MATH 145

Introduction to Topology
Spring 2018

Instructor

Prof. Martin Scharlemann
Office: SH 6718
Office hours:  MW 3:00-4:00
Email: mgscharl@math.ucsb.edu

Teaching assistant:
Modjtaba Shokrian Zini
Office: 6431V
Office hours:  T 3-5
Office hours @ Mathlab T 5-7
Email: shokrian@math.ucsb.edu

Classes

Arts 1349 MWF 2-2:50pm

You are responsible for all material presented in class, including announcements about course procedures. Exams, pop-quizzes, and homework may include questions on material presented only in class. It pains me to have to actually say this, but, yes, attendance is expected.

Prerequisites

Math 8 plus either Math 108A or Math 117, each with a grade of B- or better.

Topology is a highly abstract subject, and Math 145 will emphasize writing convincing proofs. If you had a hard time with this in Math 8, 108 or 117, you are unlikely to succeed in this course.

Text

Required: Bert Mendelson, Introduction to topology, available for very little at the bookstore or, for as little as $7.19, as an ebook at Dover Publications. Note that an ebook is easily searchable, whereas a paper book may be more convenient. At these prices, why not get both!?

Recommended: Colin Adams and Robert Franzosa, Introduction to topology, pure and applied. This is a more recent (and much more expensive!) textbook with lots of examples, applications and extra material. Unfortunately, the text moves from topological spaces to metric spaces, the direction opposite to that of our text, so it will not work as a substitute text. A copy has been put on reserve at the UCSB library.

Homework

Homework will generally be turned in at the Wednesday class of the following week. For example, the first assignment (listed below under 4/2-4/6) is due Wednesday 4/11. No late homework will be accepted. Do all problems assigned.  Not all will be read. Feel free to work with each other on the problems, but please then write them up on your own.

Masterclass

For those of you who are interested in honing your proof-writing skills, I hope to add a Wednesday evening Masterclass: Those taking part will be expected to volunteer to show their own solutions to homework problems to the rest of the master class. My role will NOT be to show you how to do the problems, but instead to offer a real-time critique of YOUR solutions.

Exams

Check your schedule now, for there will be no make-up exams.
 

Grade

 
Midterm 30%
Final 40%
Homework and discussion 30%

Tentative schedule
Date Read from Mendelson
Introduction to topology		 Do from Mendelson
4/2-4/6 1.1-1.6, 1.8
 §1.4 (p. 9) #3, 5
§1.5 (p. 11) #1,3
§1.6 (p. 14) #1, 2, 3 [look at 4]
4/9-4/13 1.9, 2.1, 2.2 §1.8 (p. 21) # 2, 3
§1.9 (p. 25) #4
§ 2.2 (p. 34) #3, 4, 7 [look at 8]
4/16-4/20 2.3-2.5 §2.3 (p. 39) #1, 3
§2.4 (p. 45) #2, 6, 8
§2.5 (p. 51) #1, 3, 6 [look at 2, 7]
4/23-4/27 2.6, 3.1,3.2 §2.6 (p. 57) #1, 3, 5
§3.2 (p. 74) #2, 4, 6
4/30-5/4
 3.4-3.5 §3.4 (p. 86) #1, 2, 5, 13
§3.5 (p. 91) #1, 3
5/7 Review  
5/9 Midterm Chapters 1-3.4
5/11 3.6 §3.6 (p. 96) #1, 2, 4
5/14-5/18 3.7, 4.1, 4.2 §3.7 (p. 100) #2, 6
§4.2 (p. 118) #2, 3
5/21-5/25 4.3-4.5 §4.3 (p. 122) #1, 2
§4.4 (p. 129) #1, 2 [look at 3]
§4.5 (p. 133) #1, 2
5/28 HOLIDAY   Memorial Day  
5/30-6/1 4.6, 5.1-5.2 §4.6 (p. 138) #2, 4
§5.2 (p. 164) #1, 2, 5
6/4-6/8 5.3-5.4 §5.3 (p. 168) #2, 3
§5.4 (p. 171) #1, 2 [look at 3]
Which of the nine intervals listed in Theorem 3.3 are homeomorphic to each other? (Justify your answer.)
FINAL EXAM Monday June 11, 4-7pm