Math symbols Mathematical Thinking- Stanford About instructor Assignment & Quiz The course contents sub documents as below: MTS W8 Quiz MTS W8 Assignment 0 MTS W7 Assignment 0 MTS W6 Assignment 8 MTS W5 Quiz MTS W4 Assignment 0 MTS W3 Assignment 5 MTS W3 Assignment 0 MTS W2 Assignment 4 MTS W2 Assignment 3 MTS W2 Quiz MTS W1 Assignment 2

This is the answer to the questionnaire to Open course Data Scientest Original questionnaire: Data Scientist - [EN] Describe your academic / professional background to date. 5 sentence minimum I majored in E-commerce of 3 years in Wuhan Vocational & Technical College of China. Diploma of Collegial Studies (DCS)/ Post-secondary education / Associate Degree, Vocational Technology Education and Training What were your motivations for applying for this courses? 5 sentence minimum in the past 10+ years, I have been working in the environmental, agriculture and food supply chain sectors for both e-commerce and non profit organizations in Asia, it’s interesting to research the data. ...

¬ [$∃x$A(x)] = $∀x$[¬A(x)] ? ¬ [$∃x$A(x)] if it is not the case that at least a x satisfies A(x), then for all x are not not satisfy A(x), so for all x, ¬A(x) is true. $∀x$[¬A(x)] Prove false There is an even prime bigger than 2 x are parts of natural number set $N$, Prime number P(x), Even number E(x) $∃x$[E(x)P(x)∧(x>2)] ¬ {$∃x$[E(x)P(x)∧(x>2)]} is True $∀x$[E(x)P(x) ⇒ (2≥ x)] ...

Contrapositive 反證 if φ ⇒ ψ , then ¬ψ ⇒ ¬φ $∃x$A(x)] = $∀x$[¬A(x)] ? Assignment 7 Prove or disprove the statement “All birds can fly.” birds b, fly birds are F(b) Assume $∀b$ ⇒ F(b) True. $∃o$, there are some birds, such as ostrich o, it can not fly. $∀b$[$∃o$$(b=o)$ ⇒ ¬F(b)] so not all birds could fly, $∀b$ ⇒ F(b) False. Prove or disprove the claim (∀x, y ∈ R)[(x − y)2 > 0]. Assume (∀x, y ∈ R)[$(x − y)^2$ > 0] is True. ...

Induction: the inference of a general law from particular instances. Axiom/ principle: generally acknowledged truth. to prove $∀n$ A$(n)$ Method, principle of mathematical induction Prove A$(1)$ Dominoes: $∀n$ [ A$(n)$ ⇒ A$(n+1)$] induction step Theorem: for any n, 1+2+3 …… + n = 1/2n(n+1) if n = 1, both side equal to 1, then the identity is true. Assume A$(n)$ and deduce A$(n+1)$, the identity holds for all n 1+2+3 …… + n+1 = 1/2(n+1)[(n+1)+1] ...