecture1010NoNone
Open when course_delivery = distance OR course_delivery = online OR course_delivery = remote
Prerequisite: MA 405 and MA 426
Is the course required or an elective for a Curriculum?
No
An introduction to smooth manifolds. Topics include: topological and smooth manifolds, smooth maps and differentials, vector fields and flows, Lie derivatives, vector bundles, tensors, differential forms, exterior calculus, and integration on manifolds.

MA 555 is part of a two-course sequence that prepares students for taking a written qualifying exam in Differential Geometry.  As part of a realignment of this course sequence, MA 555 is being moved from the Spring semester to the Fall semester.  Previously, the MA 555 course description referred back to the Mathematics Dept. course listing. A course description has been added to reflect the content of the course in the newly aligned two-course sequence (MA 555-755). Overall, the content of MA 555 is not being changed.  Lastly, the prerequisites have been changed to MA 426 (Math Analysis II) and MA 405 (Intro. to Linear Algebra).


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 EngineeringMihail 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 main objective of this course is to learn how to carry out the differential and integral calculus on non-Euclidean spaces.


Student Learning Outcomes

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

1. Construct manifolds and tensor bundles.

2.  Distinguish special types of maps between manifolds: (local) diffeomorphisms, submersions, immersions, and embeddings.

3.  Carry out tensor calculus computations, including: pushforward, pullback, tensor product.

4.  Distinguish between covariant and contravariant tensors.

5. Use vector fields to construct flows and submanifolds. Compute Lie derivatives.

6. Carry out exterior calculus computations, including:~exterior product, exterior differentiation, integration of differential forms.

7. Prove Stokes' Theorem.


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
Smooth manifolds and their maps1 weekLectures
Tangent vectors, vector fields and Lie brackets2 weeksLectures
Immersions, submersions, embeddings2 weekLectures
Flows and Lie derivatives1 weekLectures
Vector bundles1 weekLectures
Cotangent bundle1 weekLectures
Tensors and tensor bundles2 weeksLectures
Exterior calculus2 weeksLectures
Integration on manifolds1 weekLectures
de Rham cohomology1 weekLectures
Distributions, integral manifolds, foliations1 weekLectures
mlnosbis 4/15/2016: No overlapping courses. Consultation notes are listed above.

ghodge 4/15/2016 Ready for ABGS reviewers. Comment: Assuming this courses uses a standard grading scale. Please consider adding the grading scale to the syllabus.

ABGS Reviewer Comments:
-Syllabus does not meet university or Graduate School standards.

ghodge 4/21/2016 return to department with guidelines for syllabus. RESOLVED.
Key: 3507