├── .github └── workflows │ └── ci.yml ├── .gitignore ├── LICENSE ├── README.md ├── docs ├── courses │ ├── ads-final-review.md │ ├── high-dim-prob │ │ ├── index.md │ │ └── lec1.md │ ├── imgs │ │ ├── ads │ │ │ ├── ads_review_RBTree_complexity.png │ │ │ ├── ads_review_binary_tree.png │ │ │ ├── ads_review_master_theorem.png │ │ │ ├── ads_review_master_theorem_log.png │ │ │ └── heaps.png │ │ ├── prob │ │ │ └── high-dim │ │ │ │ └── overview.drawio.png │ │ └── toc │ │ │ ├── 2.1.drawio.png │ │ │ ├── 2.2.drawio.png │ │ │ ├── 2.3.drawio.png │ │ │ ├── 2.4.png │ │ │ ├── 3.1.jpg │ │ │ ├── 3.2.jpg │ │ │ ├── 3.3.jpg │ │ │ ├── 3.4.jpg │ │ │ ├── 3.5.png │ │ │ ├── 3.6.jpg │ │ │ ├── 3.7.png │ │ │ ├── 3.8.jpg │ │ │ ├── 3.9.png │ │ │ ├── 4.4.png │ │ │ ├── 4.5.png │ │ │ ├── 4.6.png │ │ │ ├── 4.7.png │ │ │ ├── 4.8.png │ │ │ ├── 4.9.png │ │ │ └── 5.1.png │ ├── index.md │ ├── info-theory.md │ ├── numerical │ │ ├── algebra │ │ │ ├── 1.md │ │ │ ├── 2.md │ │ │ ├── 3.md │ │ │ ├── 4.md │ │ │ ├── 5.md │ │ │ ├── 6.md │ │ │ ├── 7.md │ │ │ └── index.md │ │ ├── analysis │ │ │ ├── 1.md │ │ │ ├── 2.md │ │ │ ├── 3.md │ │ │ ├── 4.md │ │ │ ├── 5.md │ │ │ ├── 6.md │ │ │ ├── 7.md │ │ │ ├── 8.md │ │ │ ├── 9.md │ │ │ └── index.md │ │ └── index.md │ ├── physics │ │ ├── 2-current.md │ │ ├── 2-electromagnetics.md │ │ ├── 2-electrostatics.md │ │ ├── 2-optics.md │ │ ├── 2-quantum.md │ │ └── index.md │ ├── probability │ │ ├── basics.md │ │ ├── feature_basics.md │ │ ├── feature_pro.md │ │ ├── index.md │ │ ├── normal_distr.md │ │ ├── prob_lim.md │ │ └── rand_var_vec.md │ └── toc │ │ ├── after_story.md │ │ ├── context_free.md │ │ ├── finite_automata.md │ │ ├── index.md │ │ ├── languages.md │ │ ├── turing_machine.md │ │ └── undecidability.md ├── css │ ├── counter.css │ ├── custom.css │ ├── font.css │ ├── fonts │ │ ├── KaTeX_AMS-Regular.ttf │ │ ├── KaTeX_AMS-Regular.woff │ │ ├── KaTeX_AMS-Regular.woff2 │ │ ├── KaTeX_Caligraphic-Bold.ttf │ │ ├── KaTeX_Caligraphic-Bold.woff │ │ ├── KaTeX_Caligraphic-Bold.woff2 │ │ ├── KaTeX_Caligraphic-Regular.ttf │ │ ├── KaTeX_Caligraphic-Regular.woff │ │ ├── KaTeX_Caligraphic-Regular.woff2 │ │ ├── KaTeX_Fraktur-Bold.ttf │ │ ├── KaTeX_Fraktur-Bold.woff │ │ ├── KaTeX_Fraktur-Bold.woff2 │ │ ├── KaTeX_Fraktur-Regular.ttf │ │ ├── KaTeX_Fraktur-Regular.woff │ │ ├── KaTeX_Fraktur-Regular.woff2 │ │ ├── KaTeX_Main-Bold.ttf │ │ ├── KaTeX_Main-Bold.woff │ │ ├── KaTeX_Main-Bold.woff2 │ │ ├── KaTeX_Main-BoldItalic.ttf │ │ ├── KaTeX_Main-BoldItalic.woff │ │ ├── KaTeX_Main-BoldItalic.woff2 │ │ ├── KaTeX_Main-Italic.ttf │ │ ├── KaTeX_Main-Italic.woff │ │ ├── KaTeX_Main-Italic.woff2 │ │ ├── KaTeX_Main-Regular.ttf │ │ ├── KaTeX_Main-Regular.woff │ │ ├── KaTeX_Main-Regular.woff2 │ │ ├── KaTeX_Math-BoldItalic.ttf │ │ ├── KaTeX_Math-BoldItalic.woff │ │ ├── KaTeX_Math-BoldItalic.woff2 │ │ ├── KaTeX_Math-Italic.ttf │ │ ├── KaTeX_Math-Italic.woff │ │ ├── KaTeX_Math-Italic.woff2 │ │ ├── KaTeX_SansSerif-Bold.ttf │ │ ├── KaTeX_SansSerif-Bold.woff │ │ ├── KaTeX_SansSerif-Bold.woff2 │ │ ├── KaTeX_SansSerif-Italic.ttf │ │ ├── KaTeX_SansSerif-Italic.woff │ │ ├── KaTeX_SansSerif-Italic.woff2 │ │ ├── KaTeX_SansSerif-Regular.ttf │ │ ├── KaTeX_SansSerif-Regular.woff │ │ ├── KaTeX_SansSerif-Regular.woff2 │ │ ├── KaTeX_Script-Regular.ttf │ │ ├── KaTeX_Script-Regular.woff │ │ ├── KaTeX_Script-Regular.woff2 │ │ ├── KaTeX_Size1-Regular.ttf │ │ ├── KaTeX_Size1-Regular.woff │ │ ├── KaTeX_Size1-Regular.woff2 │ │ ├── KaTeX_Size2-Regular.ttf │ │ ├── KaTeX_Size2-Regular.woff │ │ ├── KaTeX_Size2-Regular.woff2 │ │ ├── KaTeX_Size3-Regular.ttf │ │ ├── KaTeX_Size3-Regular.woff │ │ ├── KaTeX_Size3-Regular.woff2 │ │ ├── KaTeX_Size4-Regular.ttf │ │ ├── KaTeX_Size4-Regular.woff │ │ ├── KaTeX_Size4-Regular.woff2 │ │ ├── KaTeX_Typewriter-Regular.ttf │ │ ├── KaTeX_Typewriter-Regular.woff │ │ └── KaTeX_Typewriter-Regular.woff2 │ ├── katex.min.css │ └── svg_extra.css ├── index.md ├── js │ ├── heti.js │ ├── katex.js │ └── katex.min.js ├── math │ ├── DEs │ │ ├── Intro2SDE │ │ │ ├── Brownian_noise.md │ │ │ ├── SDE.md │ │ │ ├── applications.md │ │ │ ├── index.md │ │ │ ├── intro_prob.md │ │ │ └── stochastic_integrals.md │ │ ├── ODE │ │ │ ├── general1.md │ │ │ ├── index.md │ │ │ └── system.md │ │ ├── PDE │ │ │ ├── 4linearPDEs.md │ │ │ ├── index.md │ │ │ └── introduction.md │ │ └── index.md │ ├── analysis │ │ ├── continuities.md │ │ ├── funcRvar │ │ │ ├── LebesgueMeasure.md │ │ │ ├── index.md │ │ │ └── sets.md │ │ └── index.md │ ├── geometry │ │ ├── index.md │ │ └── quaternion │ │ │ ├── basics.md │ │ │ ├── index.md │ │ │ ├── interpolation.md │ │ │ └── quaternion.md │ ├── imgs │ │ ├── Intro2SDE │ │ │ ├── 3.3_lemma2_phi.png │ │ │ ├── conditional_expectation_proj.png │ │ │ ├── first-eight-Haar-functions-and-their-integrals.png │ │ │ ├── graph-of-a-haar-function.jpg │ │ │ ├── hw1.gif │ │ │ ├── sample_paths.png │ │ │ ├── stock_trajectory.png │ │ │ └── trajectory.png │ │ ├── ODE │ │ │ └── picard.png │ │ └── quaternion │ │ │ ├── basics-axis-angle-rotation.svg │ │ │ ├── basics-orthogonal-decomposition.svg │ │ │ ├── basics-perp-rotation.svg │ │ │ ├── interpolation-Nlerp-problem.svg │ │ │ ├── interpolation-Slerp-double-cover.svg │ │ │ ├── interpolation-Slerp-triangle.svg │ │ │ ├── interpolation-Slerp.svg │ │ │ ├── interpolation-find-vt.svg │ │ │ ├── interpolation-lerp.svg │ │ │ ├── interpolation-quat-to-vec-rot-1.svg │ │ │ ├── interpolation-quat-to-vec-rot-2.svg │ │ │ ├── quaternion-double-cover-a.svg │ │ │ ├── quaternion-double-cover-b.svg │ │ │ └── quaternion-double-cover-c.svg │ ├── index.md │ └── probability │ │ └── index.md └── readings │ ├── NNbasics │ ├── einsum.md │ ├── index.md │ ├── lstm_gru.md │ └── normalization.md │ ├── diffusion │ ├── DDIM.md │ ├── DDPM.md │ ├── DE-formula.md │ ├── EDM.md │ ├── SGM.md │ ├── guidance.md │ ├── index.md │ ├── mean-flow.md │ ├── rectified-flow.md │ └── v-prediction.md │ ├── imgs │ ├── NNbasics │ │ ├── LSTM3-C-line.png │ │ ├── LSTM3-SimpleRNN.png │ │ ├── LSTM3-chain.png │ │ ├── LSTM3-focus-C.png │ │ ├── LSTM3-focus-f.png │ │ ├── LSTM3-focus-i.png │ │ ├── LSTM3-focus-o.png │ │ ├── LSTM3-gate.png │ │ ├── LSTM3-var-GRU.png │ │ ├── LSTM3-var-peepholes.png │ │ ├── LSTM3-var-tied.png │ │ ├── RNN-unrolled.png │ │ ├── bn_vs_ln.png │ │ └── normalizations.png │ └── diffusion │ │ ├── ddpm-modeling.svg │ │ ├── ddpm-pseudo-code-dark.png │ │ ├── ddpm-pseudo-code-light.png │ │ ├── edm-main-table-dark.png │ │ ├── edm-main-table-light.png │ │ ├── history-guidance-dark.png │ │ ├── history-guidance-light.png │ │ ├── mean-flow-consistency-model-dark.png │ │ ├── mean-flow-consistency-model-light.png │ │ ├── mean-flow-mean-with-t-dark.png │ │ ├── mean-flow-mean-with-t-light.png │ │ ├── mean-flow-overview-dark.png │ │ ├── mean-flow-overview-light.png │ │ ├── v-prediction-visualization-dark.png │ │ ├── v-prediction-visualization-light.png │ │ └── v-prediction-visualization.png │ ├── index.md │ └── miscs │ ├── abbrs.md │ └── metrics.md ├── hooks ├── tikzautomata.py └── utils │ ├── markdown_utils.py │ └── 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