Exploring Mathematics and Data Science with Technology

Preface Why Study Mathematics?

It's a common complaint by mathematicians that students aren't interested in mathematics for its own sake. And I (that is, me, the author, hello!) understand this temptation. I got into math because I like to solve puzzles, and who doesn't like puzzles?

But if you're like many of my students, it's not that they don't like puzzles. It's that for them, math has never been about puzzles. Many students have found that success in their math courses boils down to memorizing the formulas and tricks their teacher tells them to. And yeah, that doesn't sound like much fun to me, either.

To address this, this textbook may not be like other textbooks you've used before. Rather than focusing on a lot of formulas, definitions and worked examples, you'll be engaging with several activities designed to get you (ideally with a group of your peers) discovering as much of the mathematics for yourself. It's awesome how much more mathematical results make sense when you know why they work, not because you're told, but because you figured it out for yourself.

This skill is not limited to your math class. In an increasingly cyber-foused world, being able to replicate a skill because someone else told you how to do it is only useful to the point where it cannot be more easily automated by computers. So rather than focusing on “How is this done?”, I encourage you to consider “Why does it work?” and “Why is it useful?” -- often, how it can be accomplished is involved in answering those questions anyway. With that knowledge, either you'll be ready to do the work beyond the scope of automation, or you'll be the one automating the work!

Now this book focuses specifically on using technology for mathematics and data science. Of course, data are all around us. This book may be thought of as a sequence of written words, but it was written on a computer, it can also be thought of as a seqeunce of \(0\)s and \(1\)s on a hard disk. While computers do this kind of serialization of data from one form to another every day, data scientists also have the job of taking information about our world and converting it from one form to another. Their goal is to make that information useful to other humans, so that they can make appropriate decisions based on reality. But this is only effective if their techniques are based on solid mathematical and statistical foundations, and incompetent (or simply evil) actors can paint the wrong picture with their analysis by ignoring these foundations.

As this book was written for the Alabama School of Cyber Technology and Engineering, I will especially emphasize mathematical ideas and tools important for success in cyber technoloyg, engineering, and security. Before earning my PhD in mathematics, I co-owned and operated a cyber technology company offering a CRM ⁴ web application for several years, making us responsible for the PII ⁵ of thousands of users. Through that work and my continuing experience as a developer of open-source software, I have found that the same core techniques of inquiry and problem-solving I use in mathematics translate directly to understanding technology and security concerns.

While you don't need to be a professional mathematician to work in cyber, the cutting-edge techniques of cyber are often rooted in mathematics. For an excellent overview of the connections between cyber security and mathematics, I encourage you to read this article on CyberSecurityGuide.org⁶.

Thank you for reading this brief (?) introduction! And as I tell anyone about to dive into some fun puzzles, happy solving!