image imagewidth (px) 4 512 | latex stringlengths 1 188 | sample_id stringlengths 16 16 | split_tag stringclasses 1
value | data_type stringclasses 1
value |
|---|---|---|---|---|
\tilde{Y}^{n} | be1f5972d5f5d5b5 | train | human | |
0.5\sqrt{2} | a58b29aa8a4f4f31 | train | human | |
\frac{\partial f_{k}}{\partial x_{j}} | 554866b1352ca641 | train | human | |
{10^{218}}^{10}-\frac{\frac{4}{\sqrt{375}}}{179} | 4d59b397b0f9e669 | train | human | |
\chi=(E_{i}+E_{ea})/2 | 7f42fa1f682afbb0 | train | human | |
(8\cdot119)/5-319^{97} | 28ecab124abb9f5b | train | human | |
a=\sqrt{2\varphi^{-1}} | 07eb112ea61369cf | train | human | |
\hat{B} | d995ef9e2699ad4f | train | human | |
y=\sqrt{x^{2}-|w|^{2}}>0 | 81652621ff52a353 | train | human | |
\frac{1}{n}!=\int_{0}^{\infty}e^{-x^{n}}dx | a794cb3748b54914 | train | human | |
\frac{(3-170)}{\frac{7}{8}\cdot169} | 18588c0f98998f00 | train | human | |
0=E\{(\hat{x}-x)y\} | dd989331170f4ed9 | train | human | |
(107+393)^{\frac{10}{10}} | 5f55e3b4d0b5cbec | train | human | |
3\cdot10^{{6^{1}}^{1}} | 96759dd0136afc20 | train | human | |
||v||=\sqrt{v^{\top}v} | 7b94165cf45291de | train | human | |
\sqrt{re^{i\theta}}=\pm\sqrt{r}e^{i\theta/2} | 06f572fe66612448 | train | human | |
\frac{\frac{\frac{\sqrt{449}}{9}}{217}}{(\frac{\sqrt{318}}{313})^{3}} | 39f1ae5aa180fe91 | train | human | |
z=i\frac{log3}{4\pi} | 72815a520798140f | train | human | |
v(x_{0}) | fd5834356c996180 | train | human | |
(1)y^{\prime}=F(x,y) | a8e8e573167628f0 | train | human | |
[\begin{matrix}1&1\\ 0&1\end{matrix}] | c8a130af45f76b27 | train | human | |
\sum_{i=0}^{4}(\begin{matrix}8\\ 2i\end{matrix})(\begin{matrix}28\\ 16-i\end{matrix}) | 03bcac8d4ea1dea3 | train | human | |
\int fg=f(x)\int g | 8dbd24881a54785b | train | human | |
\sigma=\sqrt{\frac{B-ND^{2}}{N}} | 1fffcc0286cdfd52 | train | human | |
\frac{E_{1}}{E_{2}}=\frac{n_{1}}{n_{2}} | abc84973c454a7e8 | train | human | |
\omega\notin X | 57096b3c3e25de85 | train | human | |
\sqrt{-h}h^{ab}\rightarrow\eta^{ab} | 7fd44063e9cc0930 | train | human | |
m_{2}=\frac{a^{2}+ab+b^{2}}{3} | d8d32298269dd225 | train | human | |
\frac{2\chi}{\sqrt{\frac{Um_{sen}}{o^{9}}}} | 0d8041cb5a09fab5 | train | human | |
y=x^{2}\iff x=\sqrt{y} | c958660677c98097 | train | human | |
\overline{n} | bbe0d36d5a9533f9 | train | human | |
\frac{d\Phi}{dr}=-\frac{1}{\rho}\frac{dP}{dr} | f098dd4f127830ed | train | human | |
((\frac{442}{\sqrt{389}})^{8})^{395^{1}} | 06466a1065289bb5 | train | human | |
