Birth of the Riemann Curvature Tensor
Fall 2020
This course is an introduction to the Riemann curvature tensor -- the basic invariant of Riemannian metrics. It is the generalization of the Gauss curvature for surfaces to arbitrary higher dimensional spaces. We will follow the path that Riemann blazed in his discovery of this remarkable, but complicated, invariant.
This is a rather advanced topic and so knowledge of the content of MAT 322 (Analysis in higher dimensions) and MAT 362 (Differential geometry of surfaces) is strongly encouraged.
Instructor: Michael Anderson
Office: 4-110 Math
Tower
Email:
anderson at math.sunysb.edu
Web site:
http://www.math.sunysb.edu/~anderson
Zoom Office hours: Tu/Th 11-12, W 12-1pm and by appointment. Please email me well before any office hour visit to enable Zoom connection.
Class Times: Tu/Th 1:15-2:35pm, online, Zoom
Grading: Your grade will be based on your lecture presentations, your lecture notes, and class participation.
Course Text:
A Comprehensive Introduction to Differential Geometry, Volume II, by
Michael Spivak, Publish or Perish, Inc.
This text is mandatory. Unfortunately, there are not many inexpensive print copies available but there are many online PDF sources for the text. The PDF version is available in a class Dropbox folder.
Class Format:
For the first three weeks of class, I will introduce the main concepts and issues that will be the focus of the semester. Following this, each student will give two (non-consecutive) lectures on an assigned topic; I will regularly provide individual assistance and guidance on this process. Students should make their lecture notes available to everyone in the class. Frequent disucssion and questions are encouraged.
Volume II, Chapter 4 of the Spivak text is the main focus of the course.
This will be an online class, meeting on Zoom through Blackboard.
Required Syllabi Statements
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.
This is a rather advanced topic and so knowledge of the content of MAT 322 (Analysis in higher dimensions) and MAT 362 (Differential geometry of surfaces) is strongly encouraged.
Instructor: Michael Anderson
Office: 4-110 Math Tower
Email: anderson at math.sunysb.edu
Web site: http://www.math.sunysb.edu/~anderson
Zoom Office hours: Tu/Th 11-12, W 12-1pm and by appointment. Please email me well before any office hour visit to enable Zoom connection.
Class Times: Tu/Th 1:15-2:35pm, online, Zoom
Grading: Your grade will be based on your lecture presentations, your lecture notes, and class participation.
Course Text:
A Comprehensive Introduction to Differential Geometry, Volume II, by
Michael Spivak, Publish or Perish, Inc.
This text is mandatory. Unfortunately, there are not many inexpensive print copies available but there are many online PDF sources for the text. The PDF version is available in a class Dropbox folder.
Class Format:
A Comprehensive Introduction to Differential Geometry, Volume II, by Michael Spivak, Publish or Perish, Inc.
This text is mandatory. Unfortunately, there are not many inexpensive print copies available but there are many online PDF sources for the text. The PDF version is available in a class Dropbox folder.
Class Format:
For the first three weeks of class, I will introduce the main concepts and issues that will be the focus of the semester. Following this, each student will give two (non-consecutive) lectures on an assigned topic; I will regularly provide individual assistance and guidance on this process. Students should make their lecture notes available to everyone in the class. Frequent disucssion and questions are encouraged.
Volume II, Chapter 4 of the Spivak text is the main focus of the course.
This will be an online class, meeting on Zoom through Blackboard.
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.