http://drorbn.net/api.php?action=feedcontributions&user=Sidhubik&feedformat=atomDrorbn - User contributions [en]2024-03-29T00:54:06ZUser contributionsMediaWiki 1.21.1http://drorbn.net/index.php?title=07-401/Homework_Assignment_507-401/Homework Assignment 52007-03-11T08:21:22Z<p>Sidhubik: /* Solutions */</p>
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<div>{{07-401/Navigation}}<br />
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===Reading===<br />
Read chapters 16 and 17 of Gallian's book three times:<br />
* 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.<br />
* Second time like you were studying for an exam on the subject - slowly and not skipping anything, verifying every little detail.<br />
* And then a third time, again at a quicker pace, to remind yourself what bigger all those little details are there to paint.<br />
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===Doing===<br />
Solve problems 20, 22#, 24, 27#, 31#, 38, 39#, 40, 41# and 49 in Chapter 16 of Gallian's book and problems 2, 4#, 5 in Chapter 17 of the same book, but submit only the solutions the problems marked with a sharp (#).<br />
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===Due Date===<br />
This assignment is due in class on Wednesday February 14, 2007.<br />
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===Solutions===<br />
Solutions by [[User:Vickee]] are [[Media:07-401-HW5.pdf|here]].<br />
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[[Media:07-401-HW5(2).pdf|More Solutions]]</div>Sidhubikhttp://drorbn.net/index.php?title=07-401/Homework_Assignment_507-401/Homework Assignment 52007-03-11T08:20:58Z<p>Sidhubik: /* Solutions */</p>
<hr />
<div>{{07-401/Navigation}}<br />
<br />
===Reading===<br />
Read chapters 16 and 17 of Gallian's book three times:<br />
* 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.<br />
* Second time like you were studying for an exam on the subject - slowly and not skipping anything, verifying every little detail.<br />
* And then a third time, again at a quicker pace, to remind yourself what bigger all those little details are there to paint.<br />
<br />
===Doing===<br />
Solve problems 20, 22#, 24, 27#, 31#, 38, 39#, 40, 41# and 49 in Chapter 16 of Gallian's book and problems 2, 4#, 5 in Chapter 17 of the same book, but submit only the solutions the problems marked with a sharp (#).<br />
<br />
===Due Date===<br />
This assignment is due in class on Wednesday February 14, 2007.<br />
<br />
===Solutions===<br />
Solutions by [[User:Vickee]] are [[Media:07-401-HW5.pdf|here]].<br />
[[Media:07-401-HW5(2).pdf|More Solutions]]</div>Sidhubikhttp://drorbn.net/index.php?title=File:07-401-HW5(2).pdfFile:07-401-HW5(2).pdf2007-03-11T08:20:03Z<p>Sidhubik: </p>
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<div></div>Sidhubikhttp://drorbn.net/index.php?title=07-401/Homework_Assignment_407-401/Homework Assignment 42007-02-21T21:52:28Z<p>Sidhubik: /* Doing */</p>
<hr />
<div>{{07-401/Navigation}}<br />
<br />
===Reading===<br />
Read chapters 15 and 16 of Gallian's book three times:<br />
* 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.<br />
* Second time like you were studying for an exam on the subject - slowly and not skipping anything, verifying every little detail.<br />
* And then a third time, again at a quicker pace, to remind yourself what bigger all those little details are there to paint.<br />
<br />
===Doing===<br />
Solve problems 53, 54 and 62# in Chapter 15 of Gallian's book and problems 1, 2, 3#, 9, 10, 11, 12#, 13#, 15, 30 and 45# in Chapter 16 of the same book, but submit only the solutions the problems marked with a sharp (#).<br />
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[[Media:07-401-HW4.pdf|Solutions]]<br />
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===Due Date===<br />
This assignment is due in class on Wednesday February 7, 2007.<br />
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===Just for Fun===<br />
{|<br />
|- valign=top<br />
|<br />
