Difference between revisions of "10-327/Homework Assignment 5"

From Drorbn
Jump to: navigation, search
(EDIT: moved Kai's HW5 solutions to new page)
 
(8 intermediate revisions by 2 users not shown)
Line 1: Line 1:
 
{{10-327/Navigation}}
 
{{10-327/Navigation}}
{{In Preparation}}
 
 
 
===Reading===
 
===Reading===
Read sections 26 and 27 in Munkres' textbook (Topology, 2nd edition). Remember that reading math isn't like reading a novel! If you read a novel and miss a few details most likely you'll still understand the novel. But if you miss a few details in a math text, often you'll miss everything that follows. So reading math takes reading and rereading and rerereading and a lot of thought about what you've read. Also, '''preread''' sections 28 and 29, just to get a feel for the future.
+
'''Read''' sections 26 and 27 in Munkres' textbook (Topology, 2nd edition). Remember that reading math isn't like reading a novel! If you read a novel and miss a few details most likely you'll still understand the novel. But if you miss a few details in a math text, often you'll miss everything that follows. So reading math takes reading and rereading and rerereading and a lot of thought about what you've read. Also, '''preread''' sections 28 and 29, just to get a feel for the future.
  
 
===Doing===
 
===Doing===
Line 12: Line 10:
  
 
{{Template:10-327:Dror/Students Divider}}
 
{{Template:10-327:Dror/Students Divider}}
 +
 +
*Question. In 4. By bounded metric space you mean there exists a point and an epsilon where this epsilon nbd contains everything in the metric space? -Kai
 +
** Indeed so, though usually when talking about boundedness, people use the letter <math>M</math> and not the letter <math>\epsilon</math>. It makes no difference, of course.

Latest revision as of 22:54, 10 December 2010

Reading

Read sections 26 and 27 in Munkres' textbook (Topology, 2nd edition). Remember that reading math isn't like reading a novel! If you read a novel and miss a few details most likely you'll still understand the novel. But if you miss a few details in a math text, often you'll miss everything that follows. So reading math takes reading and rereading and rerereading and a lot of thought about what you've read. Also, preread sections 28 and 29, just to get a feel for the future.

Doing

Solve the following problems from Munkres' book, though submit only the underlined ones: Problems 1, 4, 5, 6, 7, 8, 9, 12 on pages 170-172, and problem 2 on page 177. (For the last, recall that d(x,A):=\mbox{inf}_{a\in A}d(x,a)).

Due date

This assignment is due at the end of class on Thursday, November 11, 2010.

Dror's notes above / Student's notes below
  • Question. In 4. By bounded metric space you mean there exists a point and an epsilon where this epsilon nbd contains everything in the metric space? -Kai
    • Indeed so, though usually when talking about boundedness, people use the letter M and not the letter \epsilon. It makes no difference, of course.