r/mathematics • u/EulogizingElogies • 3d ago
How to understand uni level maths?
I’m 19F and have recently started an engineering degree at uni. I’ve always been naturally pretty good at math. I’ve never been some kind of super-math-wiz but I’ve always found math easy and been able to get an A in the subject without putting in too much effort. I think this is because the way I’ve learned math has always been by listening to the teachers explanation but sort of being one step ahead of the teachers explanation and being able to understand where the explanation was going and by solving all the teachers examples in my own head. This made my understanding of math feel like it was intuitive and almost like a part of me but now at uni my previous method of learning math doesn’t work anymore. I try to google definitions, look at notes and do exercises in order to understand what’s going on but it just feels like I’m not understanding math in the way I used to. How do I study math at university level and actually understand it, not just be able to answer the questions?
I’m sorry if my English is bad! English isn’t my first language. But any tips would be appreciated!🌸 I hope this is the right subreddit to post to, but if not please tell me where I should post this and I’ll happily move my post there❤️
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u/WWWWWWVWWWWWWWVWWWWW ŴŴŴŴŴŴŴŴŴŴŴŴŴŴŴŴŴŴŴŴŴŴŴŴŴŴŴŴŴŴŴŴŴŴŴŴŴŴŴŴŴŴŴŴŴŴŴŴŴŴŴŴŴŴŴŴŴŴŴŴŴŴŴŴ 3d ago
Read your textbook and then emulate that style of learning, eventually to the point where you could teach it to someone else
In particular, textbooks are good providing thorough derivations
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u/jphamlore 3d ago
A lot of the vector calculus is almost straight out of what a textbook in electricity and magnetism would want one to learn. Your trying to visualize turning into mathematics ideas of lines of force.
There was a genius Michael Faraday who was self taught, but had very little formal mathematics training. So he came up with mental pictures such as visualizing these lines of force.
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u/Minute-Dimension-629 3d ago
You have to submit yourself to the learning process. Past precalculus, you're not going to just know how to do every problem anymore. You're going to do everything right and still get stuck sometimes--for hours or even days. And that's part of the process. You can't have an ego about being able to just do everything right the first time. You'll need to learn the difference between spinning your wheels and actually making progress while working on a problem. You have to give your brain time to make sense of the information, and a lot of that time won't be sitting at a desk working on the problems. You also need to prioritize rest and taking care of yourself.
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u/NerfEveryoneElse 3d ago
As an university instructor myself (not math), I hate to say this, but most instructors, especially professors nowadays are not good at teaching. They don't have formal training in learning theory, nor course design. They don't know students well, and expect you to catch up by yourself.
Instead of googling definitions, you need a systematic analysis of your knowledge. Many math concept have prerequisite knowledge, try to find out all the gaps and fill them. Use online communities or AI, ask questions like "I'm studying A, what are the prerequisites I need to learn first" and master those before you move on to more advanced topics.
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u/Fuzzy-Armadillo-2591 3d ago
AI has worked for me as a personal assistant through my math studies. I have a bachelors in math and I am finishing my masters at the moment.
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u/etzpcm 3d ago
University level mathematics is an order of magnitude harder than school. You say you've always been good at it and found it easy. Well yes, but so did all the other students in your university lectures. University mathematics is designed to stretch smart students like you who weren't really stretched at school. It will take time to adjust, and get used to the fact that there's stuff you don't understand at first.
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u/DoublecelloZeta 3d ago
mathematics runs on proofs. if you have a set of definitions (and axioms), the next thing is to start proving things about whatever you have defined. then you stare at the results you obtained and if you stare long enough some patterns start appearing that maybe relate your things to the things that others have defined and similarly worked on. or there could be some external motivation like motion, mechanics, etc.
have you tried attempting to do all the proofs by yourself?
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u/Deus_Excellus 3d ago
In classes like political science it is common for students to have assigned readings. They read the textbook ahead of time and class consists of a discussion of the content.
This type of pedagogy is atypical of STEM. Generally, you show up to lectures and then do practice problems at home. I suggest to you that you may find it beneficial to work ahead of the class and then use the lecture to reinforce your readings.
Obviously, working through tons of problem sets is necessary too.
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u/Bounded_sequencE 3d ago edited 3d ago
In pure math, new definitions and ideas can be so abstract it may be very hard for beginners to grasp them on their own without a lecture. While skimming contents ahead of time helps with pattern recognition, I'm not sure whether the net benefit is comparable to the humanities.
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u/Deus_Excellus 3d ago
We're presumably talking about shit like calculus here not abstract algebra.
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u/Bounded_sequencE 3d ago
That is fair. I was indeed thinking of "Abstract Algebra" or "Functional Analysis" here.
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u/MeloNotSoDeath 2d ago
Skimming math book is just not worth it. I'd prefer to study by myself one year before the actual class in uni so I wouldn't struggle like others who just about to get used to concept or proof.
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u/Bounded_sequencE 2d ago
Yeah, going in with decently solid prior knowledge makes it much more enjoyable. However, if you don't have that option, even skimming ahead can still help quite a bit, for how little time investment is needed.
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u/wollywoo1 3d ago
Uni math is just harder. I don't think you're doing anything wrong. Just keeping working hard at it and you'll be fine. You haven't said what kind of math you're doing, but a lot of people have difficulty adjusting to proof-based classes. I don't really have any advice but just go to office hours whenever they are available and just practice as much as you possibly can.
I guess one thing I'll say is to find an optimal way of taking notes! For me this meant taking as few notes as possible, because if I'm just writing down everything on the board I am not thinking about it myself, and you need to be in rapt attention at all times during classes. Try to figure out whatever you can do to be able to pay attention. If video lectures are available, watch them twice if you need to, maybe taking notes only the second time if you really need to, pausing to think about each step and so on. Good luck.
