Content structure survey

Dear friends,

Thank you for subscribing to quantum formalism. This is an experimental endeavour by our team, intending to help you decode the mathematics behind quantum mechanics by first exposing you to the core mathematical concepts from a mathematician’s perspective before jumping to the way a working physicist uses the same concepts.

Given the diverse background of our subscribers, before we get into the actual mathematical formalism of quantum mechanics, we're considering following the structure listed below. However, please feel free to help us adjust the final structure by taking this survey (less than 60 seconds): https://forms.gle/m7fets2MKhkgJJoV7

Foundational Content

1. Naive Set theory 101 – Covering the basics of set theory.

2. Abstract Algebra 101 – covering the basics of algebraic structures such as; groups, rings, fields, modules over rings and vector spaces over fields.

3. Topology 101 – covering the basics of topology such as; open sets, topologies, topological spaces, Hausdorff spaces, continuous functions, and homeomorphism.

4. Analysis 101 - covering the basics such as; sequences, series, continuity, limits etc.

Quantum Formalism Content

1. Quantum formalism genesis - introduction and the roots behind the Hilbert space formalism.

2. Functional Analysis – covering topics such as; topological vector spaces, normed spaces, Banach spaces, Hilbert spaces, Linear operators, Bounded & Unbounded Self-adjoint operators, C*- Algebras, etc.

3. Measure Theory – covering topics such as; Sigma – algebras, Measurable sets, Measurable spaces, Lebesgue Integrals, etc.

4. The formalism of quantum mechanics - covering wide range of topics including; the axioms of standard quantum mechanics, geometric quantization, and algebraic quantum field theory.

Finally, we’ve just created a GitHub repo where references and extra resources will be organised.

Many thanks,

Zaiku Group team

Ps- apologies for any typos!