数学（理论）分析
- MIT
- Text: Chap-3 Growth of Functions
递归分析
- MIT
- Text: Chap-4 Divide-and-Conquer
主定理
\[\begin{aligned}T(N) & =a\cdot T(N/b)+f(N)=\mathopen{\Theta}\left(N^{\log_{b}a}\right)+\sum_{\nu=0}^{n-1}a^{\nu}\cdot f(N/b^{\nu}),\qquad n\coloneqq\log_{b}N\\ & =\begin{cases} \mathopen{\varTheta}\left(N^{\log_{b}a}\right) & f(N)=\mathopen{O}\left(N^{\log_{b}a}\div N^{\epsilon}\right)\\ \mathopen{\varTheta}\left(N^{\log_{b}a}\cdot(\lg N)^{m+1}\right) & f(N)=\mathopen{\varTheta}\left(N^{\log_{b}a}\cdot(\lg N)^{m}\right)\\ \mathopen{\varTheta}\left(f(N)\right) & f(N)=\mathopen{\varOmega}\left(N^{\log_{b}a}\times N^{\epsilon}\right)\land\exists c\in(0,1)\colon\ a\cdot f(N/b)\le c\cdot f(N) \end{cases} \end{aligned}\]
概率分析
- MIT
- Text: Chap-5 Probabilistic Analysis and Randomized Algorithms
摊还分析
- MIT
- Text: Chap-17 Amortized Analysis
科学（实验）测量
- Observe some feature of the natural world, generally with precise measurements.
- Hypothesize a model that is consistent with the observations.
- Predict events using the hypothesis.
- Verify the predictions by making further observations.
- Validate by repeating until the hypothesis and observations agree.
NP-完备性
- MIT
- Text: Chap-34 NP-Completeness
问题规约
线性规划
- Princeton
- MIT
- Text: Chap-29 Linear Programming
不可解性
