What is the best way to prepare for core maths subjects in university?

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In summary, the speaker is a third year undergraduate who will be taking introductory courses in pure mathematics next year. They are concerned about their performance in second year math and want to prepare for their core subjects. They are considering starting early, reviewing previous material, and doing high school math competition problems. They also mention the importance of mastering basics and seeking different perspectives. In the end, they decide that reviewing second year material thoroughly is the best approach, with some fun high school problems mixed in. They are inspired by Terry Tao's approach of understanding simple concepts thoroughly before moving on to more advanced material.
  • #1
pivoxa15
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I will be doing my final, third year of undergrad next year and will be doing intro subjects to the main areas of pure maths like algebra, analysis, topology. The problem is I have not done well in second year maths and don't feel I understand the material. However, I really like to do well in these core subjects next year. What should I do to prepare for them?

Should I mostly concentrate on:
1) Starting next year's material early
2) Review 1st and 2nd year maths hence do them again
3) Do high school maths competition problems (I always did poorly in those) hence increase my general mathematical thinking and problem solving ability in the hope of being able to pick up mathematical concepts in my subjects quicker.

3) would be the most fun but how useful would it be? If 1) than it would involve reviewing 2nd year material as well since they are needed in order to learn the 3rd year stuff. Although 2) would mean doing them more thoroughly.
 
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  • #2
Best pick is most likely your #2; to study second year material and learn it better. This idea, in general, has helped me, although my major field was not Mathematics. If you are weak at pre-requisites, then you are not likely to succeed in the courses which use those pre-requisites.
 
  • #3
I would concentrate on 1. There's nothing like seeing material for a second time to give you a boost.
 
  • #4
I vote for #2.

A "master" in some discipline is not characterised by the amount of things he knows, but by the extend at which he masters the basics. That is the key imjo.

Also, don't review the material from the same source as you learned it the first time. Get other books. It will give you another perspective.
 
  • #5
If you study the material you're expected to know, then by default if you run into something you don't get because you don't have enough background knowledge, you'll have to learn the background knowledge.

Just some food for thought
 
  • #6
Come to think of it, 2) does seem to be the best. Although a bit of 3) would be good as well I think, at least it will be fun. I am thinking of starting everyday with one of those problems and then study some proper uni material.

The great Terry Tao would probably have recommended 2) as well when he said in an interview which can be seen in full here http://www.ms.unimelb.edu.au/~paradox/archive/issues/p06-3.pdf

"If I learned something in class that I only partly understood, I wasn’t satisfied until I was able to work the whole thing out; it would bother me that the explanation wasn’t clicking together like it should. So I’d often spend a lot of time on very simple things until I could understand them backwards and forwards, which really helps when one then moves on to more advanced parts of the subject."
 
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1. How can I improve my understanding of mathematical concepts in university?

One of the best ways to improve your understanding of mathematical concepts is to actively engage with the material. This can include attending lectures and taking thorough notes, participating in class discussions and asking questions, and completing practice problems on your own. Additionally, seeking help from your professor or a tutor can also greatly improve your understanding.

2. What study strategies can I use to improve my maths skills at university?

Some effective study strategies for maths at university include practicing regularly, breaking down complex problems into smaller, more manageable parts, and reviewing old material before moving on to new concepts. It can also be helpful to form study groups with classmates and work through problems together.

3. How can I overcome math anxiety and improve my performance in university maths courses?

Math anxiety is a common issue for many students, but there are strategies you can use to overcome it. One approach is to break down the material into smaller, more manageable pieces and focus on understanding one concept at a time. It can also be helpful to practice regularly and seek help from a tutor or professor when needed.

4. What resources are available to help me improve my maths skills at university?

Many universities offer resources such as tutoring services, study groups, and workshops specifically for maths students. Additionally, there are numerous online resources, such as Khan Academy and YouTube tutorials, that can provide additional explanations and practice problems to improve your skills.

5. How can I stay motivated to improve my maths skills at university?

Staying motivated to improve your maths skills can be challenging, but setting specific goals and tracking your progress can help. It can also be beneficial to find real-world applications of the material you are learning and reminding yourself of the long-term benefits of improving your maths skills, such as better job opportunities and problem-solving abilities.

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