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{{note|Bar-Natan_97}} D. Bar-Natan, ''Non-associative tangles,'' in ''Geometric to {{note|Bar-Natan_Le_Thurston_03}} D. Bar-Natan, T. Q. T. Le and D. P. Thurston, ''

== class note ==

....math.toronto.edu/drorbn/index.php?title=Image:Lecture3_1.jpg September 19 Note (1/5)] ....math.toronto.edu/drorbn/index.php?title=Image:Lecture3_2.jpg September 19 Note (2/5)]

...se are not necessary for the statement of the theorem, it is worthwhile to note that the invariants of the unknot, the unknotted <math>\theta</math>-graph {{note|BGRT}} D. Bar-Natan, S. Garoufalidis, L. Rozansky and D. P. Thurston, ''Whe

This is another "testing" note.

...-Natan for the Fall Session of MAT240 at the University of Toronto. Please note that this set is missing a diagram that could not be converted to PDF form. ...e lecture given on December 3rd by Professor Natan (in PDF format). Please note that there is an important diagram missing from this file. This is because

Note that the y axis and x axis in ordinary coordinate plane will become Img axi Image:Sept 20 class note scan1.jpg|Page 1

'''Note.''' The last $z$ on this blackboard should be a $z_i$.

Note that as a matter of policy I answer all general-interest questions posted o

...handout is not necessary! It is enough that <math>Z</math> be invertible. Note also that contrary to the handout, it is not known that the simultaneous ne

(Note: This can also be done abstractly, i.e. without choosing a basis, but then

{{note|Bar-Natan_95}} D. Bar-Natan, ''On the Vassiliev knot invariants,'' Topology {{note|Bar-Natan_96}} D. Bar-Natan, ''Some computations related to Vassiliev invar

Note that $c_j$ goes to $u_iw_j$, not to $0$.

...certificate of recognition. If you are interested in becoming a volunteer note-taker, please take an information form and register online, or visit the Ac

Disclamer: This is a student prepared note based on the lecures of [http://drorbn.net/dbnvp/12-267-120928.php Friday, Note that any function that is Lipschitz is uniformly continuous, and that if a

Note that this algebra is commutative

Note that for <math>n=1,2</math> this is trivial. For <math>n=3</math> we have t ...t of disjoint transpositions. Write <math>\sigma = (123)\sigma'</math> and note that <math>{\sigma'}^2 = e.</math>

== Important Note About This Page ==

The canonical <math>0</math>-framing of knots in <math>\mathbb{R}^3</math> (Note that such canonical identification only exist in <math>\mathbb{R}^3</math>.

File:October 8 note 1.jpeg|page 1 File:October 8 note 2.jpeg|page 2

Typically long equations have no closed form solutions. Yet note that Kurlin first derived the equation and only then found its solution. Wa Here are a few concrete questions to expose my ignorance of simple algebra. Note that <math>f</math> is is a rational function in its variables and their ex

Image:15-344 lecture note for Dec.8 .jpg|Page 1 Image:15-344 lecture note for Dec.8 2 .jpg|Page 2

Note my comments from [[06-240/Homework Assignment 5]]: ...here may be some computations, but nothing that will require a calculator. Note also that I may include some questions from the homework assignments verbat

There's a note by Habiro in which he shows that every strict graph clasper can be replaced

{{Begin Side Note|15%}} {{End Side Note}}

{{note|Le_Murakami_97}} T. Q. T. Le and J. Murakami, ''Parallel Version of the Uni {{note|Murakami_Ohtsuki_97}} J. Murakami and T. Ohtsuki, ''Topological Quantum Fie

...interpreted to mean <math>\sum_{k=0}^\infty\frac{M_i^kh_j^k}{k!}</math>. (Note that the number of formal parameters <math>h_j</math> need not equal the nu Note that an unreasonable algorithm for this question is readily available. Over

