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  • We define a "differential" <math>d:{\mathbb Q}[x]\to{\mathbb Q}[x,y]</math> by <math>(df)(x,y)=f(y)-f(x+y)+f(x {{Equation*|<math>e_8(x+y)-e_8(x)e_8(y)=M(x,y)-(d\epsilon)(x,y)</math>.}}
    18 KB (3,364 words) - 11:36, 28 November 2019
  • ...} conjecture and much of the Alekseev-Torossian {{ref|AT}} work on Drinfel'd associators and Kashiwara-Vergne can be re-interpreted as a study of w-knot {{note|EK}} P. Etingof and D. Kazhdan, Quantization of Lie Bialgebras, I, Selecta Mathematica, New Serie
    6 KB (887 words) - 17:47, 5 May 2014
  • ...sing combinatorics alone prove that given a 2-component link diagram <math>D</math>, with components <math>\gamma_1</math> and <math>\gamma_2</math>,
    2 KB (279 words) - 11:45, 4 May 2018
  • ... of a tricolouring as a map <math>\phi: S \rightarrow \{R,G,B\}</math>. We'd like to try to extend this to a group homomorphism <math>\phi:\langle S \mi
    2 KB (316 words) - 20:38, 9 January 2014
  • Some analysis of <math>d^{-1}</math>.
    37 B (7 words) - 12:28, 31 January 2014
  • More on pushforwards, <math>d^{-1}</math>, and <math>d^\ast</math>.
    67 B (12 words) - 14:43, 7 February 2014
  • The dual of <math>H^0(\mathcal{D}_n)</math>.
    44 B (9 words) - 13:40, 12 March 2014
  • A naive way to define <math>d^*</math>.
    39 B (8 words) - 13:43, 12 March 2014
  • The correct definition of <math>d^*</math>.
    43 B (7 words) - 13:46, 12 March 2014
  • ...in D}(\Phi_{\vec{e}}^\ast\omega_3)_{21}\prod_{\text{black}\atop \vec{e}\in D}(\Phi_{\vec{e}}^\ast\omega_1)_{10}</math>. I'll try to explain and make a p
    486 B (88 words) - 14:54, 19 March 2014
  • Read appendices A through D in our textbook (with higher attention to C and D), and solve the following problems:
    2 KB (303 words) - 15:04, 8 December 2014
  • ...00/Classnotes for Thursday October 16|Thursday]] - groups of order 12 cont'd. ...4-1100/Classnotes for Monday November 10|Monday]] - R is a PID iff R has a D-H norm, R-modules, direct sums, every f.g. module is given by a presentatio
    5 KB (648 words) - 08:27, 20 June 2015
  • ==Basic Properties of a Field (cont'd)==
    2 KB (377 words) - 01:57, 8 December 2014
  • ... a bit blurry. If anyone has suggestions for how to take better photos, I'd be very happy to hear them! (I haven't been using flash because I believe
    1 KB (226 words) - 14:14, 5 October 2014
  • ... a bit blurry. If anyone has suggestions for how to take better photos, I'd be very happy to hear them! (I haven't been using flash because I believe
    2 KB (291 words) - 14:16, 5 October 2014
  • ...mes 2</math> matrix makes no sense. Secondly, the elements <math>a, b, c, d</math> are undefined. What are they suppose to represent? Rational number \in span(S) \iff char(F)=2</math>. ''Q.E.D.''
    7 KB (1,127 words) - 15:08, 8 December 2014
  • ... theorems (currently from the textbook chapters 1.1 - 1.6 and appendices A-D, I might add more later) in this [[http://pastebin.com/igPXqtyk latex],
    4 KB (691 words) - 15:17, 8 December 2014
  • ...ies''! I had found a few mistakes my notes: there are a few places where I'd flipped <math>R^n</math> with X, and other similar errors.
    3 KB (393 words) - 14:16, 10 December 2014
  • Fourth red relation on the right should be <math>D=\partial(d)A^{-1}GA</math>
    179 B (35 words) - 13:00, 8 May 2015
  • ...Johnson homomorphism. In the Artin case, this is the action of the Drinfel'd-Kohno Lie algebra on the free Lie algebra.
    123 B (21 words) - 12:43, 19 October 2015
  • ...erm test questions will coming directly from the homework assignments, you'd probably be wise to go over these too. '''All the assignments submitted to
    5 KB (749 words) - 20:55, 1 November 2015
  • ... your student! I saw that video too and tried to make an R script of Arnol'd's proof: http://isomorphism.es/post/113720283271/commutator
    1 KB (177 words) - 06:46, 21 October 2015
  • A Drinfel'd-Kohno theorem.
