image imagewidth (px) 4 512 | latex stringlengths 1 188 | sample_id stringlengths 16 16 | split_tag stringclasses 1
value | data_type stringclasses 1
value |
|---|---|---|---|---|
S\vdash A\vee(C\wedge\neg C) | 78bca0252715ff65 | train | human | |
lim_{x\rightarrow0^{-}}x^{-1}=-\infty | 849b37bce2083c60 | train | human | |
(\frac{3}{4})^{1}/(\frac{347}{455})^{8} | 2b6ce54b9f0410b3 | train | human | |
W_{i,j}\le-1/(k-1) | 92e032da1af2d641 | train | human | |
((\frac{7}{\sqrt{3}}+8)/197+87) | f562b8eb5b1d2521 | train | human | |
\int sinx^{2}dx | cea9adeea5bb266e | train | human | |
v\in(F_{2})^{d} | ee50fca868bb5cb8 | train | human | |
\prod_{j<k=1}^{N}(z_{j}-z_{k})^{2p} | f910eb0986d873b7 | train | human | |
H(\varphi,\eta;x,t) | 64b800da07f97301 | train | human | |
[\begin{matrix}.7&.2\\ .3&.8\end{matrix}] | bf53390b0034c3f6 | train | human | |
R=\prod_{i=1}^{n}R_{i} | dd38de18cc2fa5ac | train | human | |
A=-\frac{1}{3}U | 84481b144276d844 | train | human | |
(\frac{7}{284}-5)^{56\cdot302^{282}} | 5d077237b4d171d1 | train | human | |
0\notin\Phi | c643b15a82db52c7 | train | human | |
\prod_{i\in I}X_{i} | 0894b28fb6b0478a | train | human | |
[\begin{matrix}A&B\\ C&D\end{matrix}] | 76d1a1404b0e250b | train | human | |
\rho_{G_{1}...G_{m}}^{P_{G_{k_{1}}...G_{k_{q}}}} | 65ddc2961ad6f2c8 | train | human | |
\overline{y}_{x}=\frac{\sum_{i}y_{xi}}{n_{x}} | 71d947bae4dad961 | train | human | |
-\sqrt{3} | 5750a1bb08047ae0 | train | human | |
\underline{P}(Cl_{t}^{\ge}) | c0e2dd252f9f8f05 | train | human | |
2+\frac{24}{\sqrt{13}} | 52f3fd16e79ca72d | train | human | |
\frac{(\frac{9}{6}+309)}{\frac{10}{10}} | 438ede34108f0029 | train | human | |
T_{c}=\frac{\sum_{x}xl_{x}m_{x}}{\sum_{x}l_{x}m_{x}} | b411b06138d068f3 | train | human | |
(\frac{6}{10})^{(\frac{58}{399}\cdot395)} | 77c7058a1b693ac7 | train | human | |
b_{1}(\theta)sin(\theta) | 1957784acbfe3b09 | train | human | |
\sqrt{xi} | 2b29fb7349c5fafb | train | human | |
(\begin{matrix}n\\ k\end{matrix})=(\begin{matrix}n-1\\ k\end{matrix})+(\begin{matrix}n-1\\ k-1\end{matrix}) | d4f5fdaa86381357 | train | human | |
33.\overline{3} | 8a99a05732303937 | train | human | |
\frac{\beta_{n+1}}{\beta_{n}}=\frac{A(n)}{B(n)} | 17f04c303a9ce7f4 | train | human | |
\frac{df}{d\tau}=\sum_{\alpha=1}^{n}\frac{dx^{\alpha}}{d\tau}\frac{\partial f}{\partial x^{\alpha}} | 608e58545d55df31 | train | human | |
y=\sqrt{x} | 93bd0663cc59b1ee | train | human | |
\frac{\partial L}{\partial y} | 756c220a948fe027 | train | human | |
\frac{(5-5)^{7}}{7\cdot7} | 19a8086128c598fb | train | human | |
\theta^{\prime}=0 | b2f743c1d74ea564 | train | human | |
r_{ky}=\frac{\overline{ky}}{\sqrt{\overline{k^{3}}\overline{y^{3}}}} | 0d656dc718f32f3e | train | human | |
\hat{A}(t) | 4197226b1250f11b | train | human | |
s\{\begin{matrix}2\\ 4\end{matrix}\} | 91995199e8585059 | train | human | |
t_{i}=\frac{\hat{\epsilon}_{i}}{\hat{\sigma}\sqrt{1-h_{ii}}} | 2f06d7d78544d305 | train | human | |
\int e^{-x}cos(x)dx | c2b2cb888e0e541a | train | human | |
(\begin{matrix}X\\ k\end{matrix}) | 0b82d748530be385 | train | human | |
\frac{27}{25} | b74f574113814058 | train | human | |
\frac{\partial\omega}{\partial k} | 7abf519ac8546e02 | train | human | |
\frac{\partial(x,y)}{\partial(s,t)} | 830369b3735bcbde | train | human | |
\overline{l} | 8ca768c98ae05582 | train | human | |
r=k\frac{[O_{3}]^{2}}{[O_{2}]} | 24fdec2ca9af7f4c | train | human | |
\frac{171}{1}-8^{\sqrt{1}} | 3dd885eb110b048c | train | human | |
\overline{\alpha} | 233030df2af303cb | train | human | |
\frac{j}{i+j}<\rho | 0109fffecab3f15c | train | human | |
