University at Albany, College of Arts and Sciences

Department of Mathematics and Statistics

AMAT 540A: Topology I, Fall 2013


Prof. Marco Varisco,,
Office: ES-120C, Office Hours: MWF 9:10–10:15, or by appointment.


MWF 10:25–11:20 in ES-153.


Permission of instructor. (See the University’s Graduate Bulletin.)


From Wikipedia: Topology (from the Greek τόπος, “place”, and λόγος, “study”) is the mathematical study of shapes and spaces. It is a major area of mathematics concerned with the most basic properties of space, such as connectedness, continuity and boundary. It is the study of properties that are preserved under continuous deformations including stretching and bending, but not tearing or gluing. […] Topology developed as a field of study out of geometry and set theory, through analysis of such concepts as space, dimension, and transformation. Ideas that are now classified as topological were expressed as early as 1736. Toward the end of the 19th century, a distinct discipline developed, referred to in Latin as the geometria situs (“geometry of place”) or analysis situs (Greek-Latin for “picking apart of place”). This later acquired the name topology. By the middle of the 20th century, topology had become an important area of study within mathematics.


None is required — but the following books are recommended references:


Weekly homework assignments, quizzes, midterm and final exams.

You are expected to attend all class meetings. The maximum number of absences permitted to receive credit for this course is 5 (five). Excessive tardiness may count as absence.

Of course, you are expected to follow the University’s Standards of Academic Integrity.

This syllabus is subject to change. All official announcements and assignments are given in class, and this web page may not be up to date.
Marco Varisco.