MAT 530 
TOPOLOGY/GEOMETRY I 
Stony Brook - Fall 2000 

 
 
  • INSTRUCTOR:


    • André de Carvalho
    Math Tower 4-103 
    tel. 632-8266
    E-mail: andre@math.sunysb.edu
     

  • OFFICE HOURS:


    • Tuesdays and Thursdays 1 to 2pm and by appointment.
  • TEXT: 

    • Topology: Second Edition by James R. Munkres, Prentice-Hall, 2000. 
    This text is required for the course. In addition there are two books on reserve at the Math-Physics Library, which are worth examining: 
    • Topology by Hocking and Young. 
    • An Introduction to Algebraic Topology by A. Wallace. 
  • COURSE DESCRIPTION: 

    • This course is an introduction to Topology, a subject which had its beginnings in questions in Analysis in the late 19th century. It has since become a central and important part of mathematics, with strong ties to most branches of mathematics. 
    About 2/3 of this semester will be concerned with foundations, namely point-set topology. Given this underpinning, we then move on to the beginning aspects of algebraic topology.
  • SYLLABUS: 

    • Students will be assumed to be familiar with the main aspects of Chapter 1. Most of Chapters 2 through 8 of the text will be covered, except Chapter 5 (covered only briefly), and Chapter 6 (not at all). This comprises the point-set part of the course. We then move on to algebraic topology with the study of the fundamental group and covering spaces (Chapters 9 and 13), the Seifert-van Kampen Theorem (Chapter 11) and the classification of surfaces (Chapter 12). A rough, hopefully not too optimistic timetable is: 
     
    Ch. 2  2 weeks 
    Ch. 3 1½ weeks 
    Ch. 4 2 weeks
    Ch. 5 ½ week
    Ch. 7 1 week
    Ch. 8  ½  week
    Ch. 9 
     2 weeks
     Ch. 13 
    1½ weeks
    Ch. 11
    1½ weeks
     Ch. 12  1½ weeks 
  • HOMEWORK:

    • Homework exercises from the text will be assigned approximately weekly, and due the following week. 
  • EXAMS:

    • There will be one Midterm Exam, near the middle of the semester (right after we cover Ch. 8), during lecture time. 
    The Final exam is scheduled for Thursday, December 21, 8:00 - 10:30 am. 
  • GRADES:

    • The homework and the midterm will represent each 30% of your grade, and the Final Exam 40%. 
  • SPECIAL NEEDS: 

    • If you have a physical, psychological, medical or learning disability that may impact on your ability to carry on assigned course work, please contact the staff in the Disabled Student Services office (DSS), Room 133 Humanities, 632-6748/TDD. DSS will review your concerns and determine, with you, what accomodations are necessary and appropriate. All information and documentation of disability is confidential. 
This syllabus is available at: http://www.math.sunysb.edu/courses/mat530.fall1999.html