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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