\hat{p}_{x}=\frac{\hbar}{i}\frac{\partial}{\partial x} | 59f5275087852fb8 | train | human | |
\eta(x)\frac{\partial w}{\partial t} | 5bea403edb9ea380 | train | human | |
\frac{10^{145}}{\frac{\frac{10}{376}}{234}} | cdd8957b0d1898c6 | train | human | |
\frac{dy}{dt} | 2a440755153ed387 | train | human | |
(\begin{matrix}2\\ 6\end{matrix}) | 56b80f7b52f83fa2 | train | human | |
WE[g(Y_{t},\theta)]=0 | 54fe3842d76a03b0 | train | human | |
(pq-1)\cdot t | 0bd84ae9694c9d7e | train | human | |
(J_{r})_{ij}=\frac{\partial r_{i}(\beta^{(s)})}{\partial\beta_{j}} | fbc37b44307d0557 | train | human | |
\sqrt{10} | 0234386eeed49158 | train | human | |
\frac{\overline{Y}_{2}-\overline{Y}_{1}}{\sqrt{\sigma_{1}^{2}/n+\sigma_{2}^{2}/n}} | 6acfc6f8e679cee5 | train | human | |
\Delta\gamma=\gamma_{1}+\gamma_{2}-\gamma_{12} | f15090801c1ad61b | train | human | |
\tilde{d}=1 | a62faf4bc665f4f6 | train | human | |
\prod l_{i}=N>4\sqrt{q} | 479fc6cbddf0fb01 | train | human | |
\hat{\pi} | 3f9744fb4bbe78d6 | train | human | |
\beta=\frac{4}{\sqrt{4-\frac{d^{9}}{c^{9}}}} | f25fae774d0d0b6a | train | human | |
Av_{t}=\mu_{t}dx | c1e6544120dfa4bf | train | human | |
\rho=\frac{1}{q(n\mu_{n}+p\mu_{p})} | a05285c0200c9e90 | train | human | |
\hat{f}(x) | 9a28e244a51c8f01 | train | human | |
\frac{\frac{\frac{5}{322}}{10}}{(\frac{\sqrt{10}}{70})^{8}} | 892dd28230e6e692 | train | human | |
D(f)= | 0655b1592c615555 | train | human | |
\prod_{i=1}^{n}f(x_{i}) | 0fd7cb8c5b9217bc | train | human | |
\sum_{n=0}^{\infty}\frac{(-1)^{n}}{n!}x^{2n} | c2e6719ff4067f22 | train | human | |
\overline{\nu}_{2} | 424e6db90d47c3e7 | train | human | |
{1^{10}}^{\frac{500}{8}-234} | 9acceb638a209b43 | train | human | |
\tilde{\Gamma} | 3fa08600cd151388 | train | human | |
(P,J,E) | 25998b238e20d621 | train | human | |
\hat{y}=X\hat{\beta} | 0a01112be323f983 | train | human | |
\beta\le0.984\sqrt{2} | b6480963f5ade5f7 | train | human | |
\frac{\dot{\sigma}}{E}+\frac{\sigma}{\eta}=\dot{\epsilon} | 1018967cd2ea53b1 | train | human | |
M_{A}=\frac{qL^{2}}{2} | 365bf7eee4e34b77 | train | human | |
\overline{z_{l}} | 8b43b50f22325f7b | train | human | |
w(2)=\frac{2}{\sqrt{\pi}} | ead82180589a0012 | train | human | |
f=\prod_{i=1}^{deg(f)}f_{i}^{i} | dcbeb8aac9671a17 | train | human | |
J(y)=\int_{a}^{b}yy^{\prime}dx | 35d621ce9aab99cf | train | human | |
R=\frac{4\pi A}{P^{2}} | a668c3297332180c | train | human | |
\hat{W}_{T} | fe85ec0343d73938 | train | human | |
(\begin{matrix}8\\ 4\end{matrix}) | b1536efb24c83bb1 | train | human | |
\int d\mu O_{i}Ge^{iS} | 4cd5f66232fc73c0 | train | human | |
\langle\hat{T}\rangle | 3b61b623be09a161 | train | human | |
\int|\kappa(s)|ds | 8af680221c3f352e | train | human | |
(\begin{matrix}X\\ k\end{matrix}) | c837cefd68f76174 | train | human | |
\langle\sqrt{R}e^{i}\varphi,Z_{R}\rangle | 1e019e7db7e7da27 | train | human | |
tc=\frac{1}{t_{n}-t_{1}} | 8eb0de391817ac1e | train | human | |
(\begin{matrix}6\\ 3\end{matrix}) | 44a61e297b4b8137 | train | human | |
L=g_{\mu\nu}\frac{dx^{\mu}}{ds}\frac{dx^{\nu}}{ds} | f2da8d6e4386a823 | train | human | |
n^{2}=\sum_{i=1}^{n}2i-1 | 92a064758c0aaebb | train | human | |
V_{+}\oplus g_{0}\oplus V_{-} | 0c37099e2ce5aebc | train | human | |
W=\int VdP | 1477d941737fd8d1 | train | human | |
\frac{x_{j}-x_{m}}{x_{j}-x_{m}}=1 | ad9223c347e0cc4e | train | human | |
(1-p^{2})^{N-2} | b913e9fc18360748 | train | human | |
\hat{5} | a72b1f22f0300a9a | train | human | |
=(\frac{Q^{2}}{2gm^{2}y^{4}})+y | c631688b7976baa3 | train | human |
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