{{12-267/Good Deeds|uid=Eyjaffe|points=2|deeds=Video note; 2-3 typo corrections}} '''Note.''' This page is protected. Its [[Talk:12-267/Register of Good Deeds|discus

Much of this note comes from the paper "Finite type invariants of classical and virtual knots Note the additional information in the Gauss diagram about the overpasses and un

It's interesting to note that paracompactness (every open cover has a subcover such that every point

...on of finite groups of order 84. This was a project that I did in MAT 347. Note that there is a mistake when calculating the order of the automorphism grou

{{note|Le_Murakami_97}} T. Q. T. Le and J. Murakami, ''Parallel Version of the Uni {{note|Murakami_Ohtsuki_97}} J. Murakami and T. Ohtsuki, ''Topological Quantum Fie

(Note that when the class photo page was introduced I said there would be '''Note.''' This page is protected. Its [[Talk:09-240/Register of Good Deeds|discus

(Note by [[User:Cameron.martin]]). The unknot $0_1$ and the figure-eight knot $4_

...the topology in question is the trivial topology", or something like that. Note that the resulting topology may also depend on the direction of the line <m

'''Note added March 8, 2008.''' The problem this paperlet addresses remain interest {{note|Bar-Natan}} Dror Bar-Natan, ''[http://www.math.toronto.edu/~drorbn/papers/C

...ular <math>K</math>, <math>Z(K) = D_K +</math> diagrams of higher degree. (Note that a universal finite type invariant is '''not''' an finite type invarian

==Dror's Note==

Considering just the set without the identification, we note this is a group with the operation being concatenation of words followed by Note: <math>G_1 *_H G_2</math> is equivalent to { words in <math>G_1\cap G_2\}/

* Note the unusual time! We will have our next lunch on Wednesday July 2, at the u

Note the conference "Braids in Paris", September 17-20 2008, http://tresses08.in

# Note that we also automatically use the list on meta: http://meta.wikimedia.org/

'''Note.''' By $\partial(g\triangleright e)=g\partial(e)g^{-1}$, the image of $\par

Note 1: As is assumed in this section of the course, our map p is continuous, ou Note 2: Recall that connected does NOT imply locally connected. Indeed recall th

(Note that when the class photo page was introduced I said there would be no pena Note that this page is protected. Its [[Talk:08-401/Register of Good Deeds|discu

== Scanned Lecture Note for September 17 ==

...but submit only the solutions of the problems marked with the letter "S". Note that the word "subring" was not defined in class, but its simple definition

{{note|Drinfeld_90}} V. G. Drinfel'd, ''Quasi-Hopf algebras,'' Leningrad Math. J. {{note|Drinfeld_91}} V. G. Drinfel'd, ''On quasitriangular Quasi-Hopf algebras and

Note: This will be archived once the package is more complete. Note: You could do computations in Free Lie Algebras with more generators if yo

Disclamer: This is a student prepared note based on [http://drorbn.net/dbnvp/12-267-121002-2.php the lecure of Tuesday

File:monday Nov 10.jpg|Nov 10 note

{{Begin Side Note|30%}} {{End Side Note}}

# Prove that <math>O(3)</math> is not solvable (though note that the similarly-defined group <math>O(2)</math> is solvable).

* Note that the numbers <math>1^6-1=0</math>, <math>2^6-1=63</math>, <math>3^6-1=7

{{note|Bar-Natan_97}} D. Bar-Natan, ''Non-associative tangles,'' in ''Geometric to {{note|Drinfeld_90}} V. G. Drinfel'd, ''Quasi-Hopf algebras,'' Leningrad Math. J.

