Math 543 syllabus
Course Description: A continuation of MA 542. Topics covered include the fundamental group, triangulations,
classification of surfaces, homology, the Euler-Poincare formula, the Borsuk-Ulam
theorem, the Lefschetz fixed-point theorem, knot theory, covering spaces, and applications.
Prerequisites: MA 542 Minimum Grade of C or MA 434 Minimum Grade of C.
Algebraic topology by Allen Hatcher, Cambridge University Press, Cambridge, 2002;
Knots and links by Dale Rolfsen, Corrected reprint of the 1976 original, Mathematics Lecture Series, No. 7, Publish or Perish Inc., Houston, TX, 1990.
Learning outcomes: Upon the successful completion of the course a student will:
Understand the core concepts of fundamental groups, covering spaces, and homology
groups, which form the foundations of algebraic topology.
Be familiar with the application of fundamental groups, covering spaces, and homology groups to proving theorems such as the classification of surfaces, the Borsuk-Ulam theorem, and fixed-point theorems.
Understand the introductory concepts of knots and links in the 3-sphere.
Be familiar with introductory applications of fundamental groups, covering spaces, and homology groups to the study of knots and links in the 3-sphere.