(\frac{3^{8}}{209}-3/2) | 3dbedacb32fb18b2 | train | human | |
((10\cdot496)-8)^{317\cdot\sqrt{8}+3} | 1876794d7755a785 | train | human | |
Z[p^{-1}] | 4f5026e7364c078a | train | human | |
(\begin{matrix}n\\ p\end{matrix}) | a44632d92e2b7d3d | train | human | |
3,\frac{8}{3},\frac{11}{4},\frac{19}{7},\frac{87}{32},... | a3d7b3b345e4f331 | train | human | |
dsin\theta_{n}=n\lambda | e666ef7c09700c13 | train | human | |
(\begin{matrix}N\\ 2\end{matrix}) | 9e8c89381b09d69b | train | human | |
p=\frac{m+u}{\sqrt{6-\frac{u^{2}}{c^{2}}}} | 906edd61c6be9435 | train | human | |
x^{(3)}=x_{4} | d7508f56a94b00f6 | train | human | |
\frac{4^{4}}{4}=64<70=(\begin{matrix}8\\ 4\end{matrix}) | e3ede36163cbcf60 | train | human | |
N\equiv\sqrt{-\frac{g}{\rho}\frac{d\rho}{dz}} | c8db92bbc341612b | train | human | |
V_{q}=\frac{4\pi e^{2}}{\epsilon q^{2}L^{3}} | 5a6711b016d8e32e | train | human | |
\mu=\beta(1+\frac{\alpha^{2}}{2}) | d162376373527d34 | train | human | |
[\begin{matrix}12&12&123&124\\ \end{matrix}] | 27943634325d1bd0 | train | human | |
273^{4}+26+403 | 4441173467e06747 | train | human | |
\frac{D_{P1}}{D_{P2}}=\frac{\rho_{P2}}{\rho_{P1}} | 711d84cab90d29a4 | train | human | |
{(H^{f})}^{\xi} | 35aa471f328144b0 | train | human | |
{(\frac{{w_{z}}^{4}}{{w_{a}}^{4}}-1)}^{4}\ge0 | 89ffac05e75cdfe8 | train | human | |
\lfloor\frac{37+3}{4}\rfloor=10 | a3b491d845aba9e6 | train | human | |
\alpha=\frac{lnC}{T-1} | c3207a4076e6f2a4 | train | human | |
{{417^{103}}^{4}}^{\frac{7}{46}} | c4d268c84416c188 | train | human | |
\overline{x_{i}} | 36e0c51d779bc1e5 | train | human | |
\tilde{\gamma} | 4a077549da4d749c | train | human | |
bf(m\tilde{T}) | 96cd8e0cfbc92a2e | train | human | |
\frac{(3-\sqrt{2})}{\frac{1^{6}}{7}} | 364bf97c6fdd967d | train | human | |
\underline{P}(Cl_{1}^{\le})=\{x_{1},x_{5}\} | 3537d3c8cd31fa86 | train | human | |
W=-\int Fdx | be3365e04f7d6b46 | train | human | |
||f_{\theta}-f_{\theta^{\prime}}||_{L_{1}}\ge\alpha | c8cb375cc1c4678e | train | human | |
F(r)=\frac{C(r)}{Rr^{3}} | ad30c2589c7c39d6 | train | human | |
\int_{0}^{1}3x^{2}+2x+5dt | 05dde2352693762a | train | human | |
\frac{(b-a)^{3}}{36}f^{(2)}(\xi) | 9432e5e59a773a98 | train | human | |
lim_{n\rightarrow\infty}z^{\pm n} | 4c87ab92cc5dfbfa | train | human | |
GZ=GM\cdot sin\phi | 28dc474c88ad0dfd | train | human | |
Af=i\frac{d}{dx}f | 3913db154ee42480 | train | human | |
I_{n}=\int sin^{n}x | 9b1e5bedd3aad447 | train | human | |
(\begin{matrix}0&i\\ i&0\end{matrix}) | a5d201921f51aaa2 | train | human | |
