# Winter 2018

 Instructor: David Duncan Email: duncand[at]math.mcmaster.ca Office: Hamilton Hall 319 Office Hours: Tu 3:20-4:20 and Th 12:30-1:30. Office hours are also available by appointment. Class location: Hamilton Hall 217 Class times: Tu, Th, F 2:30-3:20

## Homework

Homework will be due at the beginning of class, on the due date.

Homework 4 Due Thursday, Mar 1 (Note that this due date has changed from the original posting.) Here are some partial solutions.

Homework 1 Due Tuesday, Jan 16 (Changed from Friday, Jan 12)

## Final Exam

The Final Exam will be held on Tuesday, April 24 from 4 to 6 in BSB 106. Here is a study guide. At least one problem on the final will be taken directly from the study guide.

The exam will cover a subset of the following topics:

axioms for a topology

basis (and how to generate a topology from a basis)

subspace topology

Hausdorff spaces

closed subsets

standard topology (on R^n)

discrete topology

dictionary order topology

finite-complement topology

product topology

box topology

metric spaces

continuity (definition, examples, properties)

connectedness (definition, examples, properties)

compactness (definition, examples, properties)

the intermediate value theorem

the extreme value theorem

the supremum (on R)

surfaces (examples, basic properties; these show up on at most 5% of the exam)

manifolds (definitions, examples, nonexamples; these show up on at most 5% of the exam)

There are 9 problems in total on the exam. There are 5 short answer problems, where you are asked to give the answer and briefly explain your reasoning (no formal proof needed). The remaining 4 problems are proof-based. Two of these proof-based problems are 'Choose Your Own Adventure Problems'. (There are no multiple choice/TF questions.)

As usual, you are free to use any result from the textbook or lecture, provided you are not being asked to prove exactly that result (or a very slight modification of it). If you are unsure during the exam, just ask.

To study, I suggest you look at the following (in descending order of importance): the study guide, the homework assignments (including suggested problems), proofs of theorems from class, previous tests and their study guides.

My usual office hours are no longer applicable, now that classes are over. However, I will be holding extra office hours on April 17 and April 24 from 12 to 2.

## Midterm Test 2

The second midterm will be held on Friday, Mar. 16 from 2:30 to 3:20 in ABB 136. Here is a study guide. The midterm will cover the material from Sections 1-24 (excluding 22) in the text that also appeared in lecture, the homework, or the study guide. At least one problem on the midterm will be taken directly from the study guide. Here are solutions to the test.

## Midterm Test 1

The first midterm will be held on Friday, Feb. 9 from 2:30 to 3:20 in ABB 136. Here is a study guide. The midterm will cover the material from Sections 1-18 in the text that also appeared in lecture, the homework, or the study guide. At least one problem on the midterm will be taken directly from the study guide. Here are solutions to the test.

## Announcements

There has been a change to the dates of the midterms. The dates and locations are now as follows:

Midterm Test 1: Friday, February 9 from 2:30 to 3:20 in ABB 136;

Midterm Test 2: Friday, March 16 from 2:30 to 3:20 in ABB 136.

## Other Information

A student in our class, Sang Woo Park, has kindly offered to type up and post notes after each lecture. They can be found here: Lecture Notes

Last modification: April 7, 2018