Category Archives: Math

Marsaglia’s MWC (multiply with carry) Random Number Generator for Object Pascal

In the past, I’ve tended to use the Mersenne Twister for generating pseudo-random numbers. This is a widely used generator because it has a very long period of 2^{19937} – 1. The one issue is that it’s not the fastest … Continue reading

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A look at the Euler’s number: e

I’ve never particularly liked the way , Euler’s number, is introduced in textbooks. Most approaches give me a very limited intuitive feel for what actually is. Modern textbooks appear to use one of four common ways to introduce e, and … Continue reading

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Plotting 3D graphs using Python and Tellurium

As an example I wanted to show how one could plot a 3D phase plot. A great example to use for this is the Lorenz Attractor. This system is interesting because it displays chaotic behavior. The differential equations for the … Continue reading

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-1 times -1 = +1 ?

My brother asked me the other day why -1 times -1 was +1. It’s the sort of rule we learn at high school and perhaps never think about again. I thought I’d add a note to prove and show why … Continue reading

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Solving ODEs using Mathematica

Solving ODEs using Mathematica I have found that the documentation that comes with Mathematica is not always very helpful. At least it is not very helpful when you want to know the most common operations. One of those is solving … Continue reading

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Useful LaTex Documents

Here are some very useful documents on LaTeX that I have come across over the years: 1. Comprehensive Symbol List The comprehensive symbol list includes 5913 symbols and the corresponding LaTeX command by Scott Pakin 2. Math Mode A highly … Continue reading

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Proportional and Relative Changes

There is an excellent description of the difference between logarithmic and linear scales in the book “Mathematical Analysis for Economists” by R Allen which I describe here. Consider the following two sequences of numbers: 100,  150,  200,  250,    300,     100,  … Continue reading

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