2^{O(\sqrt{k})}n^{O(1)} | 5dfbd67654f854ce | train | human | |
\epsilon_{2}=\lambda^{\lambda^{\lambda^{\cdot^{\cdot^{\cdot}}}}} | df77854b3f98473f | train | human | |
({\sqrt{56}^{5}}^{1}+10^{\sqrt{5}}) | aebf5691c09ed4a3 | train | human | |
P_{max}=P_{m}+H | 0afebcff2eab2d0b | train | human | |
(\begin{matrix}n\\ k\end{matrix})=(\begin{matrix}n-1\\ k-1\end{matrix})+(\begin{matrix}n-1\\ k\end{matrix}) | f3181fa678fc5e5a | train | human | |
\hat{\rho} | 8f8f0a10114a79a5 | train | human | |
\pi-\psi=\angle AKP_{2} | b1935edf11cd74c9 | train | human | |
\frac{\partial}{\partial c}P_{c}^{n}(c) | b24910dd4e5a697e | train | human | |
c_{c}=1 | 5f5abcf6fd3a473d | train | human | |
\frac{\sqrt{\frac{(d_{1}n)^{d_{1}}d_{7}^{d_{7}}}{(d_{1}n+d_{7})^{d_{1}+d_{7}}}}}{nU(\frac{d_{1}}{7},\frac{d_{7}}{7})} | 7adb6ef7f655dd5d | train | human | |
(\begin{matrix}n\\ c\end{matrix}) | 831fbf3ee29135fa | train | human | |
p=\frac{e^{\theta}}{1+e^{\theta}}= | f6594b46c7ef3083 | train | human | |
x^{p/q}=\sqrt[q]{x^{p}} | 27e4ed62587415be | train | human | |
w^{+\frac{(V+M)^{2}}{2{(s_{V})}^{2}}} | 93a68d7d96cec163 | train | human | |
\frac{\frac{2}{3}}{\frac{\frac{7}{300}}{1}} | 7e3c2db34885f8ac | train | human | |
\prod_{j\ne i}(x_{i}-x_{j}) | 412500632a50c3d8 | train | human | |
(\frac{378}{4}+(\frac{143}{10})^{196}) | d1f46a8ca9091110 | train | human | |
RC=\Delta_{T}(\frac{1-\alpha}{\alpha}) | e94f2702384c2872 | train | human | |
c_{n}=\prod_{i=1}^{n}p_{i} | e86a0d1a3dbae839 | train | human | |
\tilde{v}_{ij} | 2b95997b1dbbc841 | train | human | |
=\frac{(\begin{matrix}K\\ k\end{matrix})(\begin{matrix}N-K\\ n-k\end{matrix})}{(\begin{matrix}N+1\\ n+1\end{matrix})} | f14ca7618d191b18 | train | human | |
\hat{S_{z}} | 7a2392e6a2b333b4 | train | human | |
\frac{k-1}{k} | f0cd3b34bf9e9673 | train | human | |
\frac{(5-5)^{7}}{7\cdot7} | 452aab155f72bb1f | train | human | |
F=x^{2}-y^{2}-z^{2} | 024a00b093eb3886 | train | human | |
\{\begin{matrix}3\\ 5\end{matrix}\} | 9d74b841c1d9ede3 | train | human | |
\tilde{m}=\frac{rhp}{\sqrt{\frac{r_{1}r_{2}}{r_{1}-r_{2}}}} | 6da3f05378d2c237 | train | human | |
e^{k}k^{O(logk)}log|V| | 391e8e07e399429e | train | human | |
\frac{(210^{9}/4)}{\frac{(\sqrt{9}+317)}{\sqrt{5}}} | 7a055c0ae01a06d0 | train | human | |
\sqrt{\frac{\alpha\lambda}{\beta}}(x-\mu) | 15dc2648d6f2f527 | train | human | |
{149^{4}}^{\frac{20^{197}}{306}} | 72bf2f84fbb1b614 | train | human |
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