image imagewidth (px) 4 512 | latex stringlengths 1 188 | sample_id stringlengths 16 16 | split_tag stringclasses 1 value | data_type stringclasses 1 value |
|---|---|---|---|---|
(\begin{matrix}y_{1}^{\prime}\\ y_{2}^{\prime}\end{matrix})=\frac{1}{x_{3}^{\prime}}(\begin{matrix}x_{1}^{\prime}\\ x_{2}^{\prime}\end{matrix}) | d8b3a6e05fb94d04 | train | human | |
\hat{c}_{p} | 1e956e238c3e5b20 | train | human | |
\frac{1}{h^{2}} | c544452c34efe2fa | train | human | |
(\frac{4}{7}-9)^{204\cdot\sqrt{5}} | 75e01f2e3266c749 | train | human | |
\frac{\partial C}{\partial\sigma} | 1cbc2ddec0b1a27d | train | human | |
R=[\begin{matrix}R_{1}\\ 0\end{matrix}] | a5e72c63ea48cc71 | train | human | |
\prod_{i\in I}U_{i} | b17bb0c2e11488e2 | train | human | |
\frac{\partial D}{\partial G}<0 | d51fee3b10eb50f8 | train | human | |
\sqrt{a}+\sqrt{b}=d-\sqrt{c} | 5fa9a29d3fbca353 | train | human | |
\frac{\pi^{2}}{16}\cong0.61685 | ef009b530dc63cf6 | train | human | |
log_{b}(x)=\frac{log(x)}{log(b)} | 0bdb2d14efde5194 | train | human | |
\frac{9}{112}\cdot(\frac{27}{392})^{218} | c8b1bfb49962d4ba | train | human | |
\emptyset\in C\Rightarrow g(\emptyset)=0 | cd5e388dd05bf1cb | train | human | |
r=\frac{\alpha\Delta t}{\Delta x^{2}} | c32167b333568159 | train | human | |
K(\sqrt{1-k^{2}}) | 21cf6f569807b0a4 | train | human | |
\frac{2^{5}}{\frac{1^{3}}{375}} | dc47b784025d0ca4 | train | human | |
=\prod_{k=1}^{n}[k]_{q} | 332d79ce2e36be1f | train | human | |
(\frac{15}{14}\div\frac{16}{15}=\frac{225}{224}) | 618270a8c9b920ef | train | human | |
f(g(x))=\sum_{n=0}^{\infty}c_{n}x^{n} | aee3aeb8bd0e540d | train | human | |
N\backslash S\notin W | e9f8c4a82d2b82b8 | train | human | |
\frac{dk}{dt} | 7b488a5d5c9faff8 | train | human | |
,r | baf32bc63e705acf | train | human | |
\langle\cdot,\cdot\rangle_{H^{2}(\Omega)} | 11e9caaef94ba876 | train | human | |
\sum_{n=1}^{\infty}\frac{H_{n}^{2}}{n^{2}}=\frac{17}{360}\pi^{4} | 77086abe0b6dd4cd | train | human | |
(\begin{matrix}7\\ 3\end{matrix})=35 | dc56b82efaa854bc | train | human | |
somb(\rho)=\frac{2J_{1}(\pi\rho)}{\pi\rho} | 96b5c60b184a85d8 | train | human | |
\int_{\Omega}fw=0 | 6a7f4fd0d0268c3e | train | human | |
\int_{0}^{T}g(t)dt | 8671e713fa10219f | train | human | |
u_{*}=\sqrt{\frac{\tau_{w}}{\rho}} | 59e2d63b96a6ddf3 | train | human | |
\frac{dy}{dx}=x+y | 2a616577ba225ee0 | train | human | |
\frac{\partial u_{i}}{\partial p_{j}} | f14e9d2a484fc8b7 | train | human | |
\tau_{ax}=(\frac{1}{k_{B}T})\frac{F_{eq}}{2} | 2e4ae906ef3a3d43 | train | human | |
(\begin{matrix}A&B\\ C&D\end{matrix}) | b912a972b3063a45 | train | human | |
\frac{34^{4}}{(4\cdot7)} | e1af0cfcd29d3419 | train | human | |
n!=\prod_{i=1}^{n}i | 572ce346fe23c848 | train | human | |
\lfloor\sqrt{\varphi(r)}log_{2}(n)\rfloor | d0729fc9c1f02aab | train | human | |
u:=\int_{a}^{b}v(t)dt | b5662887c38dabd8 | train | human | |
7^{7^{\cdot^{\cdot^{\cdot^{u}}}}} | 5035fec1974fbb7b | train | human | |
\Delta u(x_{1},x_{2})=0 | 3cb200c3e454d5d3 | train | human | |
\tilde{D}_{n} | aa70ddf782608fc8 | train | human | |
\frac{\partial M}{\partial\alpha} | f2b4ed18f9c959ea | train | human | |
\sqrt{gh_{0}} | 9a3c2d12d80b23b1 | train | human | |
\frac{\alpha+n}{\beta+n\overline{x}} | cc38a0510e5ce78d | train | human | |
A_{\mu}=\frac{Q}{R}k_{\mu} | f7dbab63dc449323 | train | human | |
\frac{sin(\pi x)}{(x^{2}-4)^{2}} | 92918a2134d58c20 | train | human | |
70^{70^{70^{70^{...}}}} | 42728510706121d2 | train | human | |
A\le\tilde{A} | c0610b0d85b08de6 | train | human | |
