The Road Ahead - Infinity is Really Big

My plans for this blog are ambitious.

My main goal for Infinity is Really Big is to bring you excellence in mathematical content for your personal and professional growth.

YouTube-Related Content

As of the early January 2019, my YouTube channel, “Bill Kinney Math“, is moderately successful. It has over half a million views and over 4400 subscribers. The videos I’ve made are not slickly produced, but I work hard to make the content interesting, detailed, and helpful.

Currently, my most viewed video, with about 30,000 views and a decent 40:1 likes-to-dislikes ratio, is my first lecture of a Real Analysis course I taught at Bethel University in the fall of 2016.

I’ve received many messages from people around the world thanking me for the helpfulness of the videos from this course. I also want to thank you for your complements.

I want to help a broader audience gain knowledge and skills from this course. Therefore, some of my initial posts at Infinity is Really Big will delve into details about the lectures from it.

Another popular topic of videos on my YouTube channel is Financial Mathematics, with an emphasis on helping budding actuaries prepare for “Exam 2” (a.k.a. “Exam FM”). My initial lecture on the topic currently has about 18,000 views and a 100:1 likes-to-dislikes ratio.

Furthermore, I’ve put a lot of time into making shorter problem-solving videos over the past couple years. I solve problems mostly from the ACTEX text “Mathematics of Investment & Credit“, by Samuel A. Broverman. In some of my initial posts I will explore and expand on details related to these videos.

I am on sabbatical during the winter and spring of 2019, so I think I’ll also have time to post on other topics. I’m planning to write posts about mathematical details found in some videos on one of my favorite YouTube channels, 3Blue1Brown. And I’m also hoping to write posts about differential equations, probability, and general problem-solving.

Looking further into the future, I want to continue creating both video content and blog content about calculus (including multivariable), linear algebra, abstract algebra, complex analysis, statistics, and advanced modeling for actuarial science (for example, models of random variables that are present values contingent on future lifetimes).

Mathematica-Related Content

Finally, in much of what I do, I also want to bring the content to life by making it dynamic. I plan to do this by making use of the Wolfram Research program Mathematica. Hopefully, embedded Computable Document Format (CDF) files produced by Mathematica will run in the future (there are difficulties with various browsers in early 2019). But at the moment, it seems we have to be satisfied with movies from the CDF files. Unfortunately, these are not interactive.

For example, the movie below shows the graph of $y =\sin(bx)$ as $b$ increases from 1 to 5. This makes the period of the function decrease from $2\pi$ to $\frac{2\pi}{5}$ . Note: the LaTeX code to generate these mathematical expressions seems to work better in some browsers than in others (Chrome works best for me). You might also try refreshing the page if it doesn’t look right in your browser.

It’s probably better to view this as an animated GIF.

This is just the most basic use of Mathematica‘s dynamic features. There will be much more to come.

For those who are interested, I will often describe and show the Mathematica code that generates dynamic content. In the case of the animations above, the code below generates a static graph of $y=\sin(bx)$ for any fixed value of $b>0$ (you would need to define or plug in the value of $b$ that you want to use.)

Mathematica code to create a static plot for a fixed value of b (you would need to define a particular value of b)

Making this code the input of the dynamic function “Manipulate” in the following way will give an animation as $b$ increases from 1 to 5: