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}a&b\\ b&1-a\end{matrix})
4d0542cc564a1443
train
human
\frac{\sum_{k=1}^{n}\delta_{x_{k}}}{n}\Rightarrow\mu
8c54efc509cc8656
train
human
\phi_{e}\notin F
9c2ee2d88eba73ea
train
human
d_{1}=d_{2}
23c2ee286726fa77
train
human
{7^{398}}^{\frac{(4-2)}{10}}
c4393eed093e2ce4
train
human
|A+A|\ge2|A|-1
7ab06fb59618e337
train
human
v=\frac{dr}{dt}
b9890b74e37b218b
train
human
PQ+r=PQ^{\prime}+r^{\prime}
f41ce5e6873b43c3
train
human
E=v^{2}/2-GM/r
7048c512af73786b
train
human
8\cdot9+(5-6-8)
c22b320737ac417b
train
human
(\iota x.\phi)
99cd6a769c6a804e
train
human
f^{\prime}\rightarrow1
bb0c267bcd0f0a28
train
human
\int(\int f(r)dv)dr
ad0d5625c75550d3
train
human
\rho=\frac{\partial V}{\partial r}
5edfec6d54cbcf49
train
human
w_{u}^{h}
7dff9035528deb76
train
human
|AB|=\frac{|AC||FE|}{|FC|}
8edc625a8e2d84f5
train
human
Y_{j}=y_{j}
3c723cba27ed2d6c
train
human
\tilde{\varphi}:\mathbb{S}^{\lambda}E\rightarrow M
189f84d274d6171c
train
human
7^{7^{\cdot^{\cdot^{\cdot^{u}}}}}
cb98009c621f6874
train
human
\hat{f}_{i}
d8131f5a033644be
train
human
\sum_{i=0}^{4}(\begin{matrix}8\\ 2i\end{matrix})(\begin{matrix}28\\ 16-i\end{matrix})
7c9e60465dd43077
train
human
\frac{\partial u}{\partial t}=\Delta u+F(u)
d243bebcf3a1e5bf
train
human
m_{zal}=\frac{m_{5}}{\sqrt{1-\frac{p^{6}}{c^{6}}}}
9bcfd322e00439b6
train
human
G=K_{III}^{2}(\frac{1}{2\mu})
bffc7894488ebb65
train
human
\delta(y)=\frac{e^{-\frac{y^{7}}{7}}}{\sqrt{7\pi}}
5e615d0163dfe926
train
human
\frac{\dot{Q}}{T}
893ff88ccd879172
train
human
\frac{\frac{c_{n-1}b_{n}}{c_{n}}+\frac{c_{n+1}}{c_{n}b_{n}}}{2}
4f30f3bd115cb4cb
train
human
P=\frac{dy}{dx}
d25e5d4fa1f7db49
train
human
u_{s}=dx_{s}(t)/dt
e6ded50ff3cf1302
train
human
\sqrt{\frac{2Gm}{r}}
9d81a1751cd653ec
train
human
\mu_{e}=\frac{C_{1}}{\Sigma\frac{l}{\mu A}}
633b610810a31201
train
human
\frac{P_{1}}{P_{2}}
eab7225ce4e0f7d3
train
human
B^{\prime}=B\cdot\sqrt{4\pi/\mu_{0}}
b95af5d122820a7b
train
human
\hat{\Pi}_{\rho_{X^{n}(m-1)},\delta}
733bbd7ad3c3fb02
train
human
Z_{0}=\sqrt{\frac{L}{C}}
3aed366e08603ba2
train
human
e^{\int f(x)dx}
126ef9a6ec6cd210
train
human
H=\int\rho hdV
10a3ee929a871a1a
train
human
P(G-uv,k)
649ca5af16ccbaf1
train
human
(\begin{matrix}n\\ i\end{matrix})2^{-n}
bcfcf273a8c5401e
train
human
N\approx\frac{v_{N}-v_{F}}{2c}
562679e5b3cb579b
train
human
p=\frac{m+u}{\sqrt{6-\frac{u^{2}}{c^{2}}}}
17ed8b86250c3b60
train
human
\tilde{n}=n+z^{2}
497080fd824b79b1
train
human
\frac{\partial u}{\partial x}
bdbe7a5715246185
train
human
Z=\frac{y\cdot c^{6}}{\sqrt{3-\frac{|v|^{6}}{c^{6}}}}
802dfc7225e9dcf0
train
human
ntan\frac{\pi}{n}
d09391492d895ab7
train
human
\mathbb{Z}[\alpha]
760deb5cac2ab667
train
human
N\ge(\begin{matrix}n\\ i\end{matrix})
ddab92f0efec07ca
train
human
|H(s)|^{2}=H(s)\overline{H(s)}
376dfac6d8d4ec21
train
human
Z=[\begin{matrix}X_{i}&Y_{-i}\end{matrix}]
6dce19a02351f792
train
human
