03-012: How to Study and Understand Complex Topics

When I was younger, I used to struggle with learning new or difficult subjects. Through the years, and about a decade of university and grad school, I’ve developed a strategy for how to study and understand complex topics. Typically, I apply this learning system to subjects such as algorithms and software engineering, but it can be applied to any topic.

While there are a near-infinite set of study strategies out there, I like this approach because it utilizes a divide and conquer strategy, focusing on breaking a complex topic into easy-to-understand components and then putting the pieces back together at the end to see how they all work together.


System for How to Study

Let’s take a case study example: Understanding how logarithms work. Logarithms are used throughout the fields of mathematics and computer science. However, unless you use them regularly, it’s easy to get rusty on them.


Step 1: Start with the Core Concept

The first task that I will do is take a piece of paper and write Logarithm in the center and circle it.


Step 2: Break Down the Components

Next, I’ll go to a comprehensive post on the topic, such as one on Wikipedia. In reading the first sentence, I come across a few terms that are a bit fuzzy:

I will stop reading the logarithm article and go and read those two articles until I feel comfortable with what they represent. After I feel good about those two items, I write them as their own circles that connect to the Logarithm circle. I will also add any examples that will help me understand what the terms mean if necessary.


Step 3: Build a Mind Map

Next, I’ll go back to the original Logarithm post and keep going through the article, repeating this process until the entire page is filled with a mind map that explains each component that makes up logarithms and how they work together. This may include base case examples, such as:

64 = 2^6 is the same as log₂(64) = 6

Why This Approach Works

If this seems like a dead-simple approach to studying… it is. The goal of studying is to learn a topic, and one of the easiest ways to understand a complex subject is to break it into easy-to-comprehend components.

For example, if you’re trying to understand an advanced algorithm in computer science from scratch, you may feel a little intimidated. However, if you break the algorithm down into small enough components, you’ll see that it’s essentially a process of steps made up of connecting simple modules such as:

A problem is only hard when you try to think of it as a whole. However, any concept can be understood if you simplify it down to easy-to-comprehend pieces. Obviously, the more complex the topic, the longer it will take to deconstruct. However, I am a firm believer that anyone can understand any topic, assuming they dedicate themselves and put the work in.


Final Thoughts

I hope that you can leverage this mind mapping process to understand complex topics and that it will help you learn how to study properly and truly learn.

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