Quantum Mechanics
Classical physics is a good approximation.
Is it possible to learn Quantum Mechanics without a proper grasp of mathematics or classical mechanics, is it possible to jump in at what most would consider the "deep-end"? Intuitively we would say no, learning has always been designed in a linear trajectory, start simple and increase complexity in a specific order. This is an attempt to skip the "correct" order mainly due to the constrain of time.
Learning Method
The idea is to attempt to take the shortest path to level which could be described as an understanding of QM. Having attempted to start by reading books for non-physicists the issue is that there are too many concepts often introduced in too short a period of time; waves, particles, energies, measurements, state vectors etc it quickly starts to feel insurmountable. An idea I would like to explore is how to learn the most fundamental aspects, in the simplest case; the 1-D, one electron, or whatever other simplications we can make to the problem space.
Learning is always best by doing, taking notes and writing in general is a good start, but building experiments or software is even better. A secondary goal will be to try and represent the learnings through a software package, which can represent an interactive simulation.
One other (possible) benefit of being uneducated in classical physics is that we can try and skip some of the intuitions that this would place upon trying to understand QM. If we look at the concept of wave particle duality, we can be confused right away, is an electron a wave or a particle? The universe is not wavering between the two, unable to make up it's mind, it is therefore important to leave these intuitions behind and and accept the electron for whom he/she truly is!