Drorbn - User contributions [en]

1617-257/Homework Assignment 1 Solutions

2017-03-31T20:11:37Z

Stefan.divic: /* Student Solutions */

{{1617-257/Navigation}}

==Doing==

'''Solve''' problems 1abc in section 1; problems 2, 6 in section 2; problems 4abc, 6, 7, 9abcdefgh in section 3, but submit only the underlined problems/parts.

==Student Solutions==
[[Media:1617-257_homework1_solutions_1.1_2.6_3.4.pdf|Student 1]]

[[Media:1617-257-pset1.pdf|Student 2]]

1617-257/homework 15 assignment solutions

2017-03-31T05:29:43Z

Stefan.divic: /* Student Solutions */

{{1617-257/Navigation}}

==Doing==

==Student Solutions==
[[Media:222mat257_15.pdf|Student 1, LaTeX PDF]]

[[Media:1617-257-pset15.pdf|Student 2]]

File:1617-257-pset15.pdf

2017-03-31T05:29:11Z

Stefan.divic: Partial, unofficial solutions to problem set 15.

Partial, unofficial solutions to problem set 15.

File:1617-257-pset11.pdf

2017-03-31T05:15:46Z

Stefan.divic: Stefan.divic uploaded a new version of "File:1617-257-pset11.pdf": Partial, unofficial solutions to problem set 11.

Partial, unofficial solutions to problem set 11.

1617-257/homework 11 assignment solutions

2017-03-31T05:12:03Z

Stefan.divic: /* Student Solutions */

{{1617-257/Navigation}}

==Doing==
See {{Pensieve link|Classes/1617-257b-AnalysisII/HW11.pdf|HW11.pdf}}.

==Student Solutions==

[[Media:1617-257_hw solutions student 1.pdf|Student 1]]

[[Media:1617-257-HW_11_solution-wangy306.pdf|Student 2]]

[[Media:1617-257-pset11.pdf|Student 3]]

File:1617-257-pset11.pdf

2017-03-31T05:11:59Z

Stefan.divic: Partial, unofficial solutions to problem set 11.

Partial, unofficial solutions to problem set 11.

1617-257/Homework Assignment 10 Solutions

2017-03-31T04:56:49Z

Stefan.divic: /* Student Solutions */

==Doing==
'''Solve''' ''all'' the problems in section 15, but submit only your solutions of problems 1, 3, and 6. In addition, solve and submit your solution of the following problem:

'''Problem A.''' Consider the function <math>f\colon[0,\infty)\to{\mathbb R}</math> defined by <math>f(x)=\sin(x^2)</math>. Show that
# The limit <math>\lim_{x\to\infty}f(x)</math> does not exist.
# The limit <math>\lim_{N\to\infty}\int_0^Nf(x)dx</math> does exist (yet do not attempt to compute it).
# The extended integral <math>\int_{(0,\infty)}f</math> does not exist.

==Student Solutions==

[[Media:1617-257_HW_10-solution-wangy306.pdf|Student 1]]

[[Media:1617-257-pset10.pdf|Student 2]]

File:1617-257-pset10.pdf

2017-03-31T04:56:19Z

Stefan.divic: Partial, unofficial solutions to problem set 10.

Partial, unofficial solutions to problem set 10.

1617-257/Homework Assignment 8 Solutions

2017-03-31T04:52:24Z

Stefan.divic: /* Student Solutions */

{{1617-257/Navigation}}

==Doing==
'''Solve''' ''all'' the problems in section 12, but submit only your solutions of problem 3. In addition, solve and submit your solution of the following problem:

'''Problem A.''' Let <math>Q=[0,1]^3</math> and let <math>f\colon Q\to{\mathbb R}</math> be given by <math>f(x,y,z)=1</math> if <math>x<y<z</math>, and <math>f(x,y,z)=0</math> otherwise. Compute <math>\int_Qf</math>. (This problem is merely about computations. You may assume without proof that <math>f</math> and all other functions you may encounter along the computation are integrable).

[[Media:1617-257_HW8_assignment.pdf|HW8 pdf]]

==Student Solutions==
[[media:1617-257-HW8-solution-wangy306.pdf|Student1]]

[[media:1617-257-HW8_Not_Hand_In_wangy306.pdf|Not Hand In]]

[[media:1617-257-pset8.pdf|Student2]]

File:1617-257-pset8.pdf

2017-03-31T04:51:54Z

Stefan.divic: Partial solutions to problem set 8.

Partial solutions to problem set 8.

1617-257/Homework Assignment 1

2017-03-31T04:48:51Z

Stefan.divic:

File:1617-257-pset1.pdf

2017-03-31T04:48:10Z

Stefan.divic: Partial solutions to problem set 1.

Partial solutions to problem set 1.

1617-257/homework 12 assignment solutions

2017-03-31T04:44:34Z

Stefan.divic: /* Student Solutions */

==Doing==
'''Solve''' ''all'' the problems in sections 23-24, but submit only your solutions of problems 3 and 6 in section 23 and problems 3 and 5 in section 24.

