Blog - Math

🖥️ 📐 “Fractals in Code: Exploring the Mandelbrot Set with Python”
In the 1990s, I was a young Gen Xer. Pearl Jam filled the air with "Jeremy." The X-Files convinced us the truth was out there. Fractals were everywhere you looked. You saw them on posters, TV, screensavers, and in the latest Star Trek movie.
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📐 🖥️ "Sklearn Linear Regression: A Complete Guide with Examples"
Linear regression is a fundamental technique in statistics and machine learning that helps model the relationship between variables. In simple terms, it allows us to predict an outcome based on one or more influencing factors. It is widely applied in real estate pricing, sales forecasting, risk assessment, and many other fields.

In this tutorial, we'll explore linear regression in scikit-learn, covering how it works, why it's useful, and how to implement it using scikit-learn. By the end, you'll be able to build and evaluate a linear regression model to make data-driven predictions.
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🖥️ 📐 “Exploring Julia Sets with Python”
In the 1990s, I was a young Gen Xer, Nirvana smelled like teen spirit, OJ Simpson pervaded the news, Seinfeld was the hottest thing on TV, and fractals were everywhere in the popular imagination — on posters, on TV, in the mountains of the latest Star Trek movie, on aspiring programmers' computer screens...
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📐 “Fractals, A Very Short Introduction - Book Review”
Years ago, I had the opportunity to meet Benoit Mandelbrot, the “Father of Fractals”, at a mathematics conference. He was a towering figure in fractal geometry, surrounded by enthusiastic students eager to speak with him. I asked him to sign my copy of The Fractal Geometry of Nature, which now holds a proud place on my bookshelf. Recently, while browsing my local library, I came across a tiny volume called Fractals: A Very Short Introduction. I picked it up on a whim and read through it in a couple of days...
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📐 "On the lower central series of the free nilpotent groups of finite rank" (Research Article based on my dissertation - Communications in Algebra, with my dissertation advistor, Russell Blyth)
In their article, “On the derived subgroup of the free nilpotent groups of finite rank” R. D. Blyth, P. Moravec, and R. F. Morse describe the structure of the derived subgroup of a free nilpotent group of finite rank n as a direct product of a nonabelian group and a free abelian group, each with a minimal generating set of cardinality that is a given function of n. They apply this result to computing the nonabelian tensor squares of the free nilpotent groups of finite rank. We generalize their main result to investigate the structure of the other terms of the lower central series of a free nilpotent group of finite rank, each again described as a direct product of a nonabelian group and a free abelian group. In order to compute the ranks of the free abelian components and the size of minimal generating sets for the nonabelian components we introduce what we call weight partitions...
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📐 "The Unreasonable Effectiveness of Mathematics in the Natural Sciences"
I recently started a job in which I, trained as a mathematician, am working with a number of colleagues who were trained as physicists. At lunch, this situation led to a discussion of the connections between the two fields, which in turn led to a discussion of Eugene Wigner’s article “The Unreasonable Effectiveness of Mathematics in the Natural Sciences.” I reluctantly admitted that although I had heard and read about the article, and thought I understood its general gist, I had never taken the time to read and digest the article for myself. To remedy this sad state of affairs I decided to carefully read it and provide a summary to increase my understanding of the article. I hope that you, the reader, find it helpful as well...
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