From Christoph's Personal Wiki
I took seven courses in calculus and linear algebra while attending university. This subject was, by far, my strongest. This category will contain articles pertaining to the subject of mathematics. I will use this category mainly for my easy reference.
CAS and numerical analysis
- wikipedia:GNU Octave — a free computer program for performing numerical computations which is mostly compatible with MATLAB
- Mathomatic — a free, portable, general purpose computer algebra system (CAS)
Note: Sandbox entry
Al-Khwārizmī's method of solving linear and quadratic equations worked by first reducing the equation to one of six standard forms (where b and c are positive integers)
- squares equal roots (x2 = bx)
- squares equal number (x2 = c)
- roots equal number (bx = c)
- squares and roots equal number (x2 + bx = c)
- squares and number equal roots (x2 + c = bx)
- roots and number equal squares (bx + c = x2)
Cool equations and numbers
- Euler's identity: eiπ + 1 = 0
- Khinchin's constant, K ~2.685252...
- The Euler-Mascheroni Constant, γ ~0.577215...
- The Monster, |M|=808017424794512875886459904961710757005754368000000000
- The Oddest Prime: 2
- Feigenbaum's constant, δ ~4.669201...
- The Golden Ratio, φ 1.618...
- pi ~ 8.88/sqrt(8)
- pi ~ (2.22+2.22)/sqrt(2)
- pi ~ 355/113 ~ 22/7
- pi ~ actual length of rivers from source to mouth and their direct length as the crow flies.
- Barbier's Theorem (see: )
Proof that 0.999... is the same as 1
a = 0.999... 10a = 9.999... 10a - a = 9.999... - 0.999... 9a = 9 a = 1
German tank equation
M = maximum serial number, S = sample size
Latitude/longitude into x,y
addend + augend ---------- = sum
minuend - subtrahend -------------- = difference
multicand * multiplier -------------- = product
dividend / divisor ------------- = quotient
- Vertically and crosswise: 46x72
4 6 | x | 7 2 4x7 4x2+6x7 6x2 15 1 # <- carry 28 50 12 =3312
- Vertically and crosswise: 24x13
2 4 | x | 1 3 2x1 2x3+4x1 4x3 1 1 # <- carry 2 10 12 =312
Wikipedia and its sister project, WikiBooks, have many really good articles on just about everything related to mathematics. I will list some of the best articles (and categories) here:
- WikiBooks - Wikiversity - School of Mathematics
- wikipedia:Table of mathematical symbols
- wikipedia:Octal (see: Online Converter for Decimal/Octal Numerals)
- wikipedia:Lotka-Volterra equation
- MathWorld — by Wolfram Research
- The Wolfram Integrator — by Wolfram Research
- PlanetMath.org — a collaboratively created, virtual community which aims to help make mathematical knowledge more accessible.
- PlanetPhysics.org — a collaboratively created, virtual community which aims to help make physics knowledge more accessible.
- The On-Line Encyclopedia of Integer Sequences (wikipedia)
- Scilab — a scientific software package for numerical computations providing a powerful open computing environment for engineering and scientific applications.
- The Octomatics Project — about a new number system which has a lot of advantages over our old decimal system.
- Pi is Wrong
- Unbiased estimates (stdev)
- Project Euler
- Surfaces and Curves — by Paul Bourke
- why g ~ π2 — about the acceleration due to gravity.
- Number Theory for Programmers, Part 1
- Who needs matrices?