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Photo by Road Trip with Raj on Unsplash

The man who got me into reading books never once told me to read a book. When I was 18, I went to therapy through my college. The therapist I met with was the catalyst who inspired my reading habit, a habit that has since changed my life.

Growing up, I mostly kept my distance from books. You could count on one hand the books I had read in the first 18 years of my life. …


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I believe that a good book changes the way you view something forever. It doesn’t always change your mind, but it changes your view. A great book from any genre does this, from self-help to journalism to fiction. The Steve Jobs biography changes your view of Steve Jobs. A good novel, like Little Fires Everywhere, changes your view of family values, adoption, etc.

In 2020, I finished 40 books. To be honest though, if you read one great book in a year, I think you’re doing well. The exact number does not really matter. One great book that changes something…


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Photo by Steve Johnson on Unsplash

When teaching linear algebra, the concept of a basis is often overlooked. My tutoring students could understand linear independence and span, but they saw the basis how you might see a UFO: confusing and foreign. And that’s not good, because the basis acts as a starting point for much of linear algebra.

We always need a starting point, a foundation to build everything else from. Words cannot be written without the foundation of an alphabet. Ancient civilizations believed the universe was formed from 4 classical elements — water, earth, fire, and air (Long ago…). …


A different take on the meaning of math

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Photo by Andrew Ridley on Unsplash

I can’t believe that teachers don’t tell you this, but math is not the study of numbers. We haven’t been lied to, but it’s like we all collectively forgot what the real point of math is.

At some point in geometry class, you probably had to prove that two triangles were congruent to each other. One way is to show that they have 2 angles and 1 side in common, and then you can conclude that the two triangles are congruent. …


Using the cartography package in R to create plots without a purpose

Your analysis is supposed to reveal something new. It should reveal an insight into a trend, or an abnormal pattern. Employers for data science jobs like to see that your analysis is useful and impactful.

But that’s boring. Instead, we can make graphs that are completely, totally useless, which is what I spent the last couple of hours doing.

The cartography package in R helps you turn your data into eye-catching maps. For example, R comes with a dataset of SIDS death in North Carolina. …


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Photo by Lucas Benjamin on Unsplash

Our eyes see color using only three types of cone cells — which take in red, green, and blue light — and yet from those three types we can see millions of colors. Beyond being a nice, efficient biological feature, this illustrates an important concept in linear algebra: the span. To explain span intuitively, I’ll give you an analogy to painting that I’ve used in linear algebra tutoring sessions.

(This is part two of a three-part series explaining linear algebra concepts using the analogy of painting. The first part is on linear dependence/independence, which you can read here. …


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Photo by Siora Photography on Unsplash

In a linear algebra college course, you get bombarded by definitions. A mini-dictionary of terms with confusing, arcane definitions riddle the textbook, and your typical college student only has a couple of months to understand eigenvalues, eigenvectors, and Hermitian matrices (and of course, more) before their tests.

It’s also discouraging because we are usually not taught intuition in these classes. Instead, we stare at matrices, eventually learning through trial and error how to get the right answers without understanding why we use the methods we use. …


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Photo by Markus Spiske on Unsplash

Even in a global pandemic, math can help us make good decisions.

Nebraska Governor Pete Ricketts announced on March 24th that the state would start ‘pooling’ tests for COVID-19. What that means is that five saliva samples would be combined into one test tube. If the test comes back negative, then you know all 5 patients don’t have COVID-19 and you’re done. If the test comes back positive, all 5 patients are re-tested.

Some people first found out about this idea from an e-mail from Kevin Patrick Mahaffey that appeared on Marginal Revolution, myself included. While many praised this…


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Image from Creative Fabrica

You know, out of all the mind-bending things we like to say to try and get people interested in math (Look! This Mobius strip is an object with only one side), saying that “some infinities are bigger than others” has got to be one of the most popular and also one of the most mind-fucking to people who don’t know what you’re talking about. If you have no idea what I’m talking about either, with “types of infinity” and some being “bigger” than others and all that, I get it. …


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Photo by FuYong Hua on Unsplash

Have you ever felt in your zone? You know, that point where you’re focused beyond belief, time seems to freeze, and your concentration is aimed like a laser towards the task in front of you. The zone shows up mysteriously in all sorts of places: you could have been kayaking through the rapids, or solving a difficult coding problem, or baking hand-made sourdough. Regardless, it felt damn good.

It‘s fantastic when we get in our zone. It’s one of those feelings that we crave. The zone gives us a sense of purpose where our skills are paying off. We want…

Mike Beneschan

Math Tutor | Orange County, CA | If you want to reach out beneschan@gmail.com

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