I'm currently attempting to consolidate my failing foundation in maths from ground zero upwards. I want to be able to do olympiad problems but the books that I'm learning from don't teach me how to solve the problems brought up in famous olympiads like the IMO even though it's from the basic level of algebra or integers. It's frustrating to me because I'm unsure of whether the way I've been learning is inadequate or rather the books I'm learning from don't address the techniques and proofs used for that level since not many people care to learn maths to such heights.
Furthermore, as result of this I've tried consulting proofs but find that I don't understand it because of the confusing symbols which I neither know how they are called or read aloud. If I knew what the symbols mean and how the statement is read it's easy for me to understand its meaning. An example would be from this book called Elementary Number Theory by Underwood Dudley on page 3:
Lemma 2. Ifd l al, dla!, .. . ,dla", then dl(clal + c2a2 + . . . +c"a,,) for any integers Cl, C2 , ••• , CII' Proof. From the definition, there are integers qI> q2,' .. ,qll such that al = dql, a2 = dq2' . .. , a" = dq". Thus clal + cza: + ... + cna" = d(Clql + C2Q! + ... + C.,.Q,,) , and from the definition again, dlcla] + CZa2 + ... + c"a".