Spring 2019
This course is an introduction to the basic structures and concepts of smooth manifolds. Topics to be covered include: smooth manifolds and mappings, tangent and tensor bundles, vector and tensor fields, differential forms, integration on manifolds, Stokes theorem, deRham cohomology, Frobenius theorem.
Instructor: Michael Anderson
Office: 4-110 Math
Tower
Email:
anderson at math.sunysb.edu
Web site:
http://www.math.sunysb.edu/~anderson
Office hours: M 12-1, M 2:30-3:30, F 1:30-2:30 in Math Tower 4-110.
Grader: Lisandra Hernandez Vazquez
Email:
lisandra.hernandezvazquez
at stonybrook dot edu
Office: Math Tower 2-105
Office hours: M 2:30-3:30 in Math Tower 2-105 and MW 1-2 in MLC
Lectures: MW 1:00-2:20pm, Math Tower 4-130.
Grading: Homework 50%, Midterm 20%, Final 30%
Course Text:
Introduction to Smooth Manifolds, 2nd Edition, by
John M. Lee, Springer Verlag 2012
Homework:
There will be weekly HW assignments, generally due in class on
Mondays.
Check the course schedule below regularly for the assignments.
Midterm:
Monday, March 11, 1 - 2:20 in class
Material: Chapters 1-9 of the text.
Final Exam:
Tuesday, May 14, 3:15-5:45pm in Math 4-130
Week of
Chapter
Problems/Assignments
Due Date
Jan 28
Ch.1 & 2: smooth manifolds and maps
Ch. 1: 1, 6, 7,9.
Ch. 2: 5, 7, 10.
Feb 4
Feb 4
Ch.3 & 4: tangent vectors and derivatives
Ch.3: 3, 4, 5, 6
Feb 11
Feb 11
Ch.4 & 5: submersions, immersions, submanifolds
Ch.4: 5, 6, 13
Ch.5: 1, 4, 6, 9, 11.
Feb 18
Feb 18
Ch.6; Sard theorem, transversality
Ch.6: 3, 6, 9, 16, 17
Feb 25
Feb 25
Ch.8 & 9; Vector fields and flows
Ch.8: 4, 10, 11ac, 12, 20
Ch.9: 3bc, 4, 5.
Mar 4
Mar 4
Ch.9 & 11; Flows & vector bundles
prepare for Midterm
--
Mar 11
Midterm, Monday March 11
---
--
Mar 18
Spring Break
---
--
Mar 25
Ch. 11 & 12: Cotangent bundle, tensors
Ch 11: 4, 5, 7ab, 9, 11.
Ch 12: 4, 5, 8
Apr 1
Apr 1
Ch. 12 & 14: Tensors, differential forms
Ch 12: 6, 7
Ch 14: 1, 5.
Apr 8
Apr 8
Ch. 14 & 15: Differential forms, orientation
Ch 14: 6, 7
Ch 15: 3, 6, 13a.
Apr 15
Apr 15
Ch. 14 - 16: Forms, orientation & integration
Ch 15: 1, 2, 5, 7.
Ch 16: 1, 2, 3.
Apr 22
Apr 22
Ch. 16: Integration
Ch 16: 9b, 10bc.
Ch 17: 1.
Apr 29
Apr 29
Ch. 17: DeRham cohomology
Ch 17: 4, 5, 7, 10, 12, 13
May 6
May 6
Ch. 17 & Ch. 19: DeRham cohomology, distributions and foliations
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---
Americans with Disabilities Act: If you have a physical, psychological, medical, or learning disability
that may impact on your ability to carry out assigned course work,
please contact Disability Support Services at (631) 632-6748
DSS
. DSS office: EEC (Educational Communications Center) Building, Room 128.
DSS will review your concerns and determine,
with you, what accommodations, if any, are necessary and appropriate. All
information and documentation is confidential.
Arrangements should be made early in the semester so that your needs
can be accommodated.
Students who require assistance during emergency evacuation are encouraged to discuss
their needs with their professors and DSS. For procedures and information go to the DSS website above.
Academic Integrity: Each student must pursue his or her academic goals honestly and be personally accountable for all submitted work. Representing another persons work as your own is always wrong. Faculty are required to report any suspected instances of academic dishonesty to the Academic Judiciary. For more comprehensive information on academic integrity, including categories of academic dishonesty, please refer to the academic judiciary website here.
Critical Incident Management: Stony Brook University expects students to respect the rights, privileges, and property of other people. Faculty are required to report to the Office of University Community Standards any disruptive behavior that interrupts their ability to teach, compromises the safety of the learning environment, or inhibits the students' ability to learn. Further information about most academic matters can be found in the Undergraduate Bulletin, the Undergraduate Class Handbook and the Faculty-Employee Handbook.
