Author Archives: jonathangerhard

About jonathangerhard

I got my BS in mathematics in 2017 from James Madison University and attended a Pure Math PhD program at the University of Michigan as a NSF Graduate Research Fellow until 2020 when I came home to help my nephews with online learning. I started this blog because I love math!

Week 3 – Displaying SageMath Colormaps with Matrix Plots and a New Background

Ok, today is a good day if you like colorful pictures! The goal today is to display the various colormaps that SageMath has to offer. Those colormaps can be called via To demonstrate these colormaps, I want to choose a … Continue reading

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Week 2 – Pictures and Matrices and Pictures

The guiding idea is that a picture is made up of pixels, each holding a color. If we line up every color used, and index them 0,1,2,3,…, then we can turn any picture into a matrix of numbers. Conversely, if … Continue reading

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Week 1 – Visualizing Unimodular Matrices

Something that has interested me recently is that a picture is just a collection of pixels which contain some color information. Which means that every image can just be turned into a matrix of numbers – what happens to our … Continue reading

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Does the bouncing DVD logo ever hit the corner?

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Mathematics and Myself from July 2013

In the process of deciding which things to take with me to Michigan, I came across something really really cool! It was a print-out of an email from July 26, 2013 that I had sent to my mom, asking for … Continue reading

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On a set that detects the convergence of a sum of reciprocals using relative density: A proposal for an indicator set and a proof of its nonexistence.

Natural Density Suppose we take a subset of the natural numbers and look at the sum of the reciprocals of its elements: One question we can ask here is: for which subsets does this sum converge? Though there are many routes … Continue reading

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Integration By Parts Table Method and Strange Sums

Today, I will be writing about calculus. How many of you have heard of the table method for integration by parts? Not many, if my tutees at the Science and Math Learning Center are any indication. If it sounds unfamiliar, then … Continue reading

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The Picture Post

This post will consist almost entirely of pictures of the objects created during the past year while using my Shapeways Education Grant. Check out my summary post for more words… The 3 by 3 Rook’s Graph The 4 by 4 Rook’s Graph … Continue reading

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3D Printing Graphs, Knots, and…Books?

It’s just about at that point where I am hit with nostalgia of the past year and excitement for the coming year. This time around, however, that excitement is accompanied by sadness – I will be graduating from James Madison … Continue reading

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On the Book Embeddings of the Rook’s Graph and the Shrikhande Graph

I’ve already 3D printed one book embedding, which was of , the complete graph on vertices, which looks like this: Just so we’re all on the same page, let me define a book embedding again. An n-page book embedding of a graph … Continue reading

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