-\delta | 88c1bd1b0a298689 | train | human | |
\underline{AB} | 774fcf9ff8224348 | train | human | |
BA=(\begin{matrix}1&0\\ 0&0\end{matrix}) | 666d3cbaed0428fa | train | human | |
k_{7}^{i} | db42c5ae9470fd5d | train | human | |
[\begin{matrix}0&1\\ 0&0\end{matrix}] | 1d8975d343ae0f68 | train | human | |
x^{2}+y^{2}=(-r)^{2} | 949a319d829efe66 | train | human | |
\frac{\frac{9}{60}}{(303\cdot246)/10} | ccf2a04d0673060a | train | human | |
\tilde{W} | ebdb9bdcf86d823d | train | human | |
\frac{1-cos\alpha}{1+cos\alpha} | 730f5da0ad3e191a | train | human | |
2\sqrt{5}\approx4.47>4 | c0774a041b7308f6 | train | human | |
2^{2^{2^{2^{43}}}} | 7dffee7f5c728166 | train | human | |
F[y]=\int_{a}^{t}|y^{\prime}|dt | 9b7668f6635cfc8a | train | human | |
\int_{a}^{b}f(x)dg(x) | a139e19179a423f6 | train | human | |
((\infty),[c,d])\notin I | 815b417aeefcc625 | train | human | |
(\begin{matrix}5\\ 0\end{matrix}) | bcf3d61f1ea337af | train | human | |
\sqrt{7+2\sqrt{10}} | a3d972924e101449 | train | human | |
m=\frac{\nu+1}{2} | 1cf2a88efda88960 | train | human | |
v_{\perp}=r\frac{d\phi}{dt}=r\omega | ab92fa5818f1a34a | train | human | |
\frac{8^{43}}{\frac{6}{165}} | 8493c36ae02adf45 | train | human | |
-2\int Edl | 4ff3159d853bc5f9 | train | human | |
=-\frac{1}{2}\int_{0}^{T}\frac{1}{T^{2}}dt | e830aaf8ed76e758 | train | human | |
E=-\frac{k_{e}e^{2}}{2a_{0}}\frac{1}{n^{2}} | 0df2eda3e3da0da4 | train | human | |
\frac{dt}{dU}=0 | 3f4820916843f1b8 | train | human | |
\frac{{5^{438}}^{164}}{\frac{\frac{386}{493}}{370}} | 2bab910bc87d5eb8 | train | human | |
(402+91)^{\frac{(25+3)}{2}} | c7ef0f22fd0b10d9 | train | human | |
q=[\begin{matrix}u\\ d\end{matrix}] | 0c0428df5732e3ab | train | human | |
Var[\frac{1}{X}]=\frac{1}{\mu\lambda}+\frac{2}{\lambda^{2}} | 493f83b4bdd6f9f3 | train | human | |
\frac{TWG}{2}-PB | 6f1e8bd4e63845b4 | train | human | |
D_{i}(g_{t})=\frac{d}{dt}g_{t} | 196574c726559ffd | train | human | |
\sigma_{z}^{2}=z^{T}Vz | 26d1753d86284c99 | train | human | |
\int_{0}^{5}xdx | 88e08012dcfcca2f | train | human | |
\frac{d}{dt}N_{2} | 9750141e4a03832c | train | human | |
(\begin{matrix}p\\ i\end{matrix}) | 909c08731a4ef170 | train | human | |
(\begin{matrix}2\\ 0\\ 19\end{matrix}) | 65792fb4dd776cee | train | human | |
A:x\mapsto2\sqrt{x} | 4d93550c3c3cf5f7 | train | human | |
\prod_{i=1}^{r}(n-i+1) | b48a63fb264ec44d | train | human | |
L(\chi_{2},s)=\beta(s) | 64b2fedef45a0f1f | train | human | |
\frac{\partial E_{A}}{\partial\theta}=0 | c637fa99d0239be6 | train | human | |
\underline{P}X=\emptyset | 9290218e8e2b7314 | train | human | |
\frac{s}{\sqrt{\frac{v^{7}}{c^{7}}-1}} | 8cec43eecf5863ff | train | human | |
o^{\prime}=\frac{o-rq}{\sqrt{1-\frac{r^{2}}{b^{2}}}} | 3402330848457ef9 | train | human | |
\lambda>\lambda_{c} | 2c4582acf0fd7183 | train | human | |
\frac{4}{\sqrt{4-\frac{v^{9}}{x^{9}}}} | a7de3034256ba3f7 | train | human | |
\frac{400}{3.56}=A^{2} | b69bb76a0bdcb89d | train | human | |
\sqrt{50} | f916b4cafc77b736 | train | human | |
x=\frac{1}{2}sinht | d59b57ce5396bad3 | train | human | |
\tilde{\nu} | 10a12ac9408f3563 | train | human | |
\frac{dr}{dt}=-r | fd2e6e0e74da37e7 | train | human | |
e^{15^{15^{15^{133}}}} | f3c487890c1c6f4a | train | human | |
R(r,s)\le(\begin{matrix}r+s-2\\ r-1\end{matrix}) | 89cbbe585fd43f44 | train | human | |
\tilde{6} | 5aa98aa6f79ae0f5 | train | human | |
\overline{K}(C) | 29c53166a353a6ba | train | human | |
\tilde{G}^{K} | 8aece665e2ec2af3 | train | human |
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