来自 傅皓政 逻辑课程 005
逻辑学 004
来自 傅皓政 逻辑课程 004 语句：由符号组成的序列 命题：符号序列的意义或内容 语词论证：S是M，所有的P都是M，所以S是P 命题论证：如果P，则Q，P，所以Q 命题逻辑语言 命题逻辑的字符集包含下列几个部分： 语句（或命题）符号：\(P, Q, R, \dots\) 连接词：\(\lnot, \land, \lor, \...
Calculus 004
From Zhenyu Qi’ Lecture 004 Some comments on our usage of logic terms Standard logic terms [\forall \varepsilon \in \mathbb{R} \, [\varepsilon > 0 \implies \exists N \in \mathbb{N} \, \forall...
Calculus 003
From Zhenyu Qi’ Lecture 003 Example: If \(a>1\), then \(\lim_{n\to\infty} \dfrac{1}{a^n} = 0\). [\dfrac{1}{(1+(a-1))^n} = \dfrac{1}{(1+b)^n} \le \dfrac{1}{1 + nb}] Ex1 (squeeze theorem): \(\l...
Stochastic Process 15
From Hao Zhang’s Lecture 15 Markov chain [{X_n}_{n=0}^{\infty}, \quad X_k \in S = {x_1, x_2, \dots } \text{ (finite or countably infinite) }] C-K equatoin [\forall m < n, \quad P_{ij}(n) = \...
Markov Chain
From Hao Zhang’s Lecture 13-18 Markov Chain Markov property: We discuss Distrete time, discrete states random process [{X_n}_{n=0}^{\infty}, \quad X_k \in S = {x_1, x_2, \dots } \text{ (finite ...
Stochastic Process 14
From Hao Zhang’s Lecture 14 From last time Markov property: \(A: \text{ past } \quad B: \text{ Now } \quad C: \text{ Future }\) [P(C \vert BA) = P(C \vert B) \iff P(CA \vert B) = P(C \ver...
Stochastic Process 13
From Hao Zhang’s Lecture 13 1 hr 33 min Markov Property We know [\begin{align} &P(X_n=x_n, \dots, X_0=x_0) = P(X_n=x_n \vert X_{n-1}=x_{n-1}, \dots, X_0=x_0) P(X_{n-1}=x_{n-1}, \dots, X_0=x...
Stochastic Process 09
From Hao Zhang’s Lecture 09
Calculus 002
From Zhenyu Qi’ Lecture 002 Upper and Lower Bound Def: Let \(S \subseteq \mathbb{R}\) and \(r \in \mathbb{R}\). We say that (1.1) \(r\) is an upper bound of \(S\) : \(\quad \forall s \in S \, [...