Datasets:
LiamYo
/
MathWritingHandwritten

Dataset card Data Studio Files
xet
 Community
1
png
imagewidth (px)
16
3.01k
txt
stringlengths
1
188
__key__
stringlengths
9
9
__url__
stringclasses
115 values
(\begin{matrix}e&0\\ 0&e\end{matrix})
000000900
/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
\hat{s}=S(S+N)^{-1}d
000000901
/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{1}{2}LI^{2}
000000902
/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
9\cdot5^{\frac{\frac{7}{399}}{324}}
000000903
/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}^{\infty}(\begin{matrix}\alpha\\ k\end{matrix})kx^{k-1}
000000904
/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_{0}=x_{0}^{T}\beta
000000905
/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}a&0\\ 0&b\end{matrix}]
000000906
/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_{33}=[\begin{matrix}A&B/2\\ B/2&C\end{matrix}]
000000907
/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_{00}=0.
000000908
/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
\pm\sqrt{-1}
000000909
/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
\alpha_{s}\approx\frac{C_{s}\cdot R^{3}}{f^{4}}
000000910
/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
{2^{492}\cdot438}^{\frac{2}{8}}
000000911
/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{\Delta r}{i}=\frac{R^{\frac{2r_{l}}{i}}-1}{R^{\frac{2r_{l}}{i}}\cdot1}
000000912
/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 p}{\partial z}=0
000000913
/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=\frac{\Delta PE}{\Delta t}
000000914
/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
(11\cdot\cdot\cdot1)v^{T}=0
000000915
/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{n}{d}\mapsto exp(\frac{n}{d}\cdot2\pi i)
000000916
/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
\hat{y}_{t}
000000917
/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
\phi(-\theta,\tau)\phi(\theta,\tau)=1
000000918
/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
2^{3*4}=2^{12}=4096
000000919
/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=log_{3}2=\frac{log2}{log3}
000000920
/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
ss\{\begin{matrix}2\\ 5\end{matrix}\}
000000921
/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\overline{B}
000000922
/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=\prod_{i=1}^{deg(f)}f_{i}^{i}
000000923
/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{dI}{ds}=j-\alpha I
000000924
/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&0\\ 1&-1\end{matrix})
000000925
/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
\gamma_{u^{x}}
000000926
/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^{inx}|n\in\mathbb{R}\}
000000927
/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
{448\cdot246^{452}}^{\frac{2}{148}}
000000928
/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})
000000929
/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\\ k\end{matrix})_{q}
000000930
/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{6}}{10}-456}{\frac{\sqrt{6}}{61}/7}
000000931
/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
q_{e}=\frac{q_{b}}{\sqrt{\frac{q_{b}}{q_{m}}}}
000000932
/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_{a}^{\infty}
000000933
/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{dy}{dx}
000000934
/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&3&2\\ 4&1&0\end{matrix}]
000000935
/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_{1}\otimes v_{2}=\epsilon\eta
000000936
/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
=7.4
000000937
/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{n}_{m}
000000938
/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=-\frac{\partial g}{\partial p}
000000939
/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 f(x)dx
000000940
/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 T}{\partial q_{k}}
000000941
/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_{L}(s^{\prime},x)\ge c_{L}(s,x)
000000942
/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&-R\\ 0&1\end{matrix}]
000000943
/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{270-87}{78}+(\frac{9}{6})^{17}
000000944
/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^{10}}^{368}\cdot\sqrt{5}^{9})
000000945
/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_{i}=(S_{i}+1)/2
000000946
/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{3}{18}}{210})^{\frac{\frac{\sqrt{312}}{10}}{400}}
000000947
/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=\frac{eB\lambda_{u}}{2\pi m_{e}c}
000000948
/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
\hat{u}
000000949
/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=2\pi\int_{-1}^{+1}I\mu d\mu
000000950
/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_{earth}=\frac{gR_{earth}^{2}}{G}
000000951
/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||=\sqrt{x\cdot x}
000000952
/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{1}{\sqrt{x^{2}+1}}
000000953
/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{1}{a}F(\frac{s}{a})
000000954
/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_{i}=\dot{m}\Delta h_{o}
000000955
/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{e}_{i}\tilde{f}_{i}
000000956
/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=[\begin{matrix}a&b\\ c&d\end{matrix}]
000000957
/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{AB}
000000958
/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_{4}^{\prime}=\frac{y_{4}-\frac{z}{c^{2}}k_{4}}{\sqrt{4-\frac{z^{2}}{c^{2}}}}
000000959
/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}{\sqrt{\frac{l^{2}}{u^{2}}+0}}
000000960
/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}{2}+\frac{sin(2x)}{4}+C
000000961
/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}a&b\\ c&1-a\end{matrix})
000000962
/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^{2}=\frac{\partial p}{\partial\rho}
000000963
/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{\frac{Z_{I2}}{Z_{I1}}}
000000964
/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{V^{+}}{I^{+}}=Z_{0}=-\frac{V^{-}}{I^{-}}
000000965
/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
\hat{Y}^{A}
000000966
/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=\{1,...,I\}
000000967
/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=gl_{n}
000000968
/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
\Phi^{a}=\Phi_{+}^{a}\cup-\Phi_{+}^{a}
000000969
/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{n+1}{n}]^{n}>n
000000970
/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\rho}{\partial t}=D\cdot\frac{\partial^{2}\rho}{\partial x^{2}}
000000971
/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=(\begin{matrix}1&-1\\ 0&1\end{matrix})
000000972
/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(x)=\frac{1}{2\pi}\sqrt{\frac{4-x}{x}}
000000973
/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{(7\cdot3)^{301}}{{10^{6}}^{3}}
000000974
/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})
000000975
/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
\chi_{(h)}^{2}
000000976
/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{t-1}{t+1})
000000977
/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{2\pi}{\lambda}=k
000000978
/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=-mc\int ds
000000979
/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_{(t_{i+1}+t_{i})/2}
000000980
/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}^{\infty}(|G_{i}|-1)
000000981
/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_{g}=\frac{\sqrt{1-r^{2}}}{r}
000000982
/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^{433}\cdot111+\sqrt{5}^{381}
000000983
/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
\Gamma
000000984
/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=(\begin{matrix}A&B\\ C&D\end{matrix})
000000985
/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\approx\frac{L^{2}}{2r}
000000986
/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=\frac{|b|}{\sqrt{\frac{1\cdot b^{5}}{n\cdot5}}}
000000987
/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{3}
000000988
/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
264-175-365-4+5
000000989
/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{\alpha^{2}}{2}
000000990
/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{d^{2}P}{dt^{2}}
000000991
/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=J\dot{\omega}+\omega\times J\omega
000000992
/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}{\sigma^{2}}e^{-x^{2}/2\sigma^{2}}
000000993
/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
h=c_{p}T=\frac{\gamma}{\gamma-1}\frac{T}{m}
000000994
/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(\epsilon)=\frac{\epsilon-1}{\epsilon+x}
000000995
/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_{p}=\frac{1}{2}\rho g\sigma^{2}
000000996
/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\\ 0.51n\end{matrix})
000000997
/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_{jk}=\frac{A+B-2J}{A+B}
000000998
/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{a}{b}|=\frac{|a|}{|b|}
000000999
/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