    26 B (3 words) - 16:50, 13 November 2015
  • ''Hint.'' In the last matrix multiplication to be carried out, you'd be multiplying the product of <math>k</math> of the matrices with the produ '''4 d) Three different boxes with at most five objects in the first box'''
    5 KB (915 words) - 01:58, 16 December 2015
  • ...erm test questions will coming directly from the homework assignments, you'd probably be wise to go over these too.
    5 KB (676 words) - 20:23, 1 March 2016
  • |colspan=3 align=center|<math>\int_M d\omega=\int_{\partial M}\omega</math>
    11 KB (1,444 words) - 09:23, 21 April 2017
  • ...dd just a bit). If we lag, we'll skip and take shortcuts. Yet <math>\int_M d\omega=\int_{\partial M}\omega</math> we will do.
    11 KB (1,918 words) - 11:45, 2 November 2016
  • ...a metric space. Prove that the metric itself, regarded as a function <math>d\colon X\times X\to{\mathbb R}</math>, is continuous. ...(x,A):=\inf_{y\in A}d(x,y)</math>, is a continuous function and that <math>d(x,A)=0</math> iff <math>x\in\bar{A}</math>.
    3 KB (519 words) - 13:26, 9 November 2016
  • ...or: red;">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).</span>
    1 KB (254 words) - 09:48, 2 November 2016
  • if <math>f : U \to \mathbb R</math> is differentiable with <math>\|D f (x)\| \leq M</math> for all <math>x \in U</math>
    554 B (106 words) - 11:34, 14 October 2016
  • ...or: red;">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).</span>
    1 KB (254 words) - 09:48, 2 November 2016
  • ...or: red;">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).</span>
    1 KB (246 words) - 09:47, 2 November 2016
  • ...a metric space. Prove that the metric itself, regarded as a function <math>d\colon X\times X\to{\mathbb R}</math>, is continuous. ...(x,A):=\inf_{y\in A}d(x,y)</math>, is a continuous function and that <math>d(x,A)=0</math> iff <math>x\in\bar{A}</math>.
    2 KB (303 words) - 16:50, 25 November 2016
  • ...or: red;">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).</span>
    2 KB (295 words) - 15:14, 2 November 2016
  • ...or: red;">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).</span>
    1 KB (229 words) - 19:17, 9 November 2016
  • ...or: red;">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).</span>
    2 KB (311 words) - 16:55, 22 November 2016
  • ...or: red;">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).</span>
    2 KB (307 words) - 18:51, 28 November 2016
  • ...or: red;">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).</span>
    2 KB (309 words) - 16:14, 30 November 2016
  • ...on for how to show the integral exists was by using Fubini's theorem. I OK'd this idea in the tutorial, but it is actually not OK. In order to use Fubin
    828 B (141 words) - 19:32, 1 December 2016
  • ...or: red;">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).</span>
    1 KB (236 words) - 07:33, 26 January 2017
  • ...n, solve the following problem, though submit only your solutions of parts d and e: <u>d</u>. Find the volume <math>V(M)</math> of <math>M</math>.
    2 KB (359 words) - 16:48, 6 February 2017
  • ...or: red;">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).</span>
    3 KB (526 words) - 00:41, 31 March 2017
  • ...or: red;">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).</span>
    1 KB (236 words) - 22:15, 15 February 2017
  • <center><math>d\omega(\xi_1,\ldots,\xi_{k+1}) = \lim_{\epsilon\to 0}\frac{1}{\epsilon^{k+1} ...or: red;">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).</span>
    2 KB (328 words) - 07:14, 2 March 2017
  • ...n, solve the following problem, though submit only your solutions of parts d and e: <u>d</u>. Find the volume <math>V(M)</math> of <math>M</math>.
    957 B (161 words) - 00:34, 31 March 2017
  • ...or: red;">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).</span>
    2 KB (274 words) - 06:49, 16 March 2017
  • ...''Problem A.'''</u> Consider <math>S^{n-1}</math> at the boundary of <math>D^n\subset{\mathbb R}^n</math>, taken with its standard orientation, and let ...x_i}\wedge\dots\wedge dx_n\right)\in\Omega^{\text{top}}(S^{n-1})</math>. I'd like to thank the students who emailed me the correction.
    4 KB (772 words) - 10:41, 20 April 2017
  • ...text{d}V=\int\limits_{\partial M_2}^{}\left\langle G,N_2\right\rangle\text{d}V</math>. ...or: red;">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).</span>
    2 KB (351 words) - 13:02, 3 April 2017
  • ...ll be coming directly from the homework assignments or the term tests, you'd probably be wise to go over these too.
