It’s hard to understand anything from just one example. One of the reason for studying other planets is that it…
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Fundamental theorem of calculus generalized
The first fundamental theorem of calculus says that integration undoes differentiation. The second fundamental theorem of calculus says that differentiation…
Continue ReadingDevelop an Intuition for Bayes Theorem With Worked Examples
Last Updated on December 9, 2019Bayes Theorem provides a principled way for calculating a conditional probability. It is a deceptively…
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Take a calculator and enter any number. Then press the cosine key over and over. Eventually the numbers will stop…
Continue ReadingStone-Weierstrass on a disk
A couple weeks ago I wrote about a sort of paradox, that Weierstrass’ approximation theorem could seem to contradict Morera’s…
Continue ReadingLebesgue’s proof of Weierstrass’ theorem
A couple weeks ago I wrote about the Weierstrass approximation theorem, the theorem that says every continuous function on a…
Continue ReadingFame, difficulty, and usefulness
Pierre Fermat is best known for two theorems, dubbed his “last” theorem and his “little” theorem. His last theorem is…
Continue ReadingAn Introduction to the Powerful Bayes’ Theorem for Data Science Professionals
Source: i. ytimg. com Let E denote the event that a red ball is chosen and A, B, and C…
Continue ReadingStatistics 101: Introduction to the Central Limit Theorem (with implementation in R)
Let’s look at an alternate approach. First, draw groups of students at random from the class. We will call this…
Continue ReadingIn Favor of Monotony in a Complex World
In Favor of Monotony in a Complex WorldDaily WisdomBlockedUnblockFollowFollowingApr 3Coordination seems to be a magical word for today’s digital age as…
Continue ReadingTowards a simple theorem prover
Why can’t it be simplified?Note: I also noticed a different problem with Cedille-Core, which may make it incompatible with the…
Continue ReadingKepler and the contraction mapping theorem
We’ll make this statement more precise and give a historically important application.Definitions and theoremA function f on a metric space…
Continue ReadingThe naive Bayes classifier
In this case, what is the probability Y belongs to a distinct class k given an observation x?πₖ is the…
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