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So I discovered halfway through my first year university math term that my foundation of mathematics is very poor. I would memorize stuff rather than understand it and still get 95+ in high school so that's what I did. I quickly realized that doesn't work at all in university. It's embarrassing but I didn't really even know what a derivative really meant and I'm in University Math!

Anyways, I passed my math courses barely with 60-70, and did way better on the finals than I did on my midterms which is a sign that I'm heading in the right direction (I went back and looked at a whole bunch of khan academy high school math concepts) but it was hard to juggle doing that and keeping up with current stuff in class.

So now the term is over and I want to prepare for next term. My question is, should I go back and review basically all the high school stuff I memorized (and forgot), or should I just start studying the new material by reading the textbook ahead and actually understanding the concepts through practice this time?

(The 2 math classes I had this previous term was Calculus 1 and Algebra/Proofs, and my next 2 classes are Linear Algebra and Calculus 2)

Thanks!

ming
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    how did you do proof questions without understanding what you was writing? – ricky Dec 23 '18 at 22:33
  • A ton of help from the tutorial centre and friends for assignments, almost failed my midterm, basically passed because of part marks and questions I recognized from the textbook, and in the Final, that's when I really started to realize what was wrong with my studying and so I studied super hard for a week so I managed to get around ~70, but I'm still lacking a lot. – ming Dec 23 '18 at 22:45
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    To be frank there is no short cut here. You need to revisit high school textbooks and read them properly. By " read properly" I mean that you should read the book completely and stop wherever you feel you are not able to make sense of a sentence and think over it. Skip problems / exercises (you may however look at some solved examples). – Paramanand Singh Dec 25 '18 at 07:46
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    Also a thing about high school textbooks. Go for the ones prescribed by the government body as a part of syllabus instead of cheap books which fill pages with drill type exercises. In short your book should have far more prose than math symbols. – Paramanand Singh Dec 25 '18 at 07:51
  • Does this answer your question? Learning mathematics as if an absolute beginner? – user1147844 May 27 '23 at 01:13

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As I'm sure is the situation with many other people, I've had friends who did well in math earlier on in school, but then got behind, mostly due to having a poor teacher. They usually never got back on track and continued having difficulty with math. More than most other topics, I believe, later math is built on understanding and using concepts learned earlier, which is an important reason why those friends weren't able to continue doing well in later years. If you don't understand those earlier topics, it will make it difficult to understand many later ones, especially those which directly use or expand on the earlier concepts. As such, instead of first trying to study ahead, I think it's best to first ensure you fully understand your high school math concepts. After that, if you have the time and interest, it would then be useful to examine the material for next year ahead of time.

Good luck in your future studies.

John Omielan
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    So what is the best way I can study previous stuff? It's not like I can go back and do high school again haha. Should I review my old notes from high school? Go through all the youtube tutorials for high school math? Idk where to start – ming Dec 23 '18 at 22:47
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    @ming Everyone is somewhat different in what is the best way for them to learn. For example, I prefer to learn by reading. Other people are more visual, so some sort of video (such as YouTube) works best for them. On top of that, I'm not sure how good or useful your old notes are. As for where to start, I suggest you try several things, see what seems to be working best for you and then continue focusing on those method(s). – John Omielan Dec 23 '18 at 22:49
  • @ming I agree with john but with more emphasis on actually learning and understanding what the definitions mean then progress to doing questions, that way you're not just copying a particular method but you actually understand the reason on why you're doing it. You'll see this definitely in Linear Algebra and MVA – ricky Dec 23 '18 at 23:01
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    @ming One thing I'm doing (many years later and for myself rather than exams) is try to identify every step that I feel I'm "taking for granted" or skating over when doing a piece of maths. This sometimes leads me back to half-explained basics which I then set about proving. Maybe you can do that: let the new material guide you back to the specific bits high school material that you need to consolidate. – timtfj Dec 23 '18 at 23:37
  • @ming If it works for you, you should then find that you understand both the new material and the more basic maths that it depends on. Also you'll be motivated to learn the earlier stuff, because you'll be focusing on the parts that you have an immediate use for. – timtfj Dec 23 '18 at 23:40