5 Tips for Studying Math at University Level

Me writing on my iPad sitting in front of my desk and computer
Me writing on my iPad sitting in front of my desk and computer

No matter if you have an exam looming or you just want to improve your math knowledge for your job or as a hobby, we all come to a point where we get overwhelmed by math and it just doesn’t make any sense and maybe we even want to quit.

Here are my tips that helped me to study math over and over in university and beyond. I have 3 essential tips that can help you right now and two bonus strategies that will set you up for success long term, but require a bit more time.

Table of Contents

Tip 1: Don’t just study the math theory, do the exercises! Then do them again.

If I could only give you one tip, it would be this one. Exercises in math are extremely powerful. Even if you are at a level where you are mostly doing theoretical proofs instead of calculating with concrete numbers, applying the theorems and rules makes your interact with the material from different viewpoints which can’t be replaced by anything else.

Example exercises in a textbook (Book: “Fundamentals of the Theory of Groups” by Kargapolov, Merzljakov)

If you are in university, you likely get coursework every week or throughout the semester. I strongly encourage you to do every single exercise even if you don’t need to do so to qualify for the exam or get good grades. If you are self-studying, find a book on your topic that includes exercises and complete those. Don’t worry if you don’t have solutions on hand, you get 90% of the benefit by just interacting and thinking deeply about the material while trying to come up with your solution.

Tip 2: Math is hard, it’s not your fault. Be patient with yourself while learning.

This one is not as practical as the first one, but many people stop when it gets hard, so following this tip might increase your learning potential the most after all.

I don’t know where you are in your math-journey, but I completed a Bachelor’s degree in largely pure math and I can assure you I felt various degrees of stupid most of that time. If you also feel overwhelmed by math sometimes, take a step back and remind yourself that even people with a Phd in math have to think a long time about new topics. You belong with math and you WILL figure it out eventually, I promise.

So be patient. Sometimes you actually have to step away from a topic for a few weeks and after some time away, you notice that it makes more sense. Which is why you shouldn’t cram-study right before the exam 😉 Math just takes time.

Tip 3: Make a cheat sheet after studying a math topic.

In our university we were allowed to bring one A4 piece of paper into the exam most times. This means you don’t have to learn everything by heart, but it also means the exams ask questions that go beyond learning something by heart. No matter the reason, I actually believe that creating this densely packed piece of paper has value by itself.

My personal cheat sheet for an algebra exam in university. The back was almost full as well of course.

So even if you’re not allowed to bring something like this or if you are not even studying for an exam, make one anyways. On this sheet you want to write down anything about the topic that you might not immediately know or remember. It makes you go through all the material and decide if it’s worth writing down and you have to think about a layout to group similar concepts. And the writing itself is a great memorization technique for many people as well.

The process of writing in a tiny font took probably 4-8 hours though and that’s after organizing all the material, so to get the most out of this task, you really have to imagine that this one sheet of paper will be your only lifeline in an exam 😉

Bonus 1: Use different sources, if you have the time.

If you’re on a tight uni schedule or otherwise have deadlines looming, this tip will not be as applicable. But if you are taking a deep dive on one topic, for example when you have to give a presentation on it, then I would highly recommend checking out at least one other author next to your primary book or lecture series.

If you notice that you have a harder time than usual understanding the concept, you are possibly not compatible with the source material. Different authors approach topics from different angles or have a different structure to their explanations and it can make a world of a difference to your enjoyment of reading and learning.

Bonus 2: Teach others the math you just learned.

This is another tip that is more of a long term strategy than a quick tip, but it is one of the most effective in my personal experience. Teach and explain!

You could study with your friends and help them with an exercise they don’t understand as well. You could start tutoring younger students. Our university offered jobs to grade coursework of modules you already finished. And of course, you can always just write it down for yourself and potentially publish it on the internet, if you feel comfortable with that.

Teaching and explaining math forces you to go through all the small steps you tend to gloss over in your mind. You should be building mental connections to other topics to make the material approachable for the listener which will strengthen your memory. And this method has built-in repetition, which is always a plus. Bonus points if your students make mistakes or ask questions that you never had to face because you always did this task a little bit different.

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