Dan Berwick-Evans
Office Hours: M 4-5, Tu 1-2 and Th 11-12 in 775 Evans
Announcements:
MIT Open Course List (free lectures) is here.
Here is a more expository, rambling (or perhaps I should say more rambling) version of what I've been covering in lecture. Let me know if you find any typos or errors. (Last updated May 1st.)
Quiz 2 will be on March 18th and will be covering metric spaces.
The average scores on the homeworks are as follows: 7.2/10 for HW1, 9.7/15 for HW2, 9.1/15 for HW3, 8.8/15 for HW4, 8.9.15 for HW5, 9.9/15 for HW6, and 9.7/15 for HW7.
FINAL EXAM INFORMATION: The final exam will take place Monday, May 18th from 5-8pm in 85 Evans (NOTE THE CHANGE). There will be 9 questions, all coming from the the review sheet (see below). You will be allowed one side of an 8.5x11 page of handwritten notes. There may be updates to the review sheet between now and Friday May 15th. Check back to be sure.
I will have office hours Monday from 1-3 pm.
Handouts and Reading:
Some notes on sets, logic and mathematical language by Professor Bergman
Student (Mis)use of mathematical definitions by Barbara Edwards and Michael Ward
How to Read Mathematics by Shair Simonson and Fernando Gouvea.
A Guide to Writing Mathematics by Kevin Lee
A Mathematical Writing Checklist by Kevin Lee
Common Errors in Writing Mathematics by S Maurer
A Mathematician's Apology by G.H. Hardy
Quiz 1 Review Sheet with some solutions
Pigeonhole Principle Examples and Practice Problems on Cut the Knot
A short pdf on Metric Spaces by J Muscat. This contains roughly everything we'll be covering.
Wikipedia Entry for Metric Spaces This contains slightly more information that we'll need, but has some good examples and discussion.
Distance functions from Cut the Knot.
Metric space problems and examples (with some solutions)
Partial Solutions to Homeworks 2 and 3 with some general comments from the grader.
The Banach Fixed Point Theorem (aka the contraction mapping theorem) on wikipedia
Homework 4 solutions with comments from the grader
A Paper on the Hausdorff Metric by Jeff Henrikson.
Quiz 2 Review Sheet and Sample Questions
Partial Solutions to Homework 7
Quiz 3 Review Sheet and Sample Questions
Partial Solutions to Homework 8
Partial Solutions to Homework 9
Final Exam Review Sheet. The final will be some subset of these questions, or slight adaptations thereof with 9 problems total.
Homework and Reading Assignments
Read Student (Mis)use of Mathematical Definitions and Some Notes on Sets, Logic and Mathematical Language. We should be most of the way through the Bergman essay by January 30th.
Homework 1 due January 28th
Homework 2 due February 4th
Howework 3 due February 18th. Will be modified on Friday, February 13th.
Homework 4 due February 25th.
The short pdf by Muscat covers everything we will on metric spaces.
Homework 5 due March 6th.
Solutions to problems 2,5 and 9 on homework 5.
The Wikipedia entry on the Banach fixed point theorem outlines the things you ought to know about the theorem.
Homework 6 due March 13th
The Wikipedia Entry on group theory contains most of the essentials. I also recommend the books, Topics in Algebra by Israel Herstein, Algebra by Michael Artin, or Groups and Symmetry by Mark Armstrong.
Homework 7 due April 8th
Homework 8 due April 15th
Homework 9 due April 24th
Allen Hatcher's Algebraic Topology is free online. I plan to cover some of pages 25-45, skipping anything that mentions CW complexes.
Homework 10 due May 6th.
Quiz 4. Please make an appointment to present one of the five problems before Wednesday May 13th.