My self-study plan for electrical engineering

Razavis RFIC is a good one too, but that’s really getting too specialized. Pozar is good for undergrad microwave.

Open Source Society University

Path to a free self-taught education in Computer Science https://github.com/ossu/computer-science also bioinformatics and data-science

Yes, you do.

"Control" is another name for "optimisation" or "systems with feedback".

It is the theory covering any system that has a closed loop in it. Optimisation is a mindbogglingly broad field with application to nearly everything in the physical world. Other branches of engineering, science and maths study this area but give it their own name.

Examples of systems with cycles:

* Any system that does optimisation: Deep learning, adaptive systems, ...

* Error control decoders in digital communications systems.

* The majority of non-trivial circuits.

* Pretty well every circuit operating at high frequencies.

* Echo cancellers in telecoms.

* Computer networks (eg. TCP congestion control)

* Systems of chemical reactions

* The brain (your area of interest) is a seething mass of feedback paths.

Optimisation (a.k.a. Control Theory) and Information Theory (some of which is covered under the name Communications Theory) are fundamentals. "Digital" in their title doesn't mean they have narrow application, as Information Theory (Shannon, ...) treats everything, including analogue, in terms of bits.

Given your background in maths, one of the first things you should do is to try to construct a "Rozetta Stone" to relate a complete list of Electrical Engineering topics back to what you already know. For example, you will have already done a lot of control theory, but have learned it as optimisation. Part of your task is to recast your existing knowledge in terms of EE jargon, identify the gaps, then fill them in. Unlike an undergraduate you're not starting from the bottom.

Edit:

A suggestion: Along with the list of EE areas you want to learn, why not add to your post a list of all the areas you already know in maths? HN readers may be able to link the areas that you want to learn with what you already know. It's hard to make such links yourself, as you don't yet know what each EE topic contains.

I want to underscore the e͟n͟g͟i͟n͟e͟e͟r͟i͟n͟g͟ in the electronics engineering. Engineering everywhere is very hands on, and you cannot