> ...and Shor's Algorithm

Better start with Simon's algorithm (solving Simon's problem) [0]; it already contains a lot of ideas that you need to understand Shor's algorithm, while not having a lot of technicalities. Then progress to Shor's algorithm, and then to Kitaev's algorithm [1] (link from [2]). The latter solves the Abelian stabilizer problem - this problem contains the more abstract mathematical essence of a lot of quantum algorithms.

[0] https://en.wikipedia.org/wiki/Simon%27s_problem

[1] https://arxiv.org/abs/quant-ph/9511026

[2] https://en.wikipedia.org/wiki/Hidden_subgroup_problem#Instan...

Don't let the terminology intimidate you. The interesting ideas in quantum computing are far more dependent upon a foundation in linear algebra rather than a foundation in mathematical analysis.

When I started out, I was under the assumption that I had to understand at least the undergraduate real analysis curriculum before I could grasp quantum algorithms. In reality, for the main QC algorithms you see discussed, you don't need to understand completeness; you can just treat a Hilbert space as a finite-dimensional vector space with a complex inner product.

For those unfamiliar with said concepts from linear algebra, there is a playlist [1] often recommended here which discusses them thoroughly.

[1] https://www.youtube.com/playlist?list=PLZHQObOWTQDPD3MizzM2x...