I don’t know that I would have anything to say that’s not a platitude, but here are some thoughts.

It’s a hard topic. Recognise that it’s hard. Don’t expect to learn everything in one go. Don’t expect to solve every problem on the first attempt. Take the time to let ideas sink in.

Don’t feel intimidated by others who do things faster, nor superior to those who do things slower. Don’t let anyone put anyone else down for finding the subject difficult, comprehending things more slowly, etc. Try to include people who feel excluded. It’s difficult for everybody, and everybody has different difficulties. We don’t need to make them worse.

Ask questions of your teachers. Chances are if you’re thinking something in a lecture was unclear, many other people are too, but not all of them are brave enough to raise their hand. And ask outside of class too if you want. For most lecturers, most of the questions they have to answer are about homework extensions, repeating for the hundredth time some administrative detail, etc. They love answering questions about their actual subject. Ask them.

If you can, find other students to work with. People vary, but for many people, working together productively with others on problems makes the whole experience much more pleasant, and it’s better for solving problems and bouncing around ideas too. Learn from others, and they can learn from you.

Be curious. Ask how and why things work. Think about the big picture and how everything fits together. Ask why we study the things we study.

Enjoy the subject. Mathematics is full of patterns, curiosities, profound truths, breathtaking theorems, hard-fought triumphs, ancient mysteries. Its roots in culture stretch back as far as humans have walked the earth. Play with the patterns, play with as much of it as you can get your hands on, it’s much better if you an understand it that way. Understand it your way, and tell stories about it.

Wonder at the profound beauty and elegance of deep theories. Take the time to properly understand and appreciate what theorems say. They surprise, they flabbergast, they connect oceans of thought. They reduce the incomprehensible to the world of the living. Their proofs are often even more instructive than their statements. These things are among the greatest achievements of humanity. They are the eternal harmonies of this tragic universe.

Also, savour the enjoyment when you solve a difficult problem. It’s a hard subject and we need to take all the wins we can get.

General tips for studying mathematics
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