MAT 530 Topology/Geometry I

Fall 2017

SUNY at Stony Brook

This course is an introduction to the basic structures and concepts of point-set topology and beginning concepts of algebraic topology. This is a core course of the PhD program, and as such, the syllabus is relatively fixed. The list of topics to be covered is here.

  • Lectures: MW 10:00-11:20am, ESS 181

  • Grading:

    Homework 30%, Midterm 30%, Final 40%

    Course Text:

    Another useful text for the last third of the semester covering algebraic topology is:

  • Algebraic Topology by Alan Hatcher. This is available as PDF download on Hatcher's website: here.
  • Homework:

    There will be weekly homework assignments, generally due in class on (Wednesdays).

    You may discuss homework problems with other students and consult other sources, but you and only you are responsible for writing the full solutions expressing your full understanding. Please also write clearly and legibly.

    Late homework policy: In general, no late homework is accepted. Exceptions are at the discretion of the grader.
    Check the course schedule below regularly for the assignments.


    Wednesday, Oct 18, in lecture class

    The material for the Midterm will be all following Sections, which you can ignore/skip: 14, 35, 38. There will be 6-8 problems, some easy, some harder, spread over all Chapters, but with a bit more emphasis on the later Chapters and Sections.

    Final Exam:

    Tuesday, Dec 19, 2:15-5pm, in MAT 4-130

    The problems on the Final Exam will mostly be on algebraic topology, but covers the following sections.
    Chapter 7: 43, 45, 47. Chapter 9, all but 57. Chapter 11: 68-71, 73, Chapter 13: all.
    Or the equivalent material in the Hatcher text. There will be 7-8 problems on the exam.
    The best preparation is to practice doing problems, e.g. problems from the Hatcher text.

    Week of



    Due Date

    Aug 28



    Sept 6

    Sept 4


    18: 2, 5, 13 19:6,7 20:4(a),8(a) 21:9

    Sept 13

    Sept 18


    21:2, 8 22:3, 4 Suppl. Ex:4, 5 23:3, 5, 11

    Sept 20

    Sept 25

    28, 29, 37

    24:8. 25:4.26:1, 7, 8.. 27:2(a)(b). 28:7.


    Sept 27

    Oct 2


    30:1a, 3, 4, 5a, 12. 31:2, 6, 8.

    Oct 4

    Oct 9

    34, 36, 35

    33:2, 4. 34:3, 4. 361,3.

    Oct 11

    Oct 16

    35, 43, Midterm



    Oct 23


    43: 1, 2, 5, 7.45: 7ab.

    Oct 25

    Oct 30


    45:2, 4(a), 5. 51: 1, 2, 3.

    Nov 1

    Nov 6


    52:4, 5. 53:3, 4, 6b. 58:5,6.

    Nov 8

    Nov 13


    54:1, 4, 5, 7, 8. 58:2(a)-(e). 59:2.

    Nov 15

    Nov 20


    No HW - Tksgv. Break.


    Nov 27




    Dec 4


    60:5 70:1, 71:2, 74:3, 4a, 79:2, 5 81:5

    Dec 6

    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.

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