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Cardinal number. Cardinality is defined in terms of bijective functions.

Cardinal number

Two sets have the same cardinality if and only if there is a bijection between them. In the case of finite sets, this agrees with the intuitive notion of size. In the case of infinite sets, the behavior is more complex. A fundamental theorem due to Georg Cantor shows that it is possible for infinite sets to have different cardinalities, and in particular the cardinality of the set of real numbers is greater than the cardinality of the set of natural numbers. Relativistic Baseball. What would happen if you tried to hit a baseball pitched at 90% the speed of light?

Relativistic Baseball

- Ellen McManis Let’s set aside the question of how we got the baseball moving that fast. MathPages. Monte Carlo method. Monte Carlo methods (or Monte Carlo experiments) are a broad class of computational algorithms that rely on repeated random sampling to obtain numerical results; typically one runs simulations many times over in order to obtain the distribution of an unknown probabilistic entity.

Monte Carlo method

They are often used in physical and mathematical problems and are most useful when it is difficult or impossible to obtain a closed-form expression, or infeasible to apply a deterministic algorithm. Monte Carlo methods are mainly used in three distinct problem classes: optimization, numerical integration and generation of draws from a probability distribution. The modern version of the Monte Carlo method was invented in the late 1940s by Stanislaw Ulam, while he was working on nuclear weapons projects at the Los Alamos National Laboratory. Immediately after Ulam's breakthrough, John von Neumann understood its importance and programmed the ENIAC computer to carry out Monte Carlo calculations. Introduction[edit] Moving average. In statistics, a moving average (rolling average or running average) is a calculation to analyze data points by creating a series of averages of different subsets of the full data set.

It is also called a moving mean (MM)[1] or rolling mean and is a type of finite impulse response filter. Variations include: simple, and cumulative, or weighted forms (described below). An Introduction To Fourier Series Representations Of Periodic Signals. An Introduction To Fourier Analysis Introduction The Fourier Series Calculating The Coefficients An Example - Repetitive Pulse Problems You are at: Basic Concepts - System Models - Fourier SeriesClick here to return to the Table of Contents What are you trying to do in this lesson?

An Introduction To Fourier Series Representations Of Periodic Signals

Sage (mathematics software) Sage (previously SAGE, System for Algebra and Geometry Experimentation[3]) is mathematical software with features covering many aspects of mathematics, including algebra, combinatorics, numerical mathematics, number theory, and calculus.

Sage (mathematics software)

The Sage notebook document interface works with most web browsers. Equation solving and typesetting using the Sage notebook web interface Features of Sage include:[5] ROOT. Description[edit] The packages provided by ROOT include those for A key feature of ROOT is a data container called tree, with its substructures branches and leaves.

ROOT

A tree can be seen as a sliding window to the raw data, as stored in a file. Data from the next entry in the file can be retrieved by advancing the index in the tree. This avoids memory allocation problems associated with object creation, and allows the tree to act as a lightweight container while handling buffering invisibly. ROOT is designed for high computing efficiency, as it is required to process data from the Large Hadron Collider's experiments estimated at several petabytes per year. The inclusion of the CINT C++ interpreter makes this package very versatile as it can be used in interactive, scripted and compiled modes in a manner similar to commercial products like MATLAB. Shogun (toolbox) Shogun is a free, open source toolbox written in C++.

Shogun (toolbox)

It offers numerous algorithms and data structures for machine learning problems. Shogun is licensed under the terms of the GNU General Public License version 3 or later. A screenshot taken under Mac OS X Currently Shogun supports the following algorithms: Support vector machinesDimensionality reduction algorithms, such as PCA, Kernel PCA, Locally Linear Embedding, Hessian Locally Linear Embedding, Local Tangent Space Alignment, Linear Local Tangent Space Alignment, Kernel Locally Linear Embedding, Kernel Local Tangent Space Alignment, Multidimensional Scaling, Isomap, Diffusion Maps, Laplacian EigenmapsOnline learning algorithms such as SGD-QN, Vowpal WabbitClustering algorithms: k-means and GMMKernel Ridge Regression, Support Vector RegressionHidden Markov ModelsK-Nearest NeighborsLinear discriminant analysisKernel Perceptrons. lineargaussianpolynomialsigmoid kernels The supported kernels for special data include: S.

Baudline. The baudline time-frequency browser is a signal analysis tool designed for scientific visualization.

Baudline

It runs on several Unix operating systems under the X Window System. Baudline is useful for real-time spectral monitoring, collected signals analysis, generating test signals, making distortion measurements, and playing back audio files. Applications[edit] Features[edit] See also[edit] References[edit] External links[edit] Scilab. Overview[edit] Scilab also includes a free package called Xcos (based on Scicos) for modeling and simulation of explicit and implicit dynamical systems, including both continuous and discrete sub-systems.

Scilab

Xcos is the open source equivalent to Simulink from the MathWorks. As the syntax of Scilab is similar to MATLAB, Scilab includes a source code translator for assisting the conversion of code from MATLAB to Scilab. Scilab is available free of cost under an open source license. Due to the open source nature of the software, some user contributions have been integrated into the main program.

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