==Student Solutions==

[[media:1617-257_HW_12-solution-wangy306.pdf|Student 1]]

[[media:1617-257-pset12.pdf|Student 2]]

File:1617-257-pset12.pdf

2017-03-31T04:43:58Z

Stefan.divic: Partial, unofficial solutions to problem set 12.

Partial, unofficial solutions to problem set 12.

1617-257/Homework Assignment 14

2017-03-31T04:41:20Z

Stefan.divic: /* Student Solutions */

{{1617-257/Navigation}}
==Reading==
Read, reread and rereread your notes to this point, and make sure that you really, really really, really really really understand everything in them. Do the same every week! Also, read, reread and rereread sections 27-29 of Munkres' book to the same standard of understanding. 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 30-31, just to get a feel for the future.

==Doing==
'''Solve''' ''all'' the problems in sections 27-28, but submit only your solutions of problem 1 in section 27 and problems 1 and 6 in section 28. In addition, solve the following problems three problems, though submit only your solutions of the first two. These problems require more creativity than the usual and the are less precisely specified. You may wish to listen carefully at the tutorials this week!

'''Problem A.''' Along the lines of our development of a theory of "tensors" and a theory of "alternating tensors", develop a theory of "symmetric tensors" <math>S^k(V)</math> (a symmetric tensor is a tensor whose values are unchanged if its arguments are permuted). Your theory should include definitions for specific tensors <math>\sigma_I</math> for <math>I\in\underline{n}^k_s</math> (what should <math>\underline{n}^k_s</math> be)?), a proof that the <math>\sigma_I</math> exist and are unique and that they form a basis of <math>S^k(V)</math>, and a computation of the dimension of <math>S^k(V)</math>.

'''Problem B.''' Find a good way of identifying <math>A^1({\mathbb R}^3)</math> and <math>A^2({\mathbb R}^3)</math> with <math>{\mathbb R}^3</math>. Under that identification, <math>\wedge\colon A^1({\mathbb R}^3)\times A^1({\mathbb R}^3)\to A^2({\mathbb R}^3)</math> becomes a map <math>P\colon{\mathbb R}^3\times{\mathbb R}^3\to{\mathbb R}^3</math>. If you chose your identifications right, <math>P</math> is the vector product of two vectors in <math>{\mathbb R}^3</math>. See to it that this is the indeed the case!

'''Problem C.''' The determinant, as a function of a list of column vectors, is alternating. Write it in terms of the elementary alternating functions <math>\psi_I</math>.

==Submission==
Here and everywhere, '''neatness counts!!''' You may be brilliant and you may mean just the right things, but if the teaching assistants will be having hard time deciphering your work they will give up and assume it is wrong.

This assignment is due in class on Wednesday February 15 by 2:10PM.

===Important===
Please write on your assignment the day of the tutorial when you'd like to pick it up once it is marked (Wednesday or Thursday).

==Student Solutions==
[[Media:1617-257-pset14.pdf|Student 1]]

1617-257/Homework Assignment 14

2017-03-31T04:40:52Z

Stefan.divic:

File:1617-257-pset14.pdf

2017-03-31T04:40:46Z

Stefan.divic: Partial, unofficial solutions to problem set 14.

Partial, unofficial solutions to problem set 14.

1617-257/homework 13 assignment solutions

2017-03-31T04:34:30Z

Stefan.divic: /* Student Solutions */

{{1617-257/Navigation}}
==Doing==
'''Solve''' ''all'' the problems in sections 25-26, but submit only your solutions of problems 4 and 8 in section 25 and problems 5 and 6 in section 26. In addition, solve the following problem, though submit only your solutions of parts d and e:

'''Problem A.''' Let <math>\alpha\colon\{(u,v)\in{\mathbb R}^2\colon u^2+v^2\leq 1\}\to{\mathbb R}^3</math> be given by <math>\alpha(u,v)=\left(u-v,\,u+v,\,2(u^2+v^2)\right)</math>. Let <math>M</math> be the image of <math>\alpha</math>.

a. Describe <math>M</math>.

b. Show that <math>M</math> is a manifold.

c. Find the boundary <math>\partial M</math> of <math>M</math>.

d. Find the volume <math>V(M)</math> of <math>M</math>.

e. Find <math>\int_MzdV</math> (where <math>z</math> denotes the third coordinate of <math>{\mathbb R}^3</math>).

==Student Solutions==

[[Media:333mat257_13.pdf| Student 1, LaTeX PDF]]

[[Media:1617-257-pset13.pdf|Student 2]]

File:1617-257-pset13.pdf

2017-03-31T04:33:50Z

Stefan.divic: Partial, unofficial solutions to problem set 13.

Partial, unofficial solutions to problem set 13.

