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...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>.

...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

...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>.

...) = 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{

...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>

==Basic Properties of a Field (cont'd)==

Read appendices A through D in our textbook (with higher attention to C and D), and solve the following problems:

<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>

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>

...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

...''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.

...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

...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

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)|

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>.}}

...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>

...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>

...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>

...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>

...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

...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>

...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>

...ll be coming directly from the homework assignments or the term tests, you'd probably be wise to go over these too.

...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>

...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>,

...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

...>\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

...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>

...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>

...} 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

...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>

...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

...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>

''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'''

...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

...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.

...erm test questions will coming directly from the homework assignments, you'd probably be wise to go over these too.

...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>

<br>2. D: B, what number's on your hat? B: I dunno. <br>3. D: A, ... A: I dunno

...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.

...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.''

...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],

|colspan=3 align=center|<math>\int_M d\omega=\int_{\partial M}\omega</math>