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:

    Homework:

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

    Midterm:

    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

    Chapter

    Problems/Assignments

    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

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

    Feb 16

    Feb 15

    Ch.3

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

    Feb 23

    Feb 22

    Ch. 4

    HW 5

    March 1

    Feb 29

    Ch.4/5

    HW 6

    March 8

    Mar 21

    Ch.5

    Ch.5: 11, 13, 17, 19

    March 29

    Mar 28

    Ch.7

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

    Apr 5

    Apr 4

    Ch. 7

    HW 9

    Apr 12

    Apr 11

    Ch. 7/8

    HW10

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

    Apr 19

    Apr 18

    Ch.8

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

    Apr 26

    Apr 25

    Ch 8, Ch. 11

    HW12

    May 3


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