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I am about to enter in second year as a math major, due to some reasons I have never been into amc and imo like stuffs, but as I am gaining interest in math, it is the regret which is hurting me again and again. So have decided to go through elementary euclidean geometry to high school algebra,and number system. The only problem is I'm afraid it will hold my rigour in mathematical proofs backwards, think like this : one morning I woke up and started studying some ring isomorphism, and then in the evening I have to study high school algebra it really making me upset about myself. Your few lines of advice will help a lot.

Long story short : How to manage these two aspects simultaneously ?

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    $\begingroup$ There's no harm in it, but do prioritise your university studies. Perhaps try an olympiad paper or 2 in the holidays (rather than during term time)? $\endgroup$
    – DanLewis3264
    Commented Aug 8, 2019 at 20:42
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    $\begingroup$ Solving Olympiad problems is way harder than a typical undergrad abstract algebra course. You shouldn't dismiss Olympiad problems as mere "high school algebra". Nothing wrong with spending time honing your problem solving ability. (And nothing wrong with studying Euclidean geometry, a subject that's often neglected in the US.) $\endgroup$
    – littleO
    Commented Aug 8, 2019 at 20:43
  • $\begingroup$ @littleO I really appreciate it sir : ) $\endgroup$
    – M Desmond
    Commented Aug 8, 2019 at 20:50

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I will answer specifically to this point,

"The only problem is i'm afraid it will hold my rigor in mathematical proofs backwards, think like this : one morning i woke up and started studying some ring isomorphism,and then in evening i have to study high school algebra"

The good news is that mentally, it should not hold your rigor back at all. Actually, being a more seasoned mathematician studying high school material, you will find yourself questioning many things you read and try and convince yourself of the answer. This may make you a better mathematician

The thing to watch out for, is that humans have only a finite amount of time to work with. So your math skill will suffer if studying high school math takes up so much time, that you are not spending enough time on university maths. So my advice is prioritize university maths, and study the high school math only when you have sufficient free time

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