## Mathpy 0.3.0 Released!

I am excited to announce the release of mathpy 0.3.0! This release adds a ton of Excel UDFs including many new statistical and number-theoretic functions, several random number generators and functions for drawing random samples from continuous and discrete probability distributions, and more! More information can be found on the...

## Combined Linear Congruential Generators with R

Combined linear congruential generators, as the name implies, are a type of PRNG (pseudorandom number generator) that combine two or more LCGs (linear congruential generators). The combination of two or more LCGs into one random number generator can result in a marked increase in the period length of the generator...

## Multiplicative Congruential Generators in R

Multiplicative congruential generators, also known as Lehmer random number generators, is a type of linear congruential generator for generating pseudorandom numbers in $U(0, 1)$. The multiplicative congruential generator, often abbreviated as MLCG or MCG, is defined as a recurrence relation similar to the LCG with $c = 0$. [latex display="true"]\large{X_{i+1} =...

## Mathpy 0.2.0 Released!

My Python library, mathpy, a collection of mathematical and statistical functions with Excel integration, has a new release! Version 0.2.0 introduces a ton of additional mathematical and statistical functions have been added in this release along with a large effort centered on documentation and testing. Installing the package is easily accomplished...

## Linear Congruential Generator in R

A Linear congruential generator (LCG) is a class of pseudorandom number generator (PRNG) algorithms used for generating sequences of random-like numbers. The generation of random numbers plays a large role in many applications ranging from cryptography to Monte Carlo methods. Linear congruential generators are one of the oldest and most...

## Simpson’s Rule for Approximating Definite Integrals in R

Simpson’s rule is another closed Newton-Cotes formula for approximating integrals over an interval with equally spaced nodes. Unlike the trapezoidal rule, which employs straight lines to approximate a definite integral, Simpson’s rule uses the third Lagrange polynomial, $P_3(x)$ to approximate the definite integral and as such can give exact results...

## The Trapezoidal Rule of Numerical Integration in R

The Trapezoidal Rule is another of Closed Newton-Cotes formulas for approximating the definite integral of a function. The trapezoidal rule is so named due to the area approximated under the integral $\int^a_b f(x) \space dx$ representing a trapezoid. Although there exist much more accurate quadrature methods, the trapezoidal rule converges...

## Numerical Differentiation with Finite Differences in R

Numerical differentiation is a method of approximating the derivative of a function $f$ at particular value $x$. Often, particularly in physics and engineering, a function may be too complicated to merit the work necessary to find the exact derivative, or the function itself is unknown, and all that is available...

## Divided Differences Method of Polynomial Interpolation

The divided differences method is a numerical procedure for interpolating a polynomial given a set of points. Unlike Neville’s method, which is used to approximate the value of an interpolating polynomial at a given point, the divided differences method constructs the interpolating polynomial in Newton form. Consider a table of values...

## Neville’s Method of Polynomial Interpolation

Neville’s method evaluates a polynomial that passes through a given set of $x$ and $y$ points for a particular $x$ value using the Newton polynomial form. Neville’s method is similar to a now-defunct procedure named Aitken’s algorithm and is based on the divided differences recursion relation (“Neville’s Algorithm”, n.d). It was...