Topology - MATH 254

Undergraduate course, University of Vermont, 2022

Introductory course on point set topology.


WEEK 1 - Welcome to M254, sets
WEEK 2 - logic statements, equivalence relation
WEEK 3 - order relation, topological space
WEEK 4 - basis for a topology, theorem always exists a basis
WEEK 5 - finer/coarser, induced topology
WEEK 6 - order topology, interior/closure
WEEK 7 - closure construction theorems
WEEK 8 - limit points, separation
WEEK 9 - continuous func definitions, homeomorphism
WEEK 10 - continuous func construction, metric topology
WEEK 11 - sequence convergence, uniform convergence
WEEK 12 - connected space, intermediate value theorem
WEEK 13 - compactness, compact and Hausdorff
WEEK 14 - extreme value theorem, uniform continuity theorem
WEEK 15 - new definition of compacness, semester review

Reading material

Munkres - Topology - 2nd Edition
Starbird, Su - Topology Through Inquiry


Spring 2022 Syllabus

Lecture notes

Handwritten instructor’s notes

Grading Notes

The course grade will depend equally on Homework and Final project (40% each). The rest (20%), will be assigned according to the student participation in the course - that includes coming to office hours, or attendance in class, or intervening during lectures - and the work done in class during the in-class quiz.
For the first 3 weeks of class, the homework and in-class quiz will be assigned and I will give feedback on the work done, but irregardless if the proofs are correct or not, the student will be given full mark if they have tried hard enough. My hope is to build up the confidence of students in proving abstract mathematical statements.