Www.dpmms.cam.ac.uk/~wtg10/2cultures.pdf. PS_cache/math/pdf/9404/9404236v1.pdf. There’s more to mathematics than rigour and proofs. 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?’ (1) What is it like to have an understanding of very advanced mathematics. Www.math.ualberta.ca/~mss/misc/A Mathematician's Apology.pdf. A map of the Tricki. This is an attempt to give a quick guide to the top few levels of the Tricki.
Mathematics. Acme Klein Bottle. Specifications for ACME Klein Bottles. 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. Computer science.
Penrose Tiles. Google Ngram Viewer. Time complexity. Time complexity is commonly estimated by counting the number of elementary operations performed by the algorithm, where an elementary operation takes a fixed amount of time to perform.
P versus NP problem. Diagram of complexity classes provided that P≠NP.
The existence of problems within NP but outside both P and NP-complete, under that assumption, was established by Ladner's theorem. The P versus NP problem is a major unsolved problem in computer science. Informally, it asks whether every problem whose solution can be quickly verified by a computer can also be quickly solved by a computer. It was essentially first mentioned in a 1956 letter written by Kurt Gödel to John von Neumann. 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.
A computational problem is understood to be a task that is in principle amenable to being solved by a computer, which is equivalent to stating that the problem may be solved by mechanical application of mathematical steps, such as an algorithm. A problem is regarded as inherently difficult if its solution requires significant resources, whatever the algorithm used. The theory formalizes this intuition, by introducing mathematical models of computation to study these problems and quantifying the amount of resources needed to solve them, such as time and storage. Closely related fields in theoretical computer science are analysis of algorithms and computability theory. Computational problems Previous monthly puzzles: May 2004. 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 ~ 0.301r / [log(100 + r) - 2] Nowadays interest rates are comprised between: 0.5 <= r <= 7 Selecting a mid-range value r = 3, we find for x x ~ 0.301 · 3 / (log103 - 2) ~ 70.35. Previous monthly puzzles: June-July 2004. 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?) Prime number checker. THE LAST DAYS OF THE POLYMATH. 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. His wife, Diane Middlebrook, thought it was a ridiculous idea.
An Introduction to Wavelets: What Do Some Wavelets Look Like? W hat do S ome W avelets L ook L ike? Table of mathematical symbols. 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, the triple bar "≡" 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. Each symbol is shown both in HTML, whose display depends on the browser's access to an appropriate font installed on the particular device, and in TeX, as an image. Guide 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). In statistics, a power law is a functional relationship between two quantities, where one quantity varies as a power of another. For instance, the number of cities having a certain population size is found to vary as a power of the size of the population.
Empirical power-law distributions hold only approximately or over a limited range. §Empirical examples of power laws §Properties of power laws §Scale invariance