440

Instructor
Jonathan Pakianathan
E-mail: jonathan.pakianathan@rochester.edu
Office: Hylan 809
Office hours in Hylan 809 or online in zoom room 5852752216.
Office hours, Wednesday, noon-1PM, Thursday 1:55-3 PM (right after class).
Class Meetings

TR12:30-1:45 PM in Hylan 203.

Videos (from past semesters with same syllabus) will also be made available later the same day on Blackboard.
Textbook

Topology, by James R. Munkres, 2nd edition (2000). ISBN:0-13-181629-2

Differential Topology, by Victor Guillemin and Alan Pollack, (1974). ISBN:0-13-212605-2
Course Description

The first half course will first introduce the basic general topological notions of topological space, metric spaces, quotient spaces, connectedness, compactness, manifolds and topological groups in a variety of settings.

The second half of the course will be an introduction to the differential topology of smooth manifolds.
Topics include Sard’s theorem, transversality, intersection theory and applications such as the Brouwer fixed point theorem, Jordan-Brouwer separation theorem, and the Borsuk-Ulam theorem. It will not cover the theory of differential forms, distributions or integration on manifolds which is usually covered in our spring graduate differentiable manifolds course.
Prerequisites

MTH 265 (real analysis) or MTH240 (undergraduate topology) or equivalent.

Multivariable calculus and linear algebra.
Scoring (500 total course points)

The course will be graded out of 500 points. 200 points will come from 10 homework sets, 100 points from the midterm and 200 points from the final. For more information on these components see below.

Midterm (100 course points=20% of course)

The midterm will be on Thursday, Oct 24, 7:30-9:30PM (Rochester night) in Hylan 1101.

No books, notes or electronics may be used during the exam.
Final (200 course points=40% of course)

The final will be on Sunday, Dec 15, 7:15-10:15PM in Hylan 1106A.

For graduate students, this counts as a prelim.
No books, notes or electronics may be used during the exam.
Homework (200 course points=40% of course)

Homework will be posted on the course schedule webpage. Written homework will be due on Gradescope on Saturdays at midnight. The first graded homework set HW1 is due Saturday, Sep 7 at midnight. There will be 11 homework sets in total worth 20 points (4% coursegrade) each but only your best 10 will be counted.

You may collaborate on homework and consult books and online resources while working on a problem but must write up the final solution in your own words and on your own (thus you should internalize the solution you find collaboratively so that when writing it up, you do not consult any other sources).

Grader

Grader: Siddarth Gurumurthy.

Office Hours: Thursday 3:30-4pm in Hylan 717.

Academic Integrity Statement

You are responsible for knowing and abiding by the University of Rochester’s academic integrity code. For a complete listing, visit the College’s web site. Any violation of academic integrity will be pursued according to the specified procedures.