MAT 531 Topology/Geometry II

Spring 2016

SUNY at Stony Brook

This course is an introduction to the basic structures and concepts of smooth manifolds. Topics to be covered include: smooth manifolds, tangent and tensor bundles, vector and tensor fields, differential forms, integration on manifolds, Stokes theorem, deRham cohomology.

  • Lectures: Tu/Th 11:30-12:50pm, Physics P122

  • Grading:

    Homework 50%, Midterm 20%, Final 30%

    Course Text:


    There will be weekly HW assignments, generally due in class on Tuesdays.
    Check the course schedule below regularly for the assignments.


    Thursday, March 10, 1-2:20pm, in lecture class

    Final Exam:

    Wednesday, May 11, 5:30-8pm, in Physics P122 (usual lecture room).

    The exam will be cumulative, covering topics for whole semester, but with an emphasis on material since the Midterm.
    There are 6 problems on the exam.

    Week of



    Due Date

    Jan 25

    Ch. 2

    Ch. 2: 9, 18, 19, 24, 27

    Feb 2

    Feb 1

    Ch. 2

    Ch.2: 7, 25, 29, 32, 33a

    Feb 9

    Feb 8


    Ch.3: 5, 7, 19, 20(a), 23(a)-(d), 24(a)-(d)

    Feb 16

    Feb 15


    Ch.3: 12, 14, 15, 25, 26, 27

    Feb 23

    Feb 22

    Ch. 4

    HW 5

    March 1

    Feb 29


    HW 6

    March 8

    Mar 21


    Ch.5: 11, 13, 17, 19

    March 29

    Mar 28


    Ch.7: 5, 6, 8, 13, 17, 20

    Apr 5

    Apr 4

    Ch. 7

    HW 9

    Apr 12

    Apr 11

    Ch. 7/8


    Correction: Spivak Ch.8 (not Ch.7) probs.

    Apr 19

    Apr 18


    Ch. 8: 13, 14, 21, 22, 32(a).

    Apr 26

    Apr 25

    Ch 8, Ch. 11


    May 3

    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.