07-401/Homework Assignment 2 - Revision history

Drorbn at 20:36, 28 June 2007

2007-06-28T20:36:32Z

← Older revision		Revision as of 16:36, 28 June 2007
Line 1:		Line 1:
	{{07-401/Navigation}}		{{07-401/Navigation}}

	===Reading===		===Reading===
	Read chapters 13 and 14 of Gallian's book three times:		Read chapters 13 and 14 of Gallian's book three times:

Drorbn: Reverted edit of 210.205.32.159, changed back to last version by Drorbn

2007-05-28T14:51:13Z

Reverted edit of 210.205.32.159, changed back to last version by Drorbn

← Older revision		Revision as of 10:51, 28 May 2007
Line 11:		Line 11:

	'''Bonus Question''' (solve and submit only if you wish, for extra credit). Let <math>{\mathcal C}</math> be the set of all Cauchy sequences of ''rational'' numbers.		'''Bonus Question''' (solve and submit only if you wish, for extra credit). Let <math>{\mathcal C}</math> be the set of all Cauchy sequences of ''rational'' numbers.
	# Prove that <math>{\mathcal C}</math> is a ring if taken with the operations <math>(a_n) (b_n):=(a_n b_n)</math> and <math>(a_n)(b_n):=(a_nb_n)</math>.		# Prove that <math>{\mathcal C}</math> is a ring if taken with the operations <math>(a_n)+(b_n):=(a_n+b_n)</math> and <math>(a_n)(b_n):=(a_nb_n)</math>.
	# What is the zero element of <math>{\mathcal C}</math>? What is its unity? Is it a field?		# What is the zero element of <math>{\mathcal C}</math>? What is its unity? Is it a field?
	# Let <math>{\mathcal A}</math> be the set of all sequences of rational numbers that converge to <math>0</math>. Prove that <math>{\mathcal A}</math> is an ideal in <math>{\mathcal C}</math>.		# Let <math>{\mathcal A}</math> be the set of all sequences of rational numbers that converge to <math>0</math>. Prove that <math>{\mathcal A}</math> is an ideal in <math>{\mathcal C}</math>.

210.205.32.159 at 06:40, 28 May 2007

2007-05-28T06:40:51Z

← Older revision		Revision as of 02:40, 28 May 2007
Line 11:		Line 11:

	'''Bonus Question''' (solve and submit only if you wish, for extra credit). Let <math>{\mathcal C}</math> be the set of all Cauchy sequences of ''rational'' numbers.		'''Bonus Question''' (solve and submit only if you wish, for extra credit). Let <math>{\mathcal C}</math> be the set of all Cauchy sequences of ''rational'' numbers.
	# Prove that <math>{\mathcal C}</math> is a ring if taken with the operations <math>(a_n)+(b_n):=(a_n+b_n)</math> and <math>(a_n)(b_n):=(a_nb_n)</math>.		# Prove that <math>{\mathcal C}</math> is a ring if taken with the operations <math>(a_n) (b_n):=(a_n b_n)</math> and <math>(a_n)(b_n):=(a_nb_n)</math>.
	# What is the zero element of <math>{\mathcal C}</math>? What is its unity? Is it a field?		# What is the zero element of <math>{\mathcal C}</math>? What is its unity? Is it a field?
	# Let <math>{\mathcal A}</math> be the set of all sequences of rational numbers that converge to <math>0</math>. Prove that <math>{\mathcal A}</math> is an ideal in <math>{\mathcal C}</math>.		# Let <math>{\mathcal A}</math> be the set of all sequences of rational numbers that converge to <math>0</math>. Prove that <math>{\mathcal A}</math> is an ideal in <math>{\mathcal C}</math>.

Drorbn at 14:36, 14 March 2007

2007-03-14T14:36:42Z

← Older revision		Revision as of 10:36, 14 March 2007
Line 5:		Line 5:
	* First time as if you were reading a novel - quickly and without too much attention to detail, just to learn what the main keywords and concepts and goals are.		* First time as if you were reading a novel - quickly and without too much attention to detail, just to learn what the main keywords and concepts and goals are.
	* Second time like you were studying for an exam on the subject - slowly and not skipping anything, verifying every little detail.		* Second time like you were studying for an exam on the subject - slowly and not skipping anything, verifying every little detail.
	* And then a third time, again at a quicker pace, to remind yourself ~~what~~ bigger all those little details are there to paint.		* And then a third time, again at a quicker pace, to remind yourself of the bigger picture all those little details are there to paint.