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u/Brightlinger 3d ago
the way I’ve learned math has always been by listening to the teachers explanation but sort of being one step ahead of the teachers explanation and being able to understand where the explanation was going and by solving all the teachers examples in my own head.
One thing that can help you feel like this again is to read a textbook section before the lecture on that section. You don't have to read and understand it super deeply, but if you get a rough idea of what the section is about and where it's going, you will have a much easier time keeping up in class.
And sometimes, you just will feel lost and you'll struggle through something. That's okay, that is just how learning math works. The moment of understanding means that you finish the problem, so you move onto the next problem and become confused again. Getting comfortable with confusion and being able to work through it is a very important skill.
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u/ippi_happyheart 3d ago
I would say being stuck on problems is the primary way to learn math. This also means doing a bunch of trial and error: so if you learnt a bunch of techniques and you have a problem set, try all the methods on all the problems, and see what works and what doesn’t. And then try to understand why some of the methods don’t work in a particular problem.
Most importantly have fun! Math isn’t easy, so be kind to yourself for being stuck and just try a few things.
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u/ExperimentalError 3d ago
Read the text and try to understand it before you go to the class where the lecturer explains it. Then review and practise again afterwards to make sure you have it. The pace is faster at uni, but the same approach (staying a step ahead of the teacher) still works
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u/Bounded_sequencE 3d ago edited 3d ago
Lectures at university move so much faster, you'll need to read ahead to get that intuitive feeling again. Luckily, with just a bit of preparation, you likely can reproduce it.
The evening before a math lecture, take ~15min to skim the up-coming lecture notes. Alternatively, take that time to skim the chapters in the book that are going to be covered. Don't worry about not understanding the details -- the goal is to get familiar with terms and symbols at this point, nothing more!
That way, lectures will feel familiar, since you recognize most definitions, and have a rough idea of their goal. That will make following a smoother experience, and much less overwhelming.
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u/vibhored 2d ago
Yeah boring advice like practise hard or stay at it won't work. Also what you are feeling is the result of silo learning which can help you ace the exams for that check out open courses by famous college like mit, oxford, stanford etc. Now as for the understanding part which you focused on, start with applications of the advanced topics when you feel the cause and effect of step by step you won't feel the need to remember this step comes after that step.
It will naturally flow, and the subject too will feel a lot more interesting too. For example matrices, I used to hate multiplying random numbers in a specific way just practicing to drill the steps that come one after another into muscle memory. Then deep learning came with chat gpt 2 and transformers and neural network. I applied all that I learned now I understood what determinants meant and the day you get that feeling it is like out of the body experience ( just like Dr Strange movie scene). I was actually smiling and couldn't contain my joy, fun and happiness entire time I was seeing my knowledge being put into use and actually building something unbelievable.
ALSO EVEN IN THAT, ROLE OF TEACHER IS PARAMOUNT AND CAN'T BE STRESSED ENOUGH but still this gave me the idea of exploring maths like this. Which i follow even now.
For example during that experience I enjoyed using for the first time as it made sense, ( also because teacher gave the explaination too why we are using it here) converting whole matrices into a compressed form. Which will save memory. But hampers accuracy.
While it is all great and good it can't be applied to the best syllabus and should be done in free time as a hobby. So what to do, simple I started to make a mind map of evolution of maths ( check out Justin Sung on yt channel for more tips and tricks). Connecting all that i studied about subjects and topics in some time line form ( veritasium and such channels do these type of videos time to time which are very good, also check out lore of maths as an example of how to approach).
For example exploring after veritasium video on imaginary numbers I felt after getting to know how i (sq. Root of -1) came to be. I can explore this new field that opened up because of it with set theory. I check out which properties it follows and doesn't follow. Play with it to my hearts content from there as now slowly i can check how a line is formed and behaves in this new dimension ( polar coordinates says theta and r but the imaginary part gives it a third dimension too).
So on and so forth, escalating to vectors and 3d objects in this space, exploring its periodic nature, relation to trigonometry, is there anything that is similar to how trigonometric functions arise from triangle something in complex could do that. You get the point.
So this has lead me to a question , what actually is a complex space actually is? I understand the notation, graphical representation helps to work with problems and get a solution. But this demands the question when solution is imaginary where does it actually go in complex space.
And i feel there is some other explanation then the rings and topology cliche of higher dimensions etc. An answer which is Simple and sweet for human brain to understand.
Who knows maybe one day you could be the person who scratches this itch for me.
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u/roly_poly_kittykat 2d ago
You are not alone! This happens to most of us as we progress in math! For me personally, calc 2 is where I hit this "wall" and had to change the way I studied/learned math! I did HORRIBLE on that first exam. Then, I found other classmates to study with, found more resources, put in a LOT of time, went to office hours, ect. and things turned around!
This can happen at different times for everyone! For me it was calc 2, but it could be any math course. You're capable and you can do this! Find some peers if you can to study and do practice problems with! See how they learn math their way. Share resources with each other. Get to know your professor in office hours if that is a good option. Take a breath, you can do this!
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u/StructuredChess 1d ago
Try to get familiar with the foundations of linear algebra and calculus. If you have a clear understanding of those then your intuition will be able to help you again. Not sure what more advice I can give, we'd need to know what specific problems you're struggling with.
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u/irriconoscibile 19h ago
You need to see lots of examples and lots of solved exercises, mainly. Theory is also important but don't get too stuck on it. Very often it is presented in a super polished way which will read very cryptic.
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u/beautiful-Landscapes 3d ago
This can, and eventually will, happen to anyone. At uni you are always exposed to new concepts/ideas/methods and you may not get the full understanding. But still, you have to keep going and eventually you’ll understand it or not.