Proof-focused books matter for JMC because Imperial is not looking only for programming enthusiasm: you need to show that you can handle definitions, induction, recurrence relations, asymptotic reasoning and complete arguments. Start with How to Think Like a Mathematician, Concrete Mathematics, Introduction to Algorithms, The Algorithm Design Manual and Mathematics: A Very Short Introduction.
Visual and lecture-based resources are most useful when they help you revisit a hard idea, not when they replace problem solving. Use 3Blue1Brown, Computerphile, Numberphile, MIT OpenCourseWare and CS50 for second explanations of linear algebra, algorithms, discrete structures or computing theory.
Podcasts are best treated as prompts for follow-up reading rather than as evidence of technical depth.
Structured courses are useful when they produce worked exercises, code, proofs or corrections you can point to later. Use Mathematics for Computer Science, Introduction to Algorithms, CS50x, A-level Mathematics for Year 12 - Course 1 and A-level Further Mathematics for Year 12 - Course 1. Keeping notes on solved problems, failed attempts and corrections gives you material for the personal statement and for any academic discussion.