1617-257/Homework Assignment 6 Solutions

2017-03-31T04:19:22Z

Stefan.divic: /* Student Solutions */

{{1617-257/Navigation}}

==Doing==
'''Solve''' problems 1, 3, 5, 6 in section 9 and problems 1, 3, 4 in section 10, but submit only the underlined problems/parts. In addition, solve the following problems, though submit only your solutions of problem A:

'''Problem A.''' Find an example of a bounded continuous function on the semi-open interval <math>(0,1]</math> which is not uniformly continuous.

'''Problem B.''' Prove that every unbounded continuous function on the semi-open interval <math>(0,1]</math> is not uniformly continuous.

==Student Solutions==

[[media:1617-257_hw6_solutions_P1_xinyi.pdf|Student 1]]

[[media:1617-257_HW6_solutions_student2.pdf|Student 2]]

[[media:1617-257_HW6_-_Not_Hand_In.pdf|Not Hand In]]

[[media:1617-257-pset6.pdf|Student 3]]

File:1617-257-pset6.pdf

2017-03-31T04:19:06Z

Stefan.divic: Partial, unofficial solutions to problem set 6.

Partial, unofficial solutions to problem set 6.

1617-257/Homework Assignment 7 Solutions

2017-03-31T04:11:23Z

Stefan.divic: /* Student Solutions */

{{1617-257/Navigation}}

==Doing==
'''Solve''' ''all'' the problems in section 11, but submit only your solutions of problems 2, 4, 6, 8, and 9.

==Student Solutions==
[[Media: 1617-257_hw7_solutions_P1_xinyi.pdf|Student1]]

[[Media: 1617-257-HW7_wangy306.pdf|Student2]]

[[Media: 1617-257-HW7-Not_Hand_In_wangy306.pdf|Not Hand In]]

[[Media: 1617-257-pset7.pdf|Student3]]

File:1617-257-pset7.pdf

2017-03-31T04:10:14Z

Stefan.divic: Partial, unofficial solutions to problem set 7.

Partial, unofficial solutions to problem set 7.

1617-257/Class Photo

2016-10-05T12:23:41Z

Stefan.divic:

Our class on September 30, 2016:

[[Image:1617-257-ClassPhoto.jpg|thumb|centre|800px|Class Photo: click to enlarge]]
{{1617-257/Navigation}}

Please identify yourself in this photo! There are two ways to do that:

* [[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.
* Send [[User:Drorbn|Dror]] an email message with this information.

The first option is more fun but less private.

===Who We Are...===

{| align=center border=1 cellspacing=1

{{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. For better line-breaking, leave a space next to the "@" in email addresses.}}



{{Photo Entry|last=Beach|first=Isabel|userid=Beach|email=isabel. beach@ mail. utoronto. ca|location=first row, third from left, burgundy U of T sweater|comments=Artist, wannabe astronomer, nature enthusiast.}}

{{Photo Entry|last=Divic|first=Stefan|userid=Stefan.divic|email=stefan. divic@ mail. utoronto. ca|location=Right behind the tall dude with the blue/white-striped shirt|comments=Interested in making music, traveling, meeting people!}}

{{Photo Entry|last=Hu|first=Janelle|userid=Janelle|email=janelle.hu@ mail. utoronto. ca|location=third row, third from the right|comments=Joined a dance crew this year.
Math related: my roommates are 4th year math specialists}}

{{Photo Entry|last=Im|first=Jeffrey|userid=jeffim|email=jim@ math. toronto. edu|location=bottom-right corner|comments=One of two TAs for this class. Student of George Elliott. Interested in C*-algebras/K-theory.}}

{{Photo Entry|last=Li|first=Xiaoyang|userid=Witchofagnesi|email=xiaoyang. li@ mail. utoronto. ca|location=fifth row, on the middle-left, head sticking out|comments=Loves classical music and poetry.}}

{{Photo Entry|last=Moore|first=Darren|userid=DarrenMoo|email=da.moore@ mail. utoronto. ca|location=fourth row, standing, white UofT shirt|comments=Wannabe game dev, mathematician, musician, etc.}}

{{Photo Entry|last=McBrien|first=Heather|userid=Heatherheather|email=heather.mcbrien@ mail. utoronto. ca|location=fourth row, standing, leaning back with the really strange facial expression and the blue sweater|comments=My name is Heather but some people (most) call me K8. I like math, and I also like breaking the fourth wall; as a jazz musician and a mathematician, my motto,}}

{{Photo Entry|last=Morton-Ferguson|first=Calder|userid=calder.oakes|email=calder. morton. ferguson@ mail. utoronto. ca|location=4th-ish row, standing and smiling with my arms around Darren and Tanny.|comments= (which Calder made up) is "it ain't got that swing if it don't mean a thing. Proof of the converse is left as an exercise."}}

{{Photo Entry|last=Moturu|first=Abhishek|userid=Abhi.saim|email=abhi.saim@ gmail.com|location=first row, third from the right, white pants|comments=Two loves: math and chicken.}}

{{Photo Entry|last=Xu|first=Xinyi|userid=Maggie|email=xinyi. xu97@ gmail. com|location=fourth row, first girl from right,with red glasses|comments=Interested in modern Origami.}}


|}