If you could understand plain English and have access to the Internet, then you can definitely study Math on your own.
After you implement everything in this guide, you’ll learn that there’s no one who can teach you faster and better than yourself. (Especially if you use Anki!)
Just a bit of a warning, though: while I said anybody can do this, I’m 100% sure not everybody will.
It’s a bit uncomfortable, actually, especially if it’s your first time doing this. (But super rewarding.)
In this post, you will learn exactly the 9-step approach I used to teach myself Mathematics without relying on someone to teach me.
- The #1 mindset many overlook when studying Math on their own
- The best resources for self-learning Math
- How to take your Math skills to the next level
Let’s get started.
Can you really self-study Math?
First of all, if you think you’re not a “Math person” (what the heck does a Math person look like, anyway) you might think that you’d need someone else to teach you Math in a classroom.
But let me tell you this…
With all the available stuff for free online — lectures, syllabi, ebooks, and MOOCS — you can certainly self-study Math pretty easily as if you were in college.
The best part is, you do it at your own pace.
No strict schedules, just self-commitment.
However, you gotta think differently about this if you want to reap the rewards.
That is, to recognize that the mental effort you spend practicing a Math topic is the price you pay for making future Math skills easier.
Or more appropriately, it’s the price you pay so you won’t make learning hard for your future self.
Mathematics is all about cumulative knowledge, you know.
Unlike school, you’re going to feel like crap because you’re not changing topics with respect to time — you’re now changing topics based on how fast you master a skill.
So here’s a guide on how you can do that.
9 Steps to Studying Math on Your Own
I’m going to interrupt you for a bit to make something clear: I created this guide to help people who feel like they’re lagging with their Math skills and want to review it, or people who just want to study Math on their own for some reason.
Each example that I’ll give you is just that–a mere example to help you get the point I’m trying to make. It’s still up to you to apply these steps to your own situation.
Step 1. First, determine where you want to end up
Math builds upon itself, so if you want to learn a subject, say, Calculus, always ask:
What subjects are the prerequisites of this subject?
In my own study, I often ask myself a “skill” based question, rather than a topical one.
“What skills do I have to learn to get better at this one?”
Problem Solving is a skill, after all. You can’t get better at problem-solving if you don’t have the tools; the individual mastery of prerequisite topics.
Which brings me to my next point.
Step 2. Determine where to start, obviously
Now that you have determined your end subject, it’s now time to decide which general topic to start with.
For example, Calculus and its applications are easier if you have the knowledge of Analytic Geometry and Trigonometry.
But Analytic Geometry has some Trigonometry elements included.
So, you can decide to start with Trigonometry.
However, if you don’t have the knowledge of “which is the prerequisite of which” I highly recommend that you find an online curriculum.
Here’s one good roadmap for someone who’s learning Math for Data Science.
Step 3. Find a Syllabus to Avoid Unnecessary Depth
If you’re lost, you go to Google Maps.
So what do you do when you don’t have a roadmap or a sequence to learn Math?
Use an already-designed Syllabus. They’ll be the roadmap to your self-studying success.
As I’ve mentioned earlier, these can be easily found online.
I mean, just a single Google Search will give you what you’re looking for.
Or, you can just look at your university’s resources and check syllabi for Math subjects.
Step 4. Gather your References, Solution Manuals, and “Solved Problems” Types of Books
Conventional Math learning requires that you go to school, attend classes, do your homework, and then wait for it to be checked before you complete the feedback loop.
I say that’s highly inefficient.
When there are solution manuals or Solved Problems types of books available, it’s better to actually use them side-by-side to your own problem-solving routine.
For this one, I like the “Schaum’s Outlines” series of books.
The problems are rather hard, the discussions are concise and straight to the point, but you’ll certainly get better at problem-solving EASILY.
Just to be clear, I’m not saying that you should look at the solutions each and every time you’re solving a problem, but whenever you get stuck, you can easily get out and actually learn the solutions faster.
This tight feedback loop is what will allow us to learn math FAST and at our OWN pace.
“What if I don’t understand the material?”
It’s either you don’t have the prerequisites mastered (or not at all), or you’re using an overly complicated book.
Lastly, common sense says that this guide is not the “end-all-be-all” of self-studying Math. You can always consult others when you really get stuck even when you have a solution manual (perhaps it has a typo error or something).
