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Markov chains - how to translate mathematically the fact that the state at $n+1$ only depends on the state at $n$?

I'll answer this question because the given scenario is really about a curious student having a misconception about Markov chains. You can't "prove" that in a Markov chain, the state $n+1$ ...
Justin Skycak's user avatar
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Importance of complex numbers knowledge in real roots

Indeed, a general cubic equations $ax^3+bx^2+cx+d=0$ can be transformed to a depressed cubic equation $x^3 - 3px - 2q = 0$ and it can be stated as $x = \root3\of{q+ \sqrt{q^2 - p^3}}+ \root3\of{q-\...
athos's user avatar
  • 737
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Why do we teach complex numbers?

Why do we teach complex numbers? because $\mathbb{C}$ is in some sense inevitable, naturally inevitable even, and it's also where the magic happens... the usual way to see the 'progression' of the ...
ac15's user avatar
  • 497
2 votes

What female mathematician can I introduce to my High School students?

Eugenia Cheng is an important researcher in category theory, and she has published two very good books on popularisation of mathematics with a special touch of 'categorical thinking' - "Cakes, ...
ac15's user avatar
  • 497
1 vote

Math textbook for secondary school using Logo like syntax

I don't know much about math textbooks, but turtle logo is still around from the Python Foundation. Python is often used as a first language because it allows students to start programming with ...
Ben I.'s user avatar
  • 361
3 votes

How to prove, without the LOTUS formula, to student that $V[aX+b]= a^2 V[X]$?

Do it in two easy steps: Prove that $V[X+b]=V[X]$. This one is easy to prove since variance is a measure of deviation from the mean, hence change of origin will not affect it. Mathematically, $ E({X+...
whoisit's user avatar
  • 131

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