    4 KB (558 words) - 07:57, 7 September 2017
  • ...w becomes a single variable minimum/maximum problem. We set <math>\frac{d}{d\epsilon}f(\epsilon)\mid_{\epsilon=0} = 0</math>, and solve for <math>x_c</m <math>\frac{d}{d\epsilon}f(\epsilon)\mid_{\epsilon=0} = \int_0^T dt(\dot{x}_c\dot{x}_q - x_q
    2 KB (308 words) - 18:26, 14 May 2018
  • Let <math>D</math> be a knot diagram for the knot <math>K</math> with <math>n</math> cr ...ystem of equation and this is exactly the set of all 3-colourings of <math>D</math>. This is a vector space of size <math>\lambda(K) =|\mathrm{Null}(M)|
    4 KB (660 words) - 14:36, 25 August 2018
  • ...ac{\partial L}{\partial q}\delta q+\frac{\partial L}{\partial\dot{q}}\frac{d}{dt}\left(\delta q\right)\right).</math> ...|_{t_i}^{t_f}=\int_{t_i}^{t_f}dt \left(\frac{\partial L}{\partial q}-\frac{d}{dt}\left(\frac{\partial L}{\partial\dot{q}}\right)\right)\delta q,</math>
    2 KB (450 words) - 12:35, 23 May 2018
  • ...>\frac{\partial L}{\partial y}=-\frac{1}{2y}\sqrt{\frac{1+y'^2}{2g}}=\frac{d}{dx}\left(\frac{\partial L}{\partial y'}\right)=\frac{1}{\sqrt{2g}}\frac{2y
    2 KB (305 words) - 13:17, 23 May 2018
  • ...) = V(y_c + \epsilon y_q)$, where $y_q(0) = y_q(L) = 0$, and set $\frac{d}{d\epsilon}f(\epsilon)\mid_{\epsilon = 0}$. For convenience, use dot notation $\frac{d}{d\epsilon}f(\epsilon)\mid_{\epsilon = 0} = \frac{mg}{s}\int_{-L}^{L}y_q\sqrt{
    2 KB (462 words) - 14:55, 30 May 2018
  • I have noticed that the d<math>x</math> always comes before the integrand. Any reason for this or it
    115 B (22 words) - 05:33, 25 May 2018
  • ... to produce a <math>k+1</math>-form and that <math>\mathrm{d}\circ \mathrm{d} =0</math>. ...rm so that <math>\mathrm{d}f \in \Omega^1(M)</math>. Thus <math>d: \mathrm{d} \Omega^0(\mathbb{R}^3) \rightarrow \Omega^1(\mathbb{R}^3)</math> is the gr
    2 KB (415 words) - 00:42, 28 June 2018
  • ...= A\wedge \mathrm{d}A</math> is invariant under <math>A\mapsto A + \mathrm{d}f</math>''' \Psi(A + \mathrm{d}f) &= (A + \mathrm{d}f)\wedge \mathrm{d}(A + \mathrm{d}f)\\
    360 B (64 words) - 14:51, 18 July 2018
  • A^{(gh)} &= (gh)^{-1}A(gh) + (gh)^{-1}\mathrm{d}(gh) \\ &= (gh)^{-1}A(gh) + (gh)^{-1}\Big((\mathrm{d}g)h + g(\mathrm{d}h)\Big)\\
    527 B (111 words) - 18:02, 26 July 2018
  • ...(A)+\frac13 \int_\mathbb{R^3}Tr(g^{-1} d g \wedge g^{-1} d g \wedge g^{-1} d g)$ $$CS(A^g)=\int_\mathbb{R^3} Tr(A^g \wedge d A^g + \frac23 A^g \wedge A^g \wedge A^g)$$
    4 KB (938 words) - 20:15, 24 August 2018
  • ...from a regular knot. I.e. there is a map $\mathcal{K} \rightarrow \mathcal{D}$ from the space of knots into the space of Gauss diagrams. A Gauss diagram
    1 KB (199 words) - 16:14, 17 August 2018
  • $$d(gs) = (dg)s+gds \implies (dg)s = d(gs)-gds$$ D_{g^{-1} A g+g^{-1} d g} (s)\\
    351 B (86 words) - 00:15, 23 August 2018
  • ...um of all $\mathcal{D}^{pb}_m$, and define $\mathcal{A}^{pb}$ as $\mathcal{D}^{pb}/\mathcal{I}$, where $\mathcal{I}$ is an ideal generated by relations
    2 KB (295 words) - 16:22, 24 August 2018
  • <br>2. D: B, what number's on your hat? B: I dunno. <br>3. D: A, ... A: I dunno
    18 KB (3,461 words) - 14:28, 21 April 2017

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