...g}$-like construction". See also {{Home link|People/Haviv/S3g.pdf|Haviv's note}}, where a ''symmetric'' invariant tensor in ${\mathfrak g}^{\otimes 3}$ is

== Lecture Note for September 15 ==

File:monday.jpg|Nov 3 note

(Note that when the class photo page was introduced I said there would be no pena Note that this page is protected. Its [[Talk:07-401/Register of Good Deeds|discu

This note closely follows the introductory parts of "Vassiliev and Quantum Invariants ...te knots, it is known that finite type invariants separate braids. In this note, we describe the process of getting a chord diagram from an m-singular brai

...s.math.toronto.edu/drorbn/dbnvp/257-161201.php today's video]</span>! (And note that your wiki account allows you to comment on specific times within the v

...s.math.toronto.edu/drorbn/dbnvp/257-170330.php today's video]</span>! (And note that your wiki account allows you to comment on specific times within the v

* Note that the numbers <math>1^6-1=0</math>, <math>2^6-1=63</math>, <math>3^6-1=7

'''Note the unusual time, place and content!''' Please let me know if you are plann Note that we will '''not''' have Knot at Lunch meetings on July 9, 16 and 23.

Here is a lecture note for today:

(Note that det(''EA'') = det(''E'')·det(''A'') and that det(''A'') may be writte

...y), a sequence of points in A can converge to only one point at most. Also note that Hausdorff condition is stronger than T1.

===Note===

* Note that the word "indivisibilities" has the largest number of repetitions of a

== lecture note on oct 18, uploaded by [[User:starash|starash]]==

{{note|AT}} A. Alekseev and C. Torossian, The Kashiwara-Vergne conjecture and Drin {{note|BP}} B. Berceanu and S. Papadima, Universal Representations of Braid and Br

:(In all that, note the absence of "cover all the details".)

Note: this proof is incorrect. It does show one of the numbers assigned to the e

'''Note.''' This page is protected. Its [[Talk:10-1100/Register of Good Deeds|discu

Note: It is usefull to "open the black box" and think about the Mayer Vietoris S Note: Technically we need to check at Mayer Vietoris sequence also works for red

...-the-week plan is in {{Pensieve Link|Classes/10-327|my own notes}}, though note that it is an '''optimistic''' plan, and in reality we will likely cover a ...es the term test without providing a valid reason (for example, a doctor’s note) within one week of the test will receive a mark of 0 on the term test. The

...lunch on Wednesday January 16, at the usual place, Bahen 6180, at 12 noon. Note that this is right after Shlomo Sternberg's third lecture at the Fields Ins

...mathbb{R}^m \}_{\alpha \in A}</math> be an atlas for <math>M\!</math>, and note that <math>\{U_\alpha\}_{\alpha \in A}\!</math> is an open cover of <math>M ...corresponding [http://en.wikipedia.org/wiki/Paracompact Wikipedia entry]. Note, in particular, that locally compact, second-countable topological spaces--

(Note that when the class photo page was introduced I said there would be no pena Note that this page is protected. Its [[Talk:06-240/Register of Good Deeds|discu

* Note that the word "indivisibilities" has the largest number of repetitions of a

We note that this is similar to the proof of the fundamental theorem of calculus, w ''Note''

...rily 1:1 as was implied in the earlier naive computations. Furthermore, we note that C_p(X) has an abelian group structure)

* Note that the word "indivisibilities" has the largest number of repetitions of a

In this note, we compute and interpret the structure constants $f_{abc}$ of $so(N)$, as Note that this also gives us the inverses $t^{(ij)(kl)} = const\cdot\delta^{ik}\

{{note|Kauffman}} L. H. Kauffman, ''An invariant of regular isotopy'', Trans. Ame

{{note|MO}} J. Murakami and T. Ohtsuki, ''Topological Quantum Field Theory for the

...on Thursday July 19, 2007, at the usual place, Bahen 6180, at 12 noon. But note that for the three weeks after that I will be traveling (in {{Home Link|Tal

<span style="color: red;">Important.</span> Note the change from an earlier version of this assignment - Franklin Vera and D

Note that a priori the second part of this question is an order of magnitude har

Though note that under the same circumstances we do not mod out by <math>b^{-1}\bar b_1

