Math is a Language. This is how you should learn it. [Math Mondays]

How to Teach yourself difficult ideas in Math for a strong career in AI, Tech, and Engineering

Jun 14, 2022

Hello hello my lovely reader,

One of the hardest things about building a strong career in any technical domain is that you will inevitably come across the need for Math. No matter how much you try to run from it, Math will eventually hunt you down. Especially when you start working in one of the big firms that operate on massive scales, and have a lot of optimization work to handle. Learning to frame and express your situation the right way is critical. And knowing Math will help with that. So how can you take the best path forward to learning Math better?

Photo by Dan Cristian Pădureț on Unsplash

In this article, I will share how I taught myself the complex Math topics required for advanced fields like Machine Learning and AI research. As someone who taught themselves the complex math required for Machine Learning, without a Master’s Degree or Spending a Ton on Tuition, my approach will be very helpful to all of you that don’t have the time/resources for full-time courses.

The highlights

This post will go over the following ideas-

Math is a language. It helps you express complex abstract ideas in quantifiable ways. Nothing else
Once you understand this, it becomes clear why so many people struggle with Math. They try to learn the topics without learning the context around the topics. Imagine how much you’d struggle with learning a language if you didn’t understand any words/sentence structures.
You have to learn Math the way you learn a language. Start with small “sentences” for specific situations. Branch out and practice till you can express more complex ideas. That’s why practice is so important. Read on for a detailed guide

I hope you’re ready for this one. I am about to share some world-changing truths with you. Try not to be too in awe of my wokeness after this.

Math is a language

Long-term followers of my work will know that I say this a lot. But what does this mean? Let me give you a concrete example. Since I am an AI researcher, I will give you an example from my domain. Let’s talk about how Machine Learning Models are trained. To keep things simple, I will be talking about Supervised Learning, which is relatively intuitive. Let’s say you had a model that would take an array of features to predict the price of a house (a classic ML example).

Here is the basic process. We take a bunch of data that we use to train the model. The training works like this:

Feed your data to the model (without the house price). Have your model predict the house price.
Compare this predicted price to the real price.
Change your model parameters relative to the error of your prediction. Big error → more model changes.
Rinse and repeat till we reach acceptable performance.

If you’re interested in learning about Machine Learning, check out my article on How to Learn Machine Learning here. It is an article that will take you through all the steps required to make you an amazing ML Engineer/Researcher. For my more advanced readers, my Medium, YouTube, LinkedIn, and Twitter contain more ML-heavy content. Make sure you check them out. Links are always shared at the end of the article.

If you’re into AI and ML, connect with me and say hi.

Getting back to the topic, why did I share the details about ML model training? To show off? Maybe. To subtly convince you to look into ML. A bit. But the main reason was a lot simpler. Go back to the ML training. And consider a very important question. What does it mean to be wrong? And how can we quantify how wrong a prediction is? The answer to this changes is based on your exact needs. Take a look at this table, showing some kinds of distances that you might use in Machine Learning.

Distances and Similarity scores should be integrated for serious ML. Source

I’ve actually even worked on projects where I had to invent my own distance metrics. Coming up with the right metric can make or break your performance in Deep Learning.

When you think about it, an error metric is the expression of an idea. It gives us a way to express how “wrong” a prediction is as a number. Math and equations are merely the languages we use to express them. No different from Eminem using English to express his desperation in Lose Yourself.

With that being said, why is Math so hard for so many people?

Why you (or someone you know) suck at Math

The talk I linked hints at this idea, but let me make it explicit. The reason Math is hard is that you study it wrong. We all now know that Math is a language. Have you studied it as such?

Imagine how hard it is for you to understand a language when you don’t know the words/sentence structures. And you have no context surrounding the words used. It’s like trying to grapple a blackbelt with no experience. Trying to beat Cristiano Ronaldo when you’ve never played football.

That changes today. I will now teach you a better way to study Math. How do I know this? I used this exact method to teach myself the complex Math required to excel in Machine Learning. And has worked for the many students I’ve worked with over the years, as they accomplish a lot.

One of my employer’s evaluations of my performance.

How to Self-Study Math Effectively

Without further ado, here is the plan I recommend using to learn complex math ideas-

Understand the context- In my post on how to study DSA, I cover how to learn about a particular DS/A, you first have to understand the problem it solves. The same applies to Math. The first step to learning a principle is to understand why this principle exists. What problem was it created to solve?
Small sentences- I didn’t start off being the best writer in the coding interview space (at least in English). I didn’t even really speak English till I was 6–7 years old. I learnt by reading the signs on posters/billboards/street signs and built up from there. Math is the same way. Immediately attempting to master a concept is foolhardy. First look to learn one single implementation of your concept. One specific problem it solves. Look to understand why this concept solves that problem, and how you frame the givens to solve the problem. Branch out from there.
Practice- Start working on similar problems to the one you covered. Try to see if the idea still applies. See what changes you need to make depending on the context. This will teach you a lot.
Compare and Contrast- As you level up, you will have learned a lot of ideas. Now is the time to really master them. Start comparing related ideas and see why one might be the best for a specific problem. Intentionally test things that you know shouldn’t work and try to understand why they break. This will teach you a lot.
Keep the journey going- The more you learn, the better you will become at this process. It will be awkward at first. However, it will pay off in spades. The versatility you develop will allow you to make epic career gainzzzzzz.
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I use this exact step-by-step to learn about cool/interesting Math ideas. The system is also something that I recommend to all my students. The results speak for themselves.

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Happy Prep. I’ll see you at your dream job.

Go kill all you popular pal,

Devansh <3

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