Mathematics

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The history of every major galactic civilization tends to pass through three distinct and recognizable phases, those of Survival, Inquiry and Sophistication, otherwise known as the How, Why, and Where phases. For instance, the first phase is characterized by the question ‘How can we eat?’, the second by the question ‘Why do we eat?’

There’s more to mathematics than rigour and proofs

http://terrytao.wordpress.com/career-advice/there%e2%80%99s-more-to-mathematics-than-rigour-and-proofs/

A map of the Tricki | Tricki

http://www.tricki.org/tricki/map This is an attempt to give a quick guide to the top few levels of the Tricki. It may cease to be feasible when the Tricki gets bigger, but we might perhaps be able to automate additions to it. Clicking on arrows just to the right of the name of an article reveals its subarticles. If you want to hide the subarticles again, then you should click to the right of them rather than clicking on the name of one of the subarticles themselves, since otherwise you will follow a link to that subarticle. What kind of problem am I trying to solve?
Mathematics

prime numbers

Mathematics

Specifications for ACME Klein Bottles

http://www.kleinbottle.com/specs_for_nice_klein_bottles.htm#Dont%20Freeze Specifications for ACME Klein Bottles No two Acme Klein Bottles are alike! Since Acme glassblowers individually hand craft each one, dimensions will vary and you may find occasional bubbles or streaks in the glass. These prove that your Acme Klein Bottle was made by real, 3-dimensional humans, adding to its unique status in a world of identical, machine made commodities. WARNING! Acme constructs each Klein Bottle from genuine Baryonic matter.
computer science

Penrose Tiles

Time complexity

In computer science , the time complexity of an algorithm quantifies the amount of time taken by an algorithm to run as a function of the length of the string representing the input [ 1 ] :226 . The time complexity of an algorithm is commonly expressed using big O notation , which excludes coefficients and lower order terms. https://en.wikipedia.org/wiki/Time_complexity#Polynomial_time

P versus NP problem

Diagram of complexity classes provided that P ≠ NP . https://en.wikipedia.org/wiki/P_versus_NP_problem

Computational complexity theory

https://en.wikipedia.org/wiki/Computational_complexity_theory Computational complexity theory is a branch of the theory of computation in theoretical computer science and mathematics that focuses on classifying computational problems according to their inherent difficulty, and relating those classes to each other.
http://www.archimedes-lab.org/pzm52b.html The problem states that any investment at r -percent interest per annum will be doubled in approximately years. a) Using simple compound interests Since the initial principal is to be doubled we have the equation ( formula for compound interests): 2 = (1 + r/100) n Taking the log of both sides: log 2 = n · log(1 + r /100) or n = log 2 / [log(100 + r ) - 2] Next we seek to find a number, x, such that when divided by r , the result is approximately n . Thus x / r = log 2 / [log(100 + r ) - 2] Then x ~ 0.301 r / [log(100 + r ) - 2]

Previous monthly puzzles: May 2004

http://richardphillips.org.uk/number/

Numbers: Facts, Figures & Fiction

Click on cover for larger image Numbers: Facts, Figures & Fiction by Richard Phillips. Published by Badsey Publications . See sample pages: 24, 82, 103. Order the book direct from Badsey Publications price £12.

Primality Proving 2.1: Finding very small primes

For finding all the small primes, say all those less than 10,000,000,000; one of the most efficient ways is by using the Sieve of Eratosthenes (ca 240 BC): Make a list of all the integers less than or equal to n (greater than one) and strike out the multiples of all primes less than or equal to the square root of n , then the numbers that are left are the primes. (See also our glossary page .) For example, to find all the odd primes less than or equal to 100 we first list the odd numbers from 3 to 100 (why even list the evens?) The first number is 3 so it is the first odd prime--cross out all of its multiples. http://primes.utm.edu/prove/prove2_1.html
People who know a lot about a lot have long been an exclusive club, but now they are an endangered species. Edward Carr tracks some down ... From INTELLIGENT LIFE Magazine, Autumn 2009 CARL DJERASSI can remember the moment when he became a writer. It was 1993, he was a professor of chemistry at Stanford University in California and he had already written books about science and about his life as one of the inventors of the Pill. Now he wanted to write a literary novel about writers’ insecurities, with a central character loosely modelled on Norman Mailer, Philip Roth and Gore Vidal.

THE LAST DAYS OF THE POLYMATH

http://moreintelligentlife.com/content/edward-carr/last-days-polymath
Probability

An Introduction to Wavelets: What Do Some Wavelets Look Like?

W hat do S ome W avelets L ook L ike? Wavelet transforms comprise an infinite set. The different wavelet families make different trade-offs between how compactly the basis functions are localized in space and how smooth they are.

Table of mathematical symbols

This is a list of symbols found within all branches of mathematics to express a formula or to replace a constant . When reading the list, it is important to recognize that a mathematical concept is independent of the symbol chosen to represent it. For many of the symbols below, the symbol is usually synonymous with the corresponding concept (ultimately an arbitrary choice made as a result of the cumulative history of mathematics), but in some situations a different convention may be used. For example, depending on context, "≡" may represent congruence or a definition. Further, in mathematical logic, numerical equality is sometimes represented by "≡" instead of "=", with the latter representing equality of well-formed formulas . In short, convention dictates the meaning.

Power law

An example power law graph, being used to demonstrate ranking of popularity. To the right is the long tail , and to the left are the few that dominate (also known as the 80–20 rule ). A power law is a type of probability distribution : if the frequency (with which an event occurs) varies as a power of some attribute of that event (e.g. its size), the frequency is said to follow a power law. For instance, the number of cities having a certain population size is found to vary as a power of the size of the population, and hence follows a power law. Empirically this relationship will hold only approximately (in the limit), not strictly. Mathematically, a strict power law is a probability distribution that is a truncated monomial :