Cantor's Archive (Page 12)

Probability Theory

Maximum Likelihood Estimate

Part 1: How to best fit a Gaussian

Geometry

To 3D and Beyond

How many spatial dimensions do we live in? How many can we directly perceive? Are the two answers the same? If they are different, what effect, if any, do any higher dimensions have on us?

Calculus

The Famous Problem of the Brachistochrone

From Newton’s “Lion Claws” to the Modern Solution

Particle Physics

Capturing the Ghosts of the Universe

70 Billion. That’s how many particles are passing through every square centimetre of your skin each second. This is not a sci-fi novel; the most fundamental laws of the universe conspire to make it so.

Set Theory

When Cantor Taught us to Count

My theory stands as firm as a rock; every arrow directed against it will return quickly to its archer. — Georg Cantor

Chaos Theory

The Chaos of Weather Prediction

Since existence, humans have been trying to predict the weather. Early methods looked to astrology and the lunar phases. Even the Bible contains references to Jesus deciphering local weather patterns!

Logic

The Proposition P is Determinately True… Regardless!

The position of what’s sometimes called semantic realism is that every statement is bivalent as well as being evidence-transcendent.

Puzzle

A Quick Mathematical Puzzle: Calendar Dice

What numbers do they need to contain to display all days of the month?

Probability Theory

A Wager, Rolling Restarts and Euler’s Number

Keep drawing integers from a random number generator (or a customized lottery machine) until you get a number that is smaller than the previous pick.

Statistics

Here’s What a Theft Taught me about Statistics and Probability

A statistics lesson that can help you protect your valuables

Category Theory

Category Theory: The Math Behind Mathematics

Category Theory was initially developed in the 1940’s by Samuel Eilenberg and Saunders Mac Lane as an attempt to create a general language that can be applied to any field of mathematics.