...right of the panel. '''Use caution!''' Such edits affect many other pages! Note that due to page-caching, such edits take some time to propagate to the pag ...es the term test without providing a valid reason (for example, a doctor’s note) within one week of the test will receive a mark of 0 on the term test. The

Note that if one tried to pushforward sets A in X, the set operations compliment It is very important to note that the <math>\varphi_0</math> and <math>\psi_0</math> are NOT the charts

===A note from the TA===

{{note|Bar-Natan_Garoufalidis_96}} Dror Bar-Natan and Stavros Garoufalidis, ''[htt

We note that this is obviously continuous and we get uniform convergence to a conti Note: Manifolds are paracompact

* Note that the word "indivisibilities" has the largest number of repetitions of a

'''Solve''' problems <u>10</u>, <u>12</u>, 13, 14abd, <u>14ce</u>, <u>15</u> (note, add "at most" before the "<math>k-1</math>"), <u>16</u>, and 18 in section

Note that these problems largely concern with material that we will not cover in

...here may be some computations, but nothing that will require a calculator. Note also that I may include some questions from the homework assignments verbat

'''Note.''' This page is protected. Its [[Talk:11-1100/Register of Good Deeds|discu

''Note'': Assignment 1 was handed back ...nces with 1's in them which correspond to the "middle" of a given segment. Note there is a slight ambiguity here for the same reason that 0.3999999... = 4

..., on how to improve the videos and / or the software used to display them. Note that "constructive" means also, "something that can be implemented relative ...remains your assignment to do, so what I'll write may sound a bit cryptic: Note that in the uniform topology, the <math>(\pm\epsilon)</math> constraint app

...ds|last=Roesler|first=Anne-Katrin|userid=aroesler|df=minor tweaks; scanned note for 9/11|pf=5|ds=cleaned notes of 11/13, 11/20, 11/27; scanned notes for 2/ Note that this page is protected. Its [[Talk:0708-1300/Register of Good Deeds|di

<span style="color:red;">'''Note the unusual due date!'''</span> This assignment is due in class on the last

As a final note I put the symbol "%" in several places above just to break the format so it

...as an exercise. The second statement is more of a convenient definition. Note that <math>A^0(V)\!</math> consists of all maps that take no vectors and re <p>As for the fourth, note that <math>0 = \omega(v_1, \ldots, v_j + v_k, \ldots, v_j+v_k, \ldots, v_p)

* Wednesday December 3, 1-3PM: Our last class. Note the unusual time - that Wednesday is a "UofT Monday".

• (Note: We can divide since we assumed that <math>(a,b) \neq 0</math>

* Note that the word "indivisibilities" has the largest number of repetitions of a

* Note that the numbers <math>1^6-1=0</math>, <math>2^6-1=63</math>, <math>3^6-1=7

'''Note.''' This page is protected. Its [[Talk:10-327/Register of Good Deeds|discus

(Note by [[User:Cameron.martin]]): (Note by [[User:Leo algknt]]):

Based largely off of a note available [http://imgur.com/a/uLSlM here] posted by [[User:Simon1|Simon1]]

...= \begin{pmatrix} -a_1 \\ -a_2 \\ \vdots \\ -a_n \end{pmatrix}</math> and note

Note: This ought to be checked from the definition of degree but was just stated

Note: We have never actually specified that p is positive axiomatically. In fact ...nt, or an antipodal point. Ie. f(x) = x or f(x) = -x for some value or x. (Note this is believed true for 2n not just 2, but the follow proof appears needs

Note: HW5 has been extended and is due in Dror's mailbox by the end of Monday, D

...Friedberg, Insel and Spence, ISBN 0-13-008451-4; it is a required reading. Note that the eratta for various printings of the 4th edition of the text is ava ...es the term test without providing a valid reason (for example, a doctor’s note) within one week of the test will receive a mark of 0 on the term test. The

..., on how to improve the videos and / or the software used to display them. Note that "constructive" means also, "something that can be implemented relative