* Take a large integer and write it in base 10. Cut away the "singles" digit, double it and subtract the result from the remaining digits. Repeat the process until the number you have left is small. Prove that the number you started from is divisible by 7 iff the resulting number is divisible by 7. Thus the example on the right shows that 86415 is divisible by 7 as 0 is divisible by 7. (I learned this trick a few months ago from [http://www.math.toronto.edu/hovinen/ Bradford Hovinen]).<br />
* Find a similar criterion for divisibility by 17 and for all other divisibilities and indivisibilities.<br />
* Note that the word "indivisibilities" has the largest number of repetitions of a single letter among all words in the English language (7 i's). I've known this fact for years but this exercise is the first time that I'm finding a semi-legitimate use for that word! (It is tied with the word honorificabilitudinitatibus for seven 'i's. You can read more about it here: http://en.wikipedia.org/wiki/Honorificabilitudinitatibus)<br />
|<br />
8641<s>5</s><br />
10<br />
----<br />
863<s>1</s><br />
2<br />
---<br />
86<s>1</s><br />
2<br />
--<br />
8<s>4</s><br />
8<br />
-<br />
0<br />
|}</div>Sidhubikhttp://drorbn.net/index.php?title=07-401/Homework_Assignment_307-401/Homework Assignment 32007-02-21T21:51:25Z<p>Sidhubik: /* Doing */</p>
<hr />
<div>{{07-401/Navigation}}<br />
<br />
===Reading===<br />
Read chapters 14 and 15 of Gallian's book three times:<br />
* 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.<br />
* Second time like you were studying for an exam on the subject - slowly and not skipping anything, verifying every little detail.<br />
* And then a third time, again at a quicker pace, to remind yourself what bigger all those little details are there to paint.<br />
<br />
===Doing===<br />
Solve problems 5, 6, 7, #12, #15, 19, #20, 30, 35, 39 and #50 in Chapter 15 of Gallian's book, but submit only the solutions the problems marked with a sharp (#).<br />
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[[07-401/Class Photo|'''Class Photo.''']] Wait for the class photo to appear on the class' web site (this should happen sometime in the evening of the day the photo is taken), identify yourself in the photo as explained on the photo page, and either add your details to the photo page as explained there or send me ({{Dror}}) an email with those details. '''Important.''' If I don't know your userid, I can't assign good deed points to you for work done on this site.<br />
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[[Media:07-401-HW3.pdf|Solutions]]<br />
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===Due Date===<br />
This assignment is due in class on Wednesday January 31, 2007.<br />
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===Just for Fun===<br />
The game of 15 is played as follows. Two players alternate choosing cards numbered between 1 and 9, with repetitions forbidden, so that the game ends at most after 9 moves (or four and a half rounds). The first player to have within her/his cards a set of precisely 3 cards that add up to 15 wins.<br />
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Does this game has a winning strategy? What is it? Who wins, the first to move or the second? Why am I asking this question at this particular time?<br />
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[[Image:07-401 Deck of Cards.png|center]]</div>Sidhubikhttp://drorbn.net/index.php?title=07-401/Homework_Assignment_107-401/Homework Assignment 12007-02-21T21:50:28Z<p>Sidhubik: /* Doing */</p>
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<div>{{07-401/Navigation}}<br />
<br />
===Reading===<br />
Read chapters 12 and 13 of Gallian's book three times:<br />
* 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.<br />
* Second time like you were studying for an exam on the subject - slowly and not skipping anything, verifying every little detail.<br />
* And then a third time, again at a quicker pace, to remind yourself what bigger all those little details are there to paint.<br />
<br />
===Doing===<br />
