Simon Fraser University
Engaging the World

Course Outlines

Fall 2022 - MATH 795 G100

Selected Topics in Applied Mathematics (3)

Topology

Class Number: 7364

Delivery Method: In Person

Overview

  • Course Times + Location:

    Sep 7 – Dec 6, 2022: Mon, Wed, Fri, 1:30–2:20 p.m.
    Burnaby

  • Exam Times + Location:

    Dec 19, 2022
    Mon, 3:30–6:30 p.m.
    Burnaby

Description

CALENDAR DESCRIPTION:

Held jointly with MATH 495-3. See description for MATH 495-3. Students may not take a 700-division course if it is being offered in conjunction with a 400-division course which they have taken previously.

COURSE DETAILS:

Point set topology: definition, continuous maps, homeomorphisms, product and quotient topologies, Hausdorff topologies, connectedness, compactness and compactifications. Algebraic topology: paths, homotopies, fundamental group, universal covering spaces.
 
COURSE DETAILS:
Topology is the study of spaces under continuous deformation and provides the foundation for many topics in modern mathematics, including geometry, differential equations, number theory, and graph theory. 
 
Topics studied in this course include:
  • Topological Spaces, Basis for a Topology, The Order Topology.
  • The Product Topology, The Subspace Topology, Closed Sets and Limit Points.
  • Continuous Functions, The Metric Topology, The Quotient Topology.
  • Connected Spaces, Components and Local Connectedness, Compact Spaces.
  • The Countability Axioms, The Separation Axioms, Normal Spaces.
  • The Urysohn Lemma, The Urysohn Metrization Theorem.
  • Homotopy of Paths, The Fundamental Group, Covering Spaces.
  • The Fundamental Group of the Circle, Retractions and Fixed Points.
  • Deformation Retracts and Homotopy Type.
  • The Fundamental Group of S^n, Fundamental Groups of Some Surfaces.
  • Simplicial and Singular Homology.
  • Additional Topics.

Grading

  • Participation 10%
  • Assignments 20%
  • Midterm 30%
  • Final 40%

NOTES:

For Fall 2022, MATH 795-G100 is cross-listed with MATH 450-G100-Topology. Students in Math 795 will have additonal problems on assignments and exams. Students who take MATH 795-G100 in Fall 2022 cannot take MATH 750 for future credit.

REQUIREMENTS:

Prerequisites: MATH 242 and MATH 340

This course is delivered in person, on campus. Should public health guidelines recommend limits on in person gatherings, this course may include virtual meetings. As such, all students are recommended to have access to strong and reliable internet, the ability to scan documents (a phone app is acceptable) and access to a webcam and microphone (embedded in a computer is sufficient).

Materials

REQUIRED READING:

Topology - 2nd edition
James Munkres
Pearson

ISBN: 0131816292

REQUIRED READING NOTES:

Your personalized Course Material list, including digital and physical textbooks, are available through the SFU Bookstore website by simply entering your Computing ID at: shop.sfu.ca/course-materials/my-personalized-course-materials.

Graduate Studies Notes:

Important dates and deadlines for graduate students are found here: http://www.sfu.ca/dean-gradstudies/current/important_dates/guidelines.html. The deadline to drop a course with a 100% refund is the end of week 2. The deadline to drop with no notation on your transcript is the end of week 3.

Registrar Notes:

ACADEMIC INTEGRITY: YOUR WORK, YOUR SUCCESS

SFU’s Academic Integrity website http://www.sfu.ca/students/academicintegrity.html is filled with information on what is meant by academic dishonesty, where you can find resources to help with your studies and the consequences of cheating. Check out the site for more information and videos that help explain the issues in plain English.

Each student is responsible for his or her conduct as it affects the university community. Academic dishonesty, in whatever form, is ultimately destructive of the values of the university. Furthermore, it is unfair and discouraging to the majority of students who pursue their studies honestly. Scholarly integrity is required of all members of the university. http://www.sfu.ca/policies/gazette/student/s10-01.html