'''Note.''' This page is protected. Its [[Talk:12-240/Register of Good Deeds|discus

...age are Mathematica 4.1 and Java 1.4 (or greater, in both cases). However, note that default installations of Mathematica 4.1 and up include a Java runtime ...n of those strands that the <code>ASeries</code> is intended to represent (Note - <code>Id[n]</code> can be used as a shortcut for the identity permutation

* Note. Many posts by [[User:Anai|Anai]] are for notes by [[User:Yvon.verberne|Yvo

...agrams under a certain set of generalized Reidemeister moves. Refer to the note at time 31:27 of the video found at http://drorbn.net/dbnvp/AKT-140127.php,

Usage note: The input Coefficient can be zero Usage note: the input LieTree can be empty.

...+\frac12x^2</math>, in explicit terms, for <math>0<t<\frac{\pi}{2}</math>. Note that <math>U_t</math> interpolates between the identity and the Fourier tra

Note that problems with writing are problems, period. Perhaps you got a low grad

''Note:'' In both the last two examples there were points in the target space that ''Note:'' The measure is not specified (indeed, for a topological space there is n

Note that since the pocket cube has no faces which would fix its overall orienta

Note that since the pocket cube has no faces which would fix its overall orienta

'''Note.''' An updated version of this section is at [[08-401/The Fundamental Theor ...time to prove the Fundamental Theorem of Galois Theory in full. Thus this note is about what we will be missing. The statement appearing here, which is a

===Note===

Note that while (&gamma;₀ &bull; &gamma;₁) &bull; &gamma;<

'''Abstract.''' The purpose of this note is to sketch my "almost proof" of mutation invariance for Khovanov homology Note that <math>p</math> and <math>q</math> here are not quite the same as <math

[[User:D|D]] 12:28, 2 October 2010 (EDT) Note on clopen (closed and open) set: In ANY topological space, an empty set is

(Note, by <math>\gamma_1:S^1\rightarrow S^1</math> we mean the identity) Note: The addition above is done in <math>\pi_1(S^1)</math> which is just <math>

Examples: char(F_2)=2, char(F_3)=3... but NOTE: char('''R''')=0

Note that problems with writing are problems, period. Perhaps you got a low grad

..., on how to improve the videos and / or the software used to display them. Note that "constructive" means also, "something that can be implemented relative **I agree but look at munkre's page 17 last sentence. Note that g compose with f is defined only when the range of f equals the domain

Note that when I write "all relations" or "all syzygies" above I really mean "a

* Wednesday December 3, 9AM-10AM: Our last class will take place at SS 2102. Note the unusual time and place - that Wednesday is a "UofT Monday".

==Dror's Note== {{note|BulloLewis_04}}Francesco Bullo and Andrew D. Lewis, <i>Geometric Control of

:Note: <math>\cong</math> represents "is isomorphic to"

: Note: '''or''' means '''inclusive or''' in math.

<b>NOTE:</b> To those of you who have a PDF of the textbook that might be outdated,

<p> Note that <math>\mathrm{dim}(\mathrm{ker}(T)) = m-n\!</math>. Hence we may find

...can use all of Mathematica's symbolic manipulations on these expressions. Note, however, that this labelling does not change the internal representation o

The good deeds were public and so are the points awarded to them. (Note that work internal to [[06-1350/Homework Assignment 4|HW4]] is given credit

...ath>, <math>-e_7(x)\epsilon(y)</math> and <math>-\epsilon(x)e_7(y)</math>. Note that since the constant term of <math>e_7</math> is 1 and since we only car {{End Side Note}}

* Note that the numbers <math>1^6-1=0</math>, <math>2^6-1=63</math>, <math>3^6-1=7

<span style="color:green">[Note: This last case is the '''only''' place where we really use this mystical f

<span style="color:red;">'''Note the unusual due date!'''</span> This assignment is due <span style="color:

===Another Accommodation Note=== "Accommodations Note" there.