Instructor: Michael Anderson
Office: 4-110 Math Tower
Email: anderson at math.sunysb.edu
Web site: http://www.math.sunysb.edu/~anderson
Office hours: M 12-1, M 2:30-3:30, F 1:30-2:30 in Math Tower 4-110.
Grader: Lisandra Hernandez Vazquez
Email: lisandra.hernandezvazquez at stonybrook dot edu
Office: Math Tower 2-105
Office hours: M 2:30-3:30 in Math Tower 2-105 and MW 1-2 in MLC
Lectures: MW 1:00-2:20pm, Math Tower 4-130.
Grading: Homework 50%, Midterm 20%, Final 30%
Course Text:
Introduction to Smooth Manifolds, 2nd Edition, by
John M. Lee, Springer Verlag 2012
Homework:
Introduction to Smooth Manifolds, 2nd Edition, by John M. Lee, Springer Verlag 2012
Homework:
There will be weekly HW assignments, generally due in class on
Mondays.
Check the course schedule below regularly for the assignments.
Midterm:
Monday, March 11, 1 - 2:20 in class
Material: Chapters 1-9 of the text.
Final Exam:
Tuesday, May 14, 3:15-5:45pm in Math 4-130
|
Week of |
Chapter |
Problems/Assignments |
Due Date |
|---|---|---|---|
|
Jan 28 |
Ch.1 & 2: smooth manifolds and maps |
Ch. 1: 1, 6, 7,9. Ch. 2: 5, 7, 10. |
Feb 4 |
|
Feb 4 |
Ch.3 & 4: tangent vectors and derivatives |
Ch.3: 3, 4, 5, 6 |
Feb 11 |
|
Feb 11 |
Ch.4 & 5: submersions, immersions, submanifolds |
Ch.4: 5, 6, 13 Ch.5: 1, 4, 6, 9, 11. |
Feb 18 |
|
Feb 18 |
Ch.6; Sard theorem, transversality |
Ch.6: 3, 6, 9, 16, 17 |
Feb 25 |
|
Feb 25 |
Ch.8 & 9; Vector fields and flows |
Ch.8: 4, 10, 11ac, 12, 20 Ch.9: 3bc, 4, 5. |
Mar 4 |
|
Mar 4 |
Ch.9 & 11; Flows & vector bundles |
prepare for Midterm |
-- |
|
Mar 11 |
Midterm, Monday March 11 |
--- |
-- |
|
Mar 18 |
Spring Break |
--- |
-- |
|
Mar 25 |
Ch. 11 & 12: Cotangent bundle, tensors |
Ch 11: 4, 5, 7ab, 9, 11. Ch 12: 4, 5, 8 |
Apr 1 |
|
Apr 1 |
Ch. 12 & 14: Tensors, differential forms |
Ch 12: 6, 7 Ch 14: 1, 5. |
Apr 8 |
|
Apr 8 |
Ch. 14 & 15: Differential forms, orientation |
Ch 14: 6, 7 Ch 15: 3, 6, 13a. |
Apr 15 |
|
Apr 15 |
Ch. 14 - 16: Forms, orientation & integration |
Ch 15: 1, 2, 5, 7. Ch 16: 1, 2, 3. |
Apr 22 |
|
Apr 22 |
Ch. 16: Integration |
Ch 16: 9b, 10bc. Ch 17: 1. |
Apr 29 |
|
Apr 29 |
Ch. 17: DeRham cohomology |
Ch 17: 4, 5, 7, 10, 12, 13 |
May 6 |
|
May 6 |
Ch. 17 & Ch. 19: DeRham cohomology, distributions and foliations |
--- |
--- |
Americans with Disabilities Act: If you have a physical, psychological, medical, or learning disability that may impact on your ability to carry out assigned course work, please contact Disability Support Services at (631) 632-6748 DSS . DSS office: EEC (Educational Communications Center) Building, Room 128. DSS will review your concerns and determine, with you, what accommodations, if any, are necessary and appropriate. All information and documentation is confidential. Arrangements should be made early in the semester so that your needs can be accommodated.
Students who require assistance during emergency evacuation are encouraged to discuss their needs with their professors and DSS. For procedures and information go to the DSS website above.
Academic Integrity: Each student must pursue his or her academic goals honestly and be personally accountable for all submitted work. Representing another persons work as your own is always wrong. Faculty are required to report any suspected instances of academic dishonesty to the Academic Judiciary. For more comprehensive information on academic integrity, including categories of academic dishonesty, please refer to the academic judiciary website here.
Critical Incident Management: Stony Brook University expects students to respect the rights, privileges, and property of other people. Faculty are required to report to the Office of University Community Standards any disruptive behavior that interrupts their ability to teach, compromises the safety of the learning environment, or inhibits the students' ability to learn. Further information about most academic matters can be found in the Undergraduate Bulletin, the Undergraduate Class Handbook and the Faculty-Employee Handbook.