Subject: 5 most critical mathematical concepts

Posted by George Richardson on 12/3/2010
In Reply To:5 most critical mathematical concepts Posted by George Richardson on 12/2/2010

Message:

I left out all ideas related to probability, statistics, and logic. For example,
- Measuring "chance" as the ratio of successes to possible outcomes.

- The fact that sample means tend to cluster around the population mean and thus have a bell-shaped distribution with a particular spread
(That's the Gauss-Markov Theorem, sort of, and the source of the Normal Distribution, which is the foundation of much of parametric statistics.)

- The contrapositive: If p implies q, then not-q implies not-p.
(That's the crucial logic behind all "proofs by contradiction," which get us things like there is an infinite number of primes, or there is an infinite hierarchy of orders of infinity, or "if Congress is being responsible about revenue and expenditures then I'm a monkey's uncle!")

I guess there are more than 10... :-)

...George

Follow Ups:

5 most critical mathematical concepts - Pedro D. Almaguer Prado 12/4/2010 
5 most critical mathematical concepts - Armando Córdova Olivieri 12/5/2010
5 most critical mathematical concepts - Pedro D. Almaguer Prado 12/3/2010