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I am starting my undergraduate in Mathematics soon and want to hear your suggestions/tips.

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Advanced undergraduate courses will cover material that is fundamentally, qualitatively different from anything you've be exposed to - after the first year or two it will be about making rigorous inferences about the behavior of abstract mathematical objects just as often if not more often than performing computations and manipulating symbols.

It's hard. No matter how quick you've been in the past, it will throw you for a loop. The fact that you're used to taking your time to learn something in it's entirety will be a huge asset. Other students who have a history of picking things up quickly without having to really study or engage with the material will perhaps do very well for the first year or two, but your steadier more disciplined approach should allow you to catch up or pass them by eventually.

IMO, the first rule of learning advanced mathematics is don't be scared of it. You need to get comfortable being deeply, extremely confused, and putting together a working understand one little piece at a time. If you're not confused the majority of the time, you're not taking challenging enough classes, and you're not learning enough. Facing that confusion without letting it cause fear or anxiety is arguably the most important skill.

The second rule is not to take life advice from other people if that advice doesn't feel right. People who are good at mathematics are usually very bad at giving advice. They don't actually know which things they did in life helped them, so they rattle off a random bullshit collection of things they did, things they didn't do but thought about doing, things they think one of their friends did, etc.

On a more practical level, many people say that this is the best way to study: make a list of questions, concepts, and example problems that together make up all the material you're trying to study, and make sure that list does not include any answers or definitions, only names of concepts and questions. Go through one at a time, try to define each concept in your own words and solve every example problem without looking at your book or notes. If you can't, look up the answer or method, finish the problem, and mark it with a star. Note that these answers and definitions go on a separate piece of paper, which you put away or throw away immediately when they're done. When you get to the end of the list, go back and solve/define all the starred problems without looking at the book or notes again. Only un-star the problem if you solve it without the book or notes this time. Repeat (within the same study session) until everything is un-starred. Perform this process every day until you get everything on the first try.

Edit: one last thing. Some people think that a person has a fixed level of innate mathematical talent. Those people are wrong. Mathematical ability is like a muscle. Maybe some people lucked out and figured out a good excercise routine early on, and it makes them look like they have natural talent. But they've just been practicing efficiently. It's all about practice - that's where mathematical skill comes from. You fundamentally *do* have it within you to become excellent at mathematics if you put in the time and work both hard and efficiently. Figuring out how to work efficiently will take time and open-mindedness. Give yourself the mental and emotional space to grow and learn.
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Invest in a good pencil!
Your professors are not Gods… approach them, introduce yourself and get to know them.
Help your classmates… one day you’ll need their help.
Explore different branches of math… I started with topology and fell in love with number theory.
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Don't be afraid of your professors, and be sure to attend office hours, review sessions, tutorials, and the like. Ask questions. If you're wondering something, chances are someone else is wondering the same thing.

Get to know your fellow students. Join the undergrad math club if there is one, and talk to students about their programs, their problems, and yours. (And also talk about non-school life stuff as appropriate.)

Learn LaTeX and typeset your assignments. Do this as you can, but learning LaTeX is never a bad idea. Typesetting your assignments helps you and the grader. You learn LaTeX, but also how to communicate your solutions effectively. Your grader can read your solutions clearly and doesn't have to struggle deciphering handwriting.
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There are a few hurdle that many people got stuck on.

Calculus: this is like, the big filter of students, many people struggle with it. Best way to prepare for this class is to make sure your fundamentals: algebra, trig, pre-calculus are up to par. Honestly, if your algebra is not good enough by the start of the first semester, I would not recommend taking Calculus I.

Real analysis and abstract algebra: this is for math major, usually in the 2nd year. For some people, this is the first time they have to write proof. But doing so is a mistake, in this class you don't just have to write proof, you're doing so while learning abstract and/or unintuitive materials. To prepare for such class, it's better if you have started to study proof beforehand. Try taking other classes that have proofs first. For example, some discrete math classes have proof, but not always, so you should check the syllabus. Logic class could theoretically teach you proof, but they generally teach formal logic which is a different kind of proof you will write. Also note: abstract algebra is completely different from the kind of algebra you had known.

Math major has a lot of focus on proof. You won't find yourself doing "practical" stuff very often.
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I’ve seen way too many students do poorly in calculus not because they couldn’t do calculus, but because they couldn’t do algebra.  Big stumbling blocks:  Square roots, powers, rational functions, and logs.
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Gl
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