Solve problems 1, <u>2</u>, 8, 12, <u>13</u>, <u>19</u>, 20, <u>22</u>, 33, 47 and 50 in Chapter 12 of Gallian's book and problems 4, 7, 12, <u>13</u>, 16, <u>24</u> and 33 in Chapter 13 of the same book, but submit only the solutions of underlined problems.<br />
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[http://individual.utoronto.ca/shender/mat401/a1.pdf Solutions]<br />
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[[Media:07-401-HW1.pdf|Another Set of Solutions]]<br />
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===Due Date===<br />
This assignment is due in class on Wednesday January 17, 2007.</div>Sidhubikhttp://drorbn.net/index.php?title=07-401/Homework_Assignment_207-401/Homework Assignment 22007-02-21T21:48:48Z<p>Sidhubik: /* Doing */</p>
<hr />
<div>{{07-401/Navigation}}<br />
<br />
===Reading===<br />
Read chapters 13 and 14 of Gallian's book three times:<br />
* 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.<br />
* Second time like you were studying for an exam on the subject - slowly and not skipping anything, verifying every little detail.<br />
* And then a third time, again at a quicker pace, to remind yourself what bigger all those little details are there to paint.<br />
<br />
===Doing===<br />
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.<br />
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'''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.<br />
# 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>.<br />
# What is the zero element of <math>{\mathcal C}</math>? What is its unity? Is it a field?<br />
# 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>.<br />
# (Hard!) Show that <math>{\mathcal A}</math> is a ''maximal'' ideal in <math>{\mathcal C}</math><br />
# Can you identify the quotient <math>{\mathcal C}/{\mathcal A}</math> as a ring (a field, by the previous part) you have seen before?<br />
# Why did I bother asking you this question? In other words, in what sense is this question"useful"?<br />
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[[Media:07-401-HW2.pdf|Solutions (including Bonus)]]<br />
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===Due Date===<br />
This assignment is due in class on Wednesday January 24, 2007.</div>Sidhubikhttp://drorbn.net/index.php?title=File:07-401-HW4.pdfFile:07-401-HW4.pdf2007-02-21T21:44:52Z<p>Sidhubik: </p>
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<div></div>Sidhubikhttp://drorbn.net/index.php?title=File:07-401-HW3.pdfFile:07-401-HW3.pdf2007-02-21T21:44:41Z<p>Sidhubik: </p>
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<div></div>Sidhubikhttp://drorbn.net/index.php?title=File:07-401-HW2.pdfFile:07-401-HW2.pdf2007-02-21T21:44:25Z<p>Sidhubik: </p>
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<div></div>Sidhubikhttp://drorbn.net/index.php?title=07-401/Homework_Assignment_107-401/Homework Assignment 12007-02-21T21:43:20Z<p>Sidhubik: /* Doing */</p>
<hr />
<div>{{07-401/Navigation}}<br />
<br />
===Reading===<br />
Read chapters 12 and 13 of Gallian's book three times:<br />
* 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.<br />
* Second time like you were studying for an exam on the subject - slowly and not skipping anything, verifying every little detail.<br />
* And then a third time, again at a quicker pace, to remind yourself what bigger all those little details are there to paint.<br />
<br />
===Doing===<br />
Solve problems 1, <u>2</u>, 8, 12, <u>13</u>, <u>19</u>, 20, <u>22</u>, 33, 47 and 50 in Chapter 12 of Gallian's book and problems 4, 7, 12, <u>13</u>, 16, <u>24</u> and 33 in Chapter 13 of the same book, but submit only the solutions of underlined problems.<br />
<br />
[http://individual.utoronto.ca/shender/mat401/a1.pdf Solutions]<br />
<br />
Another Set of Solutions: [[Image:07-401-HW1.pdf]]<br />
<br />
===Due Date===<br />
This assignment is due in class on Wednesday January 17, 2007.</div>Sidhubikhttp://drorbn.net/index.php?title=File:07-401-HW1.pdfFile:07-401-HW1.pdf2007-02-21T21:26:52Z<p>Sidhubik: </p>