s\{\begin{matrix}4\\ 4\end{matrix}\}
6b34e4ec2cfa9171
train
human
2(\sqrt{2}-1)\approx0.828
6484a87f36bf95bf
train
human
\theta_{OW}
7691bbc97a305691
train
human
\prod_{i=1}^{m}K[x]/p_{i}(x)
38ec8eabe8d79a02
train
human
\frac{\frac{10^{10}}{113}}{\frac{4}{6}}
123e820414ac395e
train
human
b=\frac{ac}{d}-c
d5506c6ecc6029bd
train
human
\hat{A}_{i}
a809176ec5fac18c
train
human
\frac{\partial^{2}z}{\partial x\partial y}
c866c8f4d30f3411
train
human
T=\frac{\partial U}{\partial S}
3c3ab134681f6953
train
human
G=\int_{0}^{T}S(t)x(t)dt
46c5d6a66abec8e0
train
human
\frac{\partial x}{\partial u}
6edd7d23636f7f88
train
human
\sqrt[\infty]{\infty!}
a67262df161fae5d
train
human
\int_{K}f(gk\cdot y)dk
f20f20ba07119555
train
human
Z_{01}=\frac{V_{1}}{I_{1}}
31e03b31b1cebf85
train
human
\{\begin{matrix}6\\ 6\end{matrix}\}
dbcaf869bdd6f0da
train
human
\frac{(287\cdot\sqrt{207})^{8}}{(122+155)}
812accb1dc9c3897
train
human
\lfloor\sigma(G)\rfloor
1181bc683a3ecba8
train
human
377^{2}-\frac{\sqrt{356}^{499}}{59}
17dc1b06d67df98a
train
human
X_{i(K+1)}=1
40ca0b699d5ceca2
train
human
(1-\gamma)n
0ffa26bb179fa935
train
human
H_{n,m}=\sum_{k=1}^{n}\frac{1}{k^{m}}
e936c8e10cd6d989
train
human
(\frac{96}{387})^{\frac{10}{2}}
c0404b4e44fa75e5
train
human
(\frac{315+194}{8})^{303/47+5}
ebd866c9b4e38ae3
train
human
r_{isco}=\frac{6GM}{c^{2}}
84160ab3bfe75eab
train
human
A=(
0353cae0d9b6afb7
train
human
S_{+}|-\rangle=\hbar|+\rangle
65fcc78a45ac97c2
train
human
\hat{Y}_{j}
4798b4d72a41dd99
train
human
h(a)_{n}=n\cdot a_{n}
90542411d873c884
train
human
X^{\prime}=\partial X/\partial s
dd06102132c81d09
train
human
\Rightarrow m_{1,2}=\pm\sqrt{\frac{n}{2}}
bf04908eb3308222
train
human
lim_{\Delta x\rightarrow0}sin\frac{1}{\Delta x}
38601e9538d269b1
train
human
\beta=\frac{Cov(r_{a},r_{b})}{Var(r_{b})}
f12fe79760d2b013
train
human
\mu(x)=\frac{F_{X}^{\prime}(x)}{1-F_{X}(x)}
c98cc6dd5de670a7
train
human
\frac{dQ_{T}}{dQ_{*}}
50abefb794a93535
train
human
F[t_{1},t_{2},...,t_{n}]
a6de456e552d6412
train
human
F(x)=\int ln(f(x))dx
3b8ea0dfe2644ac3
train
human
\int_{0}^{T}wx(t)dt
a67adcdd61c124b6
train
human
184+414+408^{163}
d02069613ea7d07b
train
human
a_{j}-\sum k_{i}b_{i}
de5bd347a0b71a89
train
human
a(x)+x^{b}b(x)=0
eaafc74e55c0dfa2
train
human
y=\int sin\psi ds
12f3e106212e9dda
train
human
\frac{\sqrt{2}}{12}
9a0a940239df154e
train
human
\omega+2
ddb67ad3a2c20130
train
human
123\cdot8-7^{\frac{\frac{164}{313}}{10}}
0fdf66fe79f00ac6
train
human
\tau_{N}=\tau_{0}e^{\frac{KV}{k_{B}T}}
c77ff4c5dcdcebe9
train
human
{(\nu^{\phi})}^{\alpha}
b7f470069d3a6245
train
human
\frac{1}{\tau_{U}}=2\gamma^{2}\frac{k_{B}T}{\mu V_{0}}\frac{\omega^{2}}{\omega_{D}}
616301d9a40e7e7d
train
human
\hat{\rho}
a770100130f43d6e
train
human
\tilde{W}_{t}
b5b081039b3290b4
train
human
|V_{o}|=\frac{V_{o}}{V_{i}}
fe1dd1d898c3aba0
train
human
\frac{1}{1\cdot h^{\frac{U\times(1\cdot U)}{5^{N+1}}}}
1dad8527708d124a
train
human