Summer of Math Exposition 2
Jeff Suliga
I have permission from Grant to use the header Pi gif
Hello! For this year’s SoME I’ve decided to make the website you’re currently on! This website marks the realization of a long-standing goal of mine, to make an online portforlio as an extension of my resume in order to place more info about me and educational content that I can point friends and future employers to. As it stands there are only a few points of interest here currently, but I have some more ideas of things to add in the future (post ideas, formal research, recruiter landing page).
If you look at the Home Page you’ll notice that I’m currently an undergraduate student at Virginia Tech, and a quick poke around the website will show you I am a long-time consumer of online educational content (3b1b of course, among many others as well). At the start of the summer, I had no experience with website design and zero knowledge of how HTML works, but with lots of online research, some help early on by my friend Jamie Simon, and a ton of trial and error, I’ve been able to learn some of the basics and produce something I’m really proud of. Github Pages is a great place to start for someone like me, I began with a pre-designed website template and over time rebuilt most of it according to my vision for the page.
While there aren’t many places to look, there’s a lot to do while you’re here. My hope is that while you look around the website’s pages you’ll be able to feel the personality behind the pages and the pursuit of discovery that I hope to lead a visitor down, present not only in the posts and puzzles, but in the site itself (hint hint). Definitely feel free to look in the repository for this page, located in the footer, to see the inner structure of how this page came to be.
I hope you find yourself looking through some of the Puzzles that I’ve enjoying putting together, but for the more math expository work that I would have as a submission to this contest, I would point you to the Posts section, where I’ve placed some of my math explanatory content ideas. The links to these specific posts can be found below.
If I had to choose any of my posts as a single submission, it would be this one. The visuals aren’t as stimulating as the other posts, and perhaps there’s less to be explained in this post compared to the others, but it approaches an idea that I first discovered in the third grade. In turn it is very accessible to anyone curious, regardless of their mathematical background. I tried to make this post such that there was some piece of content to be learned that was accessible to all levels.
A post on Palindromes arising from multiplication of ones which first explores the pattern of \(11 \times 11 = 121\) and \(111 \times 111 = 12321\), and then goes up to the more abstract level of number systems. While I was creating this post I thought of another problem along a similar vein that I explored and added my conclusions as an addendum to the post. This portion was the most fun for me because it led me on a trail of discovery and learning in the realm of number theory, which I have no prior experience with. (I would also appreciate any input/ideas you have on the discussion in the addendum, I really feel like I’m just barely scratching the surface of bigger things here)
Target Audience (Main Post): Anyone
Target Audience (Addendum): Experience with number systems
A post on Complex Numbers and the interesting way they multiply was my first math explainer that I’ve published. Complex numbers have always been fascinating to me (and the main topic of my upcoming research opportunity this fall semester), but I’ve never had much formal education on the topic, apart from my algebra classes in grade school. Everything I’ve learned about the subject has been through online resources and self-discovery.
I also include some interesting extra challenge problems at the end of this post that I think are really solidifying for someone new to the ideas mentioned, and are fun puzzles to those with prior experience on the subject. I’ve included my approach to each of these problems as well.
Target Audience: Experience with algebra on real numbers
A post on Factoring Quadratics Visually. In my experience and in talking with people about their educational math background, it seems many topics found in earlier maths classes are taught in a way that loses touch with a piece of intuition that could have otherwise made the topic more easy for students to learn and more enjoyable to learn, and hence more engaging. This is what I believe to be one of the root causes of students either believing they are inherently “bad at math,” or coming to the conclusion that they don’t like the science as a whole.
This post was originally a presentation I put together for one of my classes, and it addresses a topic that is among the worst offenders of being taught in a manner that doesn’t give the intuition justice - factoring quadratic polynomials. We’ve probably all seen the quadratic formula before, but few may have the intuition to reason through where it comes from. This video presentation guides a student through the building blocks of factoring polynomials in a visual way, all the while building up to the final challenge of the quadratic formula, which can be used to factor any quadratic polynomial. Instead of giving students the weapon to defeat a problem, I supply the tools required to build it.
Target Audience: Experience with basic algebra
A post on Stars making acute triangles in the sky was one I really enjoyed putting together, as it was an idea I first had when lying in the sand looking up at the sky. This particular problem is strange, and while I can’t fully wrap my head around some of the ideas mentioned in this video, I think a sufficient knowledge of that content might be enough to bring to the surface some flaws in my reasoning through my solution to the problem I posed in this post. It has to do with probabilities when infinity is involved, and my 17 year-old mind 3 years ago didn’t know to be cautious when thinking through such things. I’ve had arguments for and against this claim I’ll make in the post, but I think the reasoning alone and the thought process is stimulating enough for me to feel comfortable leaving the post up on my page. Whether or not the claim is true, I believe there is sufficient space for someone to learn a new way to view problems more visually.
Target Audience: Anyone with spatial curiosity
Thank you for taking the time to look through this piece of work that I have greatly enjoyed having as a summer project. This is something that I’m really happy to submit to the competition, but will continue to be a project of mine moving forward, where I will be regularly updating and adding to. I hope you enjoy your stay and don’t hesitate to contact me if you would like to connect. But for now,
\(\blacksquare\)