Datasets:
LiamYo
/
MathWritingHandwritten

Dataset card Data Studio Files
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115 values
\hat{C}_{I}
000000800
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
P=2\pi r\sqrt{\frac{r}{\mu}}
000000801
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
\frac{m_{1}}{\sigma_{1}}=\frac{m_{2}}{\sigma_{2}}
000000802
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
[\begin{matrix}1&1\\ 0&1\end{matrix}]
000000803
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
\sigma_{j}^{\eta}
000000804
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
V:=L(\underline{a}_{1},...,\underline{a}_{r})
000000805
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
c=\sqrt[3]{\frac{2\pi^{2}}{3}}\approx1.874
000000806
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
D\{J\}\subseteq\tilde{D}
000000807
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
[\begin{matrix}0&1\\ -1&0\end{matrix}]
000000808
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
d=\sqrt{2R^{\prime}h}
000000809
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
\frac{dE}{dx}=0
000000810
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
tan^{2}\alpha_{1}=-\frac{tan\beta_{1}}{tan\beta_{2}}
000000811
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
d\theta+\frac{1}{2}[\theta,\theta]=0
000000812
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
B=A^{T}A=[\begin{matrix}9&0\\ 0&4\end{matrix}]
000000813
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
S=\int_{0}^{T}E[s(t)^{2}]dt
000000814
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
\sqrt{2n}
000000815
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
c=\sum_{j=1}^{\infty}10^{-j!}
000000816
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
W=\lambda(-ln(U))^{1/k}
000000817
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
(M,g_{ab})
000000818
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
377^{2}-\frac{\sqrt{356}^{499}}{59}
000000819
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
\tilde{S_{n}^{m}}=-\frac{S_{n}^{m}}{\mu R^{n}}
000000820
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
\omega_{\hat{M}\hat{N}P}
000000821
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
\int_{b}^{a}
000000822
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
\frac{\frac{263}{4}}{409/9}
000000823
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
J_{ij}\sim|i-j|^{-\alpha}
000000824
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
{k^{l}}^{f}
000000825
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
cos\theta=1/(n\beta)
000000826
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
(\frac{8}{322}/2\cdot\frac{\frac{332}{6}}{380})
000000827
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
e^{-q\tau}\frac{\phi(d_{1})}{S\sigma\sqrt{\tau}}
000000828
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
(\begin{matrix}n\\ 2\end{matrix})
000000829
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
\overline{15}
000000830
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
a_{0}x^{0}+\cdot\cdot\cdot+a_{n}x^{n}
000000831
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
[\begin{matrix}0&1\\ 1&0\end{matrix}]
000000832
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
t_{0}=t_{f}\sqrt{1-\frac{3}{2}\cdot\frac{r_{s}}{r}}
000000833
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
1+\sqrt{2}
000000834
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
TK_{R}^{\prime\prime}
000000835
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
\frac{e^{+\frac{0}{x^{8}}}}{x}
000000836
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
\epsilon(\begin{matrix}n\\ 2\end{matrix})
000000837
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
M=K[\begin{matrix}R&t\end{matrix}]
000000838
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
\frac{\partial C}{\partial\sigma}
000000839
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
\int(1/lnx)dx
000000840
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
\sqrt{2E}
000000841
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
\tilde{q}
000000842
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
\rho^{\prime}=\frac{\rho V+MV^{\prime}\mu}{V^{\prime}}
000000843
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
\frac{\frac{4+463}{82}}{\frac{48}{142}}
000000844
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
\prod_{i\in I}
000000845
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
{{3^{\sqrt{9}}}^{468}}^{(\frac{431}{38})^{7}}
000000846
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
R=\frac{Z_{2}-Z_{1}}{Z_{2}+Z_{1}}
000000847
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
B=\prod_{i=1}^{n}[a_{i},b_{i}]
000000848
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
\varphi\vdash\neg\psi
000000849
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
\perp=I^{*}
000000850
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
y=\frac{x}{ln(x)}
000000851
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
(\begin{matrix}n\\ b\end{matrix})
000000852
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
|z|\ne\sqrt{z^{2}}
000000853
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
l_{P}=\lambda_{e}\frac{\sqrt{\alpha_{G}}}{2\pi}
000000854
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
K_{SP}=\prod_{k}{a_{k}}^{m_{k}}
000000855
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
\frac{dx}{dt}=3
000000856
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
cot^{2}\theta=csc^{2}\theta-1
000000857
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
E[Y_{n}|F_{n-1}]=Y_{n-1}
000000858
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
\int_{0}^{1}e(t)dt
000000859
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
\tilde{4}
000000860
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
\delta L=-\frac{(\partial_{\mu}A^{\mu})^{2}}{2\xi}
000000861
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
d\theta=\frac{-dv}{vtan\alpha}
000000862
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
\frac{dN(x)}{dx}
000000863
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
p=\frac{iv}{\sqrt{6-\frac{v^{7}}{f^{7}}}}
000000864
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
\frac{x(2x+1)}{(x-1)^{4}}
000000865
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
R\sim M^{-1/3}
000000866
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
s_{uy}=\frac{\overline{uy}}{\sqrt{\overline{u^{2}}\overline{y^{2}}}}
000000867
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
g(r)=\frac{n(r)}{\rho4\pi r^{2}\Delta r}
000000868
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
\sum_{k=1}^{n}\frac{1}{k}
000000869
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
G(R)=\sigma_{R}^{+}-\sigma_{R}
000000870
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
x^{2}\equiv a
000000871
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
\int vds
000000872
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
\frac{\pi^{3}}{6}R^{6}
000000873
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
\sqrt{h}
000000874
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
y_{t}=y_{t-1}+c+e_{t}
000000875
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
(\begin{matrix}f_{xx}&f_{xy}\\ f_{xy}&f_{yy}\end{matrix})
000000876
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
\frac{\frac{268+7}{236}}{88^{\sqrt{347}}}
000000877
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
\varphi(\beta/\alpha)
000000878
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
(\begin{matrix}p\\ n\end{matrix})
000000879
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
t_{4}^{\prime}=\frac{t_{4}\cdot\frac{v}{h^{4}}r_{4}}{\sqrt{1\cdot\frac{v^{4}}{h^{4}}}}
000000880
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
R(r)=CJ_{0}(\frac{k}{v}r)
000000881
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
i(t=0)=I_{0}cos(\phi)
000000882
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
\frac{\partial(x^{i_{1}},...,x^{i_{k}})}{\partial(u^{1},...,u^{k})}
000000883
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
\frac{\frac{\sqrt{235}+17}{6}}{(109\cdot6)}
000000884
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
\frac{j}{i+j}<\rho
000000885
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
\sum_{i=0}^{k}(\begin{matrix}n\\ i\end{matrix})=O(n^{k})
000000886
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
F=\frac{T_{0}+T_{sys}}{T_{0}}
000000887
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
\tilde{M}
000000888
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
(x+y)/sqrt(2)
000000889
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
10^{\sqrt{7}}+\frac{\sqrt{8}}{91}
000000890
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
|\partial_{\mu}n\rangle
000000891
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
x_{\pm}=-\frac{5}{4}\pm\frac{3}{4}\sqrt{\frac{35}{3}}
000000892
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
\sum_{i=-\infty}^{\infty}f(i)10^{-i}
000000893
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
1:\sqrt{\varphi}:\varphi
000000894
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
(\frac{3}{4})^{1}/(\frac{347}{455})^{8}
000000895
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
3/\tilde{4}
000000896
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
a_{1}b_{1}+a_{2}b_{2}=a_{3}b_{3}
000000897
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
\Delta S=\oint\frac{\delta Q}{T}
000000898
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar
\{\underline{y}_{1},\underline{y}_{2},\underline{y}_{3}\}
000000899
/tmp/hf-datasets-cache/medium/datasets/80136707134450-config-parquet-and-info-LiamYo-MathWritingHandwri-2262e7ea/hub/datasets--LiamYo--MathWritingHandwritten/snapshots/8e7da41a92b5ef5c2aecc9ed41dd325983985bf9/shards/train/shard-000000.tar