Step 5. Prioritize Deep, Concept-Based Learning
This is brought out by the point raised above, which is to use solution manuals for learning Math to create a quick feedback loop.
However, it’s highly misunderstood by some students.
They feel that when they can memorize how a difficult problem is solved, then that’s good.
It’s a BIG mistake to memorize something you don’t understand.
Relevantly, it’s also a BIG mistake to just understand something but you don’t practice it.
Learn WHY the steps work, because if you do this, you learn once, and solve many.
Step 6. Put Links to Resources in One Place
Since you’re going to be mainly self-studying using Digital Resources, it’s handy to have them all in one place.
Perhaps make them your browser’s homepage.
Make a shortcut or something.
The thing is: make it SO easy for you to access your resources so that you don’t feel friction when you want to study on your own.
This makes it easier to form your study habits–which is always better in the long run.
Step 7. Set aside time for BOTH studying and problem-solving
As I’ve mentioned earlier, just understanding isn’t enough.
You have to practice what you’ve learned.
Just as a beginner can’t play a piano masterpiece instantly after someone good teaches him how to do it, learning new things in Math doesn’t happen with your “aha” moments.
Learning happens when you recall information from your head, not when you’re trying to put things in there.
So, aside from your “absorbing” time, set aside time for practice.
Step 8. Cultivate Deep Work
While practicing, it’s important that you do so without distraction.
Working without internal and external distractions and focusing deliberately on the task at hand, aka Deep Work, improves how your neurons fire together when activated.
This happens because a sheath called myelin is formed whenever you retrieve a piece of information or practice a skill.
When your attention is channeled into practicing problem-solving, you effectively tell your brain that ONLY those neurons activated during problem-solving should be sheathed with myelin.
When you’re distracted, however, this phenomenon happens poorly, and learning chunks don’t form very well.
Step 9. Avoid “Practice, Practice, Practice”, Do This Instead
This is probably the most common advice given to students who ask “how do I get better at Math?”.
We don’t need more time to practice. We just need to practice better.
Practicing is certainly vital, but there are two kinds of practice: Unproductive, and Productive Practice.
If you do everything in a long stretch of time, infrequently during the week, and just repeating the same problem for multiple times until you “get it” before moving on to the next one, then that’s Unproductive Practice.
Productive Practice is smart practice.
Here’s how to do it. Two easy steps.
- Spread your practice throughout the day, and throughout the week
- When you get the basic idea of a concept, don’t answer multiple problems with the same solution; answer multiple, unrelated problems that are not arranged by topic. (this is called interleaved practice)
By doing these, you’re saving a TON of time and energy into learning your Math.
One easy way to automate this is by using Anki, but you’ll have to be a bit creative in creating your decks and settings.
Specifically, as I have shared in the better solving course, you can create a “main deck” and “exercises deck/master problem set” using specific deck settings based on your level of confidence. (More confident = higher intervals)
Who says learning Math should be tedious, and time-consuming? It can be efficient, but like I said…it has to be more mentally taxing.
More Resources for Studying Mathematics by Yourself
Tired of endlessly grinding hundreds of practice questions and getting sh*t grades?
Are you left not knowing how to proceed when faced with a totally new problem?
You might be practicing the wrong way.
Learn more about the difference between the right and wrong way to practice in Better Solving with Anki: Get Amazing Grades on Problem-Solving Subjects (Without the Endless Grinding). (Full disclosure: This is my own course.)
Other Metalearning
- How to Teach Yourself Math by Scott Young. Back when I started my metalearning journey, he was my go-to resource. He finished a 4-year CS course at MIT in just 12 months, after all. I highly respect people who share techniques based on their experience.
Tutorials:
MOOCS:
How to Learn More Advanced Mathematics (FREE Resources)
If you want to take your Mathematics Knowledge to the next level, here are some helpful links.
I can’t teach you myself so here are better resources that discuss the topic:
- How to Learn Advanced Mathematics Without Heading to University
- Quora – How can I best learn advanced mathematics on my own?
- Here’s How to Teach Yourself Physics and Math
- Essential Math for Data Science
Next Step: Learn how to remember formulas (by learning them better and using Anki)
Link to the next article: How to Remember Formulas (by Learning them Better)
