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...Elementary dierential geometry zhengchao wan introduction overview dierentiable manifolds tangent vectors and spaces vector elds tensor peking university connections flatness riemannian may connection submanifolds information is a branch of mathematics that applies the techniques to eld probability theory this done by taking distributions for statistical model as points manifold forming fisher metric provides reached maturity through work shun ichi amari other japanese mathematicians in s nagaoka book methods cited most works relatively young due its broad coverage signicant developments attained using up year applications can be applied where parametrized play role here an incomplete list inference time series linear systems quantum neural networks machine learning mechanics biology statistics mathematical nance...