Portal:Mathematics/Featured

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Featured learning resource

Exercises at Introduction to differentiation lead participants through calculations of compound interest that introduce Euler's number (2.7182818284...) and derivatives of functions.

Selected image

Solutions of the the Bessel differential equation.

Bessel functions arise in many mathematical models such as those for vibrating surfaces.

When mathematically analyzing a vibrating drum the boundary conditions lead to solutions that are harmonic functions. When using cylidrical coordinates, the solutions are sines, cosines or Bessel functions (in the radial direction).

Featured research project

Mersenne primes.

Marin Mersenne's name is widely known because of his interest in prime numbers that are one less than a power of two. Mersenne also did research in the area of the theory of music and musical instruments (see Wikipedia). Participants at Mersenne primes are encouraged to join the distributed computing project that allows the computing power of personal computers to help search for Mersenne prime numbers.

News

Graphical representation of a dynamical system.

"Stephen Smale awarded Wolf Prize in mathematics" by Robert Sanders
Stephen Smale, known for his work on Topology, the study of dynamical systems and a list of 18 problems in mathematics to be solved in the 21st century, known as Smale's problems.

Did you know?

The red curve is a cycloid.

The Euler-Lagrange equation of classical mechanics was discovered during attempts to find a curve for which the time taken by a frictionless particle sliding down it under uniform gravity to its lowest point is independent of its starting point.

Quotes

"A man provided with paper, pencil, and rubber, and subject to strict discipline, is in effect a universal Turing Machine." -Alan Turing

Learning projects

Boolean Algebra - College Algebra - Elementary Logic - Finite Arithmetic - Fourier transforms - Fundamentals of Probability, Statistics, Experiments and Data - Interpolation and Extrapolation - Introduction to differentiation - Introduction to Simple Substitution Cypher - Introduction to Likelihood Theory - Introduction to Limits - Limits - Partial derivative - Simple addition flashcards - Study guide:Lie algebra - Synthetic division - The Special Cubic Formula - Vectors - 3D Geometric Algebra and Special Relativity