Disclaimer: Some of this advice is specific to USYD.
Some basic principles that will make your university life much easier.
It has become a common meme in our society to say "I'm just not a maths person" or "my brain doesn't work like that". This is not true. You are a human, and humans of every age, gender and ethnicity have been doing and inventing mathematics for tens of thousands of years. Dominant beliefs about intelligence often have deep political roots and were promoted to exclude women from higher education and justify white supremacy.
There is nothing special about mathematics, and you are more than capable of taking it at the university level. You will make mistakes, there will be complex ideas that take a while to understand, and exams might be stressful. Don't attribute difficulties to personal failings.
Like any subject, mathematics is a way of thinking about the world. The goal is to understand this way of thinking, and to practice using it.
In short, the main idea is that we can reason about the world using abstractions. For example, suppose we are trying to model the spread of a disease through a forest. We remove many of the complexities that exist in the real world and create a simplified model of the situation (for example, just couting the number of infected trees). We can then use tools like calculus to precisely predict the spread of the disease in the simplified model.
University-level mathematics focuses on ideas rather than formulas. Each idea will attempt to abstract some part of the world, and come with a number of tools to understand the abstraction. Focus on understanding ideas rather than memorising facts. This takes time, and cannot be crammed. But once you have done it, you are less likely to forget it.
To help with this, constantly ask yourself (and your teachers!) the following questions: Why did people think this idea was useful or interesting? Where else can this idea be used? In what ways can this idea be extended?
Lectures will introduce you to ideas, often in a very polished way which does not cover the full range of complexity. During lectures, keep the above questions in mind when coming across a new concept. Be creative in imagining why each idea might be useful.
You won't understand everything immediately. Many of these ideas were developed over hundreds of years of collective human thought, and they have a lot of nuance to them. If you feel completely lost, it is worth asking your lecturer to clarify what's happening, because there will be other students feeling the same way. If a lecture is not being effectively communicated to you, that is usually the fault of the learning environment and not of you.
Some people might prefer to pre-read the content to give lectures more context. The channel 3Blue1Brown provides excellent, intuitive and visual introductions to both calculus and linear algebra.
Understanding an idea happens by applying it to a variety of contexts. This is why tutorials are useful, and the questions have usually been carefully written so that you approach a concept in a number of different ways. Attend every tutorial. You will often feel that after a good tutorial, you don't even need to study because your brain has already internalised the main ideas.
If possible, read the questions before the tutorial but don't work on them. Just let them settle into your brain. Find a group of people you feel comfortable being around, because this will make everything easier. Give each other equal board time when working on questions. Be patient and kind when mistakes are made, because it will happen to everyone.
Engage with your tutor! They often have years of experience and have spent a lot of time thinking about these concepts. They want nothing more than to share their knowledge, and there is nothing worse than a quiet tutorial.
Just with tutorials, look at your assignment questions as early as possible. This gives your brain time to process in the background. You might find that you have no idea where to start with a question, but three days later you can suddenly do it immediately. If you can't figure out how to approach a question after 15 minutes, give it a break. Later, try and explain the question to somebody else.
Most of your exam study should be practice problems. Look over tutorial questions, past exams, textbook questions or anything other relevant material. Again, if you find you are spending a long time on each problem, that's the time to seek help from a tutor. You might be missing some piece of content.
If you knew how to do every question immediately, you wouldn't be learning anything. When you first get stuck, look over lecture notes or tutorials to see if this is a concept you have encountered before. Sometimes you just forget something from the course!
You will often develop minor misunderstandings when starting out. Look out for cognitive dissonance, when you realise you believe two things which can't both be true. This is a perfect time to post on Ed asking for clarification. Your question will be answered much faster and more accurately than on the internet. If you feel some embarrassment, post anonymously (staff can still see your name).
If you feel lost about multiple little things or entire topics, that's when its time to go to the Learning Hub (Quad N293). It is open 10am to 4pm every weekday, and no bookings are needed. This is essentially a free, professional, in-person tutoring service with no maximum time limits.
Personally, I strongly recommend against using any form of generative AI for learning mathematics, but I am happy for people to convince me I'm wrong on this. Current generative AI models are terrible at mathematics, and students self-learning using AI show significantly worse levels of understanding.
Using generative AI outsources your thinking to a computer, which is precisely the skill you are trying to develop. You are choosing to give up an opportunity to engage with the world. Imagine learning how to play tennis by having a robot practice your serves.
You might want to cheat on assignments or exams because you feel disconnected to the learning outcomes of the course. Sometimes going to university just feels like a capatilistic exchange of your time and money for some fancy piece of paper, and this is exacerbated in enormous classes that inhibit the social aspects of university.
It does not have to feel like this. There are many people at the university, especially lecturers, tutors and friends, who are passionate about you learning the material and finding that process engaging and rewarding.
Cheating doesn't mean you're a bad person. It's often a symptom of feeling disconnected. Make sure you're looking after yourself, that you have enough food, sleep and exercise. If you start to struggle, talk to people sooner rather than later. Friends, parents, tutors, lecturers, councillors, and anyone else.
There is a certain type of person ever-present in maths classes. They are boastful, overconfident, talk over others and are constantly trying to prove their own intelligence. They often act this way out of insecurity. Try your best to ignore them. Work in a group that doesn't involve them.
If you're up for it, question their logic. That confidence might disappear quicker than you think. Call them out on any sexism and other degrading comments. Many of them will actually change this behaviour pretty quickly, and are just acting the way they see other people act to fit in. If you know people who would take your side, telling them about the situation can be helpful.
If you are a maths student at USYD and want more personal advice, I'm working at the Learning Hub drop-in centre at 10am-1pm on Wednesdays, and you can find my tutorials on the Maths and Stats timetable.