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<div></div>Sidhubikhttp://drorbn.net/index.php?title=07-401/Class_Photo07-401/Class Photo2007-01-31T22:51:06Z<p>Sidhubik: </p>
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<div>{{07-401/Navigation}}<br />
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Our class on Janury 24, 2007:<br />
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[[Image:07-401 Class Photo.jpg|thumb|centre|500px|Class Photo: click to enlarge]]<br />
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Please identify yourself in this photo! There are two ways to do that:<br />
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* [[Special:Userlogin|Log in]] to this Wiki and edit this page. Put your name, userid, email address and location in the picture in the alphabetical list below.<br />
* Send [[User:Drorbn|Dror]] an email message with this information.<br />
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The first option is more fun but less private.<br />
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===Who We Are...===<br />
<br />
{| align=center border=1 <br />
|-<br />
!First name<br />
!Last name <br />
!UserID <br />
!Email <br />
!In the photo <br />
!Comments<br />
{{Photo Entry|last=Bar-Natan|first=Dror|userid=Drorbn|email=drorbn @ math.toronto.edu|location=facing everybody, as the photographer|comments=Take this entry as a model and leave it first. Otherwise alphabetize by last name. Feel free to leave some fields blank}}<br />
{{Photo Entry|last=Abdel-Aziz|first=Mohamed|userid=Mizo|email=mohamed.abdelaziz@utoronto.ca|location=Absent|comments=no comment.}}<br />
{{Photo Entry|last=Baxter|first=Matthew|userid=MBaxter|email=matthew.baxter @ utoronto.com|location=2nd row(from back) 2nd from right|comments=no comment.}}<br />
{{Photo Entry|last=Castro|first=Caroline|userid=Carrot|email=caroline.castro @ utoronto.ca|<br />
location=the tall person at the very top of the stairs with the grey hat|comments=no comment.}}<br />
{{Photo Entry|last=Henderson|first=Sean|userid=sean_henderson|email=sean.henderson [at] utoronto.ca|location=front row, far left|comments=no comment.}}<br />
{{Photo Entry|last=Janic|first=Vega|userid=elf18|email=vega.janic @ utoronto.ca|location=second row from the back, to the left-hand side, wearing glasses and appearing to blink - drat!|comments=no comment.}}<br />
{{Photo Entry|last=Kang|first=Laura|userid=Clkkang|email=clkkang @ gmail.com|location=front row, 3rd person from right|comments=no comment.}}<br />
{{Photo Entry|last=Kim|first=Sang-Eun Vivien|userid=Vivienkim|email=vivien.kim @ utoronto.ca|location=from left, fourth row from top of page, 3rd person from the left in the black shirt|comments=no comment.}}<br />
{{Photo Entry|last=Maniak|first=Sylvia|userid=sm|email=sylvia.maniak [at] gmail.com|location=front row, the blonde wearing a black shirt|comments=no comment.}}<br />
{{Photo Entry|last=Nah|first=Theodorah|userid=Theo|email=theo.nahemt @ gmail.com|location=second row, 1/4 of my face covered|comments=no comment.}}<br />
{{Photo Entry|last=O'Brien|first=Brenna|userid=Brenna|email=brenna.obrien [at] utoronto.ca|location=4th row from bottom, far left|comments=no comment.}}<br />
{{Photo Entry|last=Sidhu|first=Bikram|userid=sidhubik|email=bikram.sidhu@utoronto.ca|location=Second Row, far right, black/white striped polo and grey/black hat|comments=no comment.}}<br />
{{Photo Entry|last=Wang|first=Chunyi|userid=ucc|email=chunyi.wang [at] utoronto.ca|location=second row, DIADORA|comments=no comment.}}<br />
{{Photo Entry|last=Muthukrishnan|first=Dilip|userid=dm_iyer|email=dm_iyer@hotmail.com|location=front row, bright yellow sweatshirt!|comments=no comment.}}<br />
{{Photo Entry|last=Wu|first=JunRu|userid=JunRu|email=junru.wu [at] utoronto.ca|location=4th row,the second person from left wearing glasses in black coat !|comments=no comment.}}<br />
{{Photo Entry|last=Wu|first=Kody|userid=Manu7|email=kody.wu@utoronto.ca|location=4th row, the first guy from the right with his mouth cut off. |comments=no comment.}}</div>Sidhubik