10/12/2015

[轉載] How to Study Math? -Paul R. Halmos



Don't just read it; fight it! Ask your own questions, look for your own examples, discover your own proofs. Is the hypothesis necessary? Is the converse true? What happens in the classical special case? What about the degenerate cases? Where does the proof use the hypothesis?


--- Paul R. Halmos

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[最佳化] C^2 函數一階逼近的餘項積分表示

令 $f: \mathbb{R}^m \to \mathbb{R}$ 為 $C^2$-函數。對 $f$ 在 $y$ 附近使用一階泰勒展開: \[ T_y(x) := f(y) + \nabla f(y)^\top (x - y) \] 則其餘項 $R(x,y)$ 訂為 $$R(...