“very prime has a succinct certificate”

\begin{equation} \text{PRIMES} : \qty {A \mid A\text{ is prime}} \end{equation}

The certificate?

\begin{equation} A \text{ prime} \Leftrightarrow \exists 1 < b < A : B, B^{2}, \dots, B^{A*2} \not \cong \ \text{mod}\ A \end{equation}

So \(\text{PRIMES} \in \text{NP}\)

But actually PRIMES is in \(P\)

The principle of induction is a technique used to prove the relationship between a smaller subset

The following three statements are equivalent.

standard induction

Suppose \(S \subset \mathbb{N}\), which is non-empty. If \(S\) is a non-empty subset such that \(0 \in S\), and for all \(n \in \mathbb{N}\), \(n \in S \implies n+1 \in S\). Then, \(S = \mathbb{N}\).

strong induction

Suppose \(S \subset \mathbb{N}\), which is non-empty. If \(S\) is a non-empty subset such that \(0 \in S\), and for all \(n \in \mathbb{N}\), \(\{0, \dots, n\} \in S \implies n+1 \in S\). Then, \(S = \mathbb{N}\).

printf("text %s\n", formatting, text, here);

• %s (string)
• %d (integer)
• %f (double)

“privacy as an individual right”

• privacy is a control of information: controlling our private information shared with others
  • free choice with alternatives and informed understanding of what’s offered
  • control over personal data collection and aggregation
• privacy as autonomy: your agency to decide for what’s valuable
  • autonomy over our own lives, and our ability to lead them
  • do you have agency?

“privacy as a social group”

• privacy as social good: social life would be severely compromised without privacy
  • privacy allows social
• privacy as a display of trust: privacy enables trusting relationships
  • “fiduciary”: proxy between you and a company
  • “should anyone who has access to personal info have a fiduciary responsibility?”

key trust questions

• who/what do we trust?
• what do we do if trust isn’t upheald?
• how to approach building trust

trust

trust: to stop questioning the responsibility of something

Remember Bayes Rule in Baysian Parameter Learning:

\begin{equation} P\qty(\theta | D) = \frac{P\qty(D | \theta) p \qty(\theta)}{\int_{\theta}P\qty(D | \theta) p \qty(\theta) \dd{\theta}} \end{equation}

we can’t actually easily compute the bottom without taking an analytic integral; instead we can sample from it.

If you want analytical form, you should hope that your likelihood function is a conjugate prior which allows us to analytically update prirors.