Math Syntax in Machine Learning

I recently revisited a book I bought when I first delved into Machine Learning - “Mathematics of Machine Learning” by Tivadar Danke. It’s an excellent resource for demystifying the math concepts in machine learning. What sets it apart is its non-traditional approach to math. The author dives right into Linear Algebra and Vectors and I’ve spent about a week on this chapter - a testament not to the complexity but to the depth of the content. In this post, I’ll attempt to explain a concept I came across both to solidify my own understanding and hopefully to show others with similar backgrounds that math isn’t so untouchable.

Here’s a definition I encountered: the space of polynomials with real coefficients. Sounds thrilling, doesn’t it? Bear with me…

\[R[x] = { \sum_{i=0}^{n} p_i x^i : p_i \in \mathbb{R}, n = 0, 1, … }\]

Intimidating, huh? Let’s break it down.

• \(R[x]\) - This represents a set notation. In this case, it means “The set of polynomials in x with real coefficients.”
• \(\sum_{i=0}^{n}\) - The Σ symbol stands for Summation. If you’re into programming, think of it like a For loop. It’s like saying “Summing up each value from i=0 to n.” What exactly is to be summed is the next piece.
• \(p_i x^i\) - This is the core of the expression where $p_i$ is our coefficient and $x^i$ our polynomial. i varies from 0 to n, a hallmark of polynomials. It’s read as “p sub i times x raised to the power of i.”
• \(p_i \in \mathbb{R}\) - The colon translates to “such that”, setting the conditions. The first one means “p sub i is a real number.”
• \(n = 0, 1, …\) - The second condition indicates “n is a non-negative number starting at 0 and increasing indefinitely.”

So, putting it all together (Shane’s version): “The set of polynomials in x with real coefficients is the sum of p sub i times x to the power of i, where p sub i is a real number and n is a non-negative integer that starts at 0 and goes on indefinitely.”

Most of us might not revisit this math stuff and let’s be real, math can be a bit of a drag for many. It’s often just a hurdle in school, right? But diving deeper into math, I’ve found it’s a neat tool for expressing complex ideas succinctly. More fascinating to me is seeing the interconnectedness in everything as I explore various fields. From Math to Psychology, Neuroscience, Computer Science, and beyond - the way these disciplines intertwine and connect us to the natural world is absolutely incredible!