Extreme Engineering Ideas: Mathematics

Who are the problems aimed at?

The intended audience include students for whom the basic curriculum is not feeding their hunger to learn, adults whose background was not primarily mathematics but had an interest in things mathematical, and professionals who want to keep their problem solving and mathematics on the edge.

Guidelines to level of difficulty:

: These problems require nothing more than a logical mind and a willingness to try things out on paper.
: Problems begin to require insights and mathematical tools. For example, geometrical problems may require the use of simple trigonometry, number problems may require knowledge of factoring, etc.
: A good knowledge of school mathematics and/or some aspects of proof will be required.
: A comprehensive knowledge of school mathematics and advanced mathematical tools will be required.

DOWNLOAD PROBLEMS

1 Star

2 Stars

3 Stars

4 Stars

Googol

A googol is the large number 10^100, that is, the digit 1 followed by one hundred zeros:

10,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000

The term was coined in 1938 by 9-year-old Milton Sirotta (1929–1981), nephew of American mathematician Edward Kasner. Kasner popularized the concept in his book Mathematics and the Imagination (1940).

Other names for googol include ten duotrigintillion on the short scale, ten thousand sexdecillionon the long scale, or ten sexdecilliard on the Peletier long scale.

A googol has no particular significance in mathematics, but is useful when comparing with other very large quantities such as the number of subatomic particles in the visible universe or the number of possible chess games. Edward Kasner used it to illustrate the difference between an unimaginably large number and infinity, and in this role it is sometimes used in teaching mathematics.

Googolplex

A googolplex is the number 10^googol, i.e. 10^{(10^100)}. In pure mathematics, the magnitude of a googolplex could be related to other forms of large number notation such as tetration, Knuth's up arrow notation, Steinhaus-Moser notation, or Conway changed arrow notation.