	===Doing===		===Doing===

Sidhubik: /* Doing */

2007-02-21T21:48:48Z

Doing

← Older revision		Revision as of 17:48, 21 February 2007
Line 17:		Line 17:
	# Can you identify the quotient <math>{\mathcal C}/{\mathcal A}</math> as a ring (a field, by the previous part) you have seen before?		# Can you identify the quotient <math>{\mathcal C}/{\mathcal A}</math> as a ring (a field, by the previous part) you have seen before?
	# Why did I bother asking you this question? In other words, in what sense is this question"useful"?		# Why did I bother asking you this question? In other words, in what sense is this question"useful"?

			[[Media:07-401-HW2.pdf\|Solutions (including Bonus)]]

	===Due Date===		===Due Date===

Drorbn at 02:38, 18 January 2007

2007-01-18T02:38:45Z

← Older revision		Revision as of 22:38, 17 January 2007
Line 1:		Line 1:
	{{07-401/Navigation}}		{{07-401/Navigation}}
	{{In Preparation}}

	===Reading===		===Reading===

Drorbn at 19:10, 17 January 2007

2007-01-17T19:10:51Z

← Older revision		Revision as of 15:10, 17 January 2007
Line 9:		Line 9:

	===Doing===		===Doing===
	Solve problems <u>29</u>, <u>41</u> and 43 in Chapter 13 of Gallian's book and problems ?? in Chapter 14 of the same book, but submit only the solutions of underlined problems.		Solve problems <u>29</u>, <u>41</u>, 43, 46 and <u>54</u> in Chapter 13 of Gallian's book and problems 3, 5, 8, 10, <u>11</u>, 12, 13, 20,25, <u>29 (what is the quotient field?)</u>, 31, <u>39</u> and 47 in Chapter 14 of the same book, but submit only the solutions of underlined problems.

	'''Bonus Question''' (solve and submit only if you wish, for extra credit). Let <math>{\mathcal C}</math> be the set of all Cauchy sequences of ''rational'' numbers.		'''Bonus Question''' (solve and submit only if you wish, for extra credit). Let <math>{\mathcal C}</math> be the set of all Cauchy sequences of ''rational'' numbers.

Drorbn at 18:40, 17 January 2007

2007-01-17T18:40:58Z

← Older revision		Revision as of 14:40, 17 January 2007
Line 10:		Line 10:
	===Doing===		===Doing===
	Solve problems <u>29</u>, <u>41</u> and 43 in Chapter 13 of Gallian's book and problems ?? in Chapter 14 of the same book, but submit only the solutions of underlined problems.		Solve problems <u>29</u>, <u>41</u> and 43 in Chapter 13 of Gallian's book and problems ?? in Chapter 14 of the same book, but submit only the solutions of underlined problems.

			'''Bonus Question''' (solve and submit only if you wish, for extra credit). Let <math>{\mathcal C}</math> be the set of all Cauchy sequences of ''rational'' numbers.
			# Prove that <math>{\mathcal C}</math> is a ring if taken with the operations <math>(a_n)+(b_n):=(a_n+b_n)</math> and <math>(a_n)(b_n):=(a_nb_n)</math>.
			# What is the zero element of <math>{\mathcal C}</math>? What is its unity? Is it a field?
			# Let <math>{\mathcal A}</math> be the set of all sequences of rational numbers that converge to <math>0</math>. Prove that <math>{\mathcal A}</math> is an ideal in <math>{\mathcal C}</math>.
			# (Hard!) Show that <math>{\mathcal A}</math> is a ''maximal'' ideal in <math>{\mathcal C}</math>
			# Can you identify the quotient <math>{\mathcal C}/{\mathcal A}</math> as a ring (a field, by the previous part) you have seen before?
			# Why did I bother asking you this question? In other words, in what sense is this question"useful"?

	===Due Date===		===Due Date===

74.99.3.116: /* Due Date */

2007-01-11T16:56:23Z

Due Date

← Older revision		Revision as of 12:56, 11 January 2007
Line 12:		Line 12:

	===Due Date===		===Due Date===
	This assignment is due in class on Wednesday January 17, 2007.		This assignment is due in class on Wednesday January 24, 2007.

Drorbn at 16:28, 11 January 2007

2007-01-11T16:28:45Z

New page

{{07-401/Navigation}}
{{In Preparation}}

===Reading===
Read chapters 13 and 14 of Gallian's book three times:
* First time as if you were reading a novel - quickly and without too much attention to detail, just to learn what the main keywords and concepts and goals are.
* Second time like you were studying for an exam on the subject - slowly and not skipping anything, verifying every little detail.
* And then a third time, again at a quicker pace, to remind yourself what bigger all those little details are there to paint.

===Doing===
Solve problems <u>29</u>, <u>41</u> and 43 in Chapter 13 of Gallian's book and problems ?? in Chapter 14 of the same book, but submit only the solutions of underlined problems.

===Due Date===
This assignment is due in class on Wednesday January 17, 2007.