Note that problems with writing are problems, period. Perhaps you got a low grad

''Note''

Note that $\calB$ can be graded (by half the number of vertices in a Jacobi We note that the precise form of the renormalization term

Note that the well known calculus laws that curl grad = 0 and div curl = 0 are j

...es the term test without providing a valid reason (for example, a doctor’s note) within one week of the test will receive a mark of 0 on the term test. The

...right of the panel. '''Use caution!''' Such edits affect many other pages! Note that due to page-caching, such edits take some time to propagate to the pag

Note: We prove this significantly differently then in Bredon

* Note that the word "indivisibilities" has the largest number of repetitions of a

(Note the word "rough" in this section header; significant variations from this o ...right of the panel. '''Use caution!''' Such edits affect many other pages! Note that due to page-caching, such edits take some time to propagate to the pag

...H)</math>. The inclusion <math>H<\operatorname{Gal}(E/E_H)</math> is easy. Note that <math>H</math> is finite since we've proven previously that Galois gro

...right of the panel. '''Use caution!''' Such edits affect many other pages! Note that due to page-caching, such edits take some time to propagate to the pag ...es the term test without providing a valid reason (for example, a doctor’s note) within one week of the test will receive a mark of 0 on the term test. The

{{note|Bar-Natan_97}} Dror Bar-Natan, ''[http://www.math.toronto.edu/~drorbn/LOP.h {{note|Kurlin_04}} Vitaliy Kurlin, ''Compressed Drinfel'd Associators'', {{arXiv|m

notebook were commited to the repository trunk. Note the Mathematica file

'''(Note: This is based off of the proof in the textbook, and may be slightly differ

...right of the panel. '''Use caution!''' Such edits affect many other pages! Note that due to page-caching, such edits take some time to propagate to the pag ...es the term test without providing a valid reason (for example, a doctor’s note) within one week of the test will receive a mark of 0 on the term test. The

...es the term test without providing a valid reason (for example, a doctor’s note) within one week of the test will receive a mark of 0 on the term test. The

...es the term test without providing a valid reason (for example, a doctor’s note) within one week of the test will receive a mark of 0 on the term test. The

'''Note.''' Earlier I made a sign mistake in the definition of and wrote <math>\ome

...f A. Let T(A) = B<Sup>t</Sup>, where B<Sup>t</Sup> is the transpose of B. (Note: Here, i is a complex number such that i<Sup>2</Sup> = -1.) Determine wheth

...true for <math>\R</math>, but do not follow from R1 to R5. For example ('''note''' that OR in mathematics denotes an "inclusive or"):

...bout 5 comments in the [[1617-257/Riddle_Repository|Riddle Repository]]; a note on [[Media:1617-257_Isometry.pdf|isometries]]}}

First, note that to a 0 manifold, assigning an orientation to the manifold is just assi

(Note, I used the symbol <math>\neq</math> to as the normal \ncong command doesn'

Note that problems with writing are problems, period. Perhaps you got a low grad

Note that for the other two, we don't have a limit, so:

...right of the panel. '''Use caution!''' Such edits affect many other pages! Note that due to page-caching, such edits take some time to propagate to the pag ...miss a term test without providing a valid reason (for example, a doctor’s note) within one week of the test you will receive a mark of 0 on that term test

...n, and I once wrote a short note explaining it, or rather, posing it. That note also explains, even if briefly, why I bother with the [[HandoutBrowser.js]]

Note that a polynomial of <math>n</math> degree has at most <math>n</math> solut

Note that problems with writing are problems, period. Perhaps you got a low grad

'''Pre-exam Office Hours.''' Please note that the information below is subject to last minute changes. If you are un

...right of the panel. '''Use caution!''' Such edits affect many other pages! Note that due to page-caching, such edits take some time to propagate to the pag

Note that the right hand side <math>{\mathcal A}_{\mathcal R}</math> of this equ

'''Pre-exam time table.''' Please note that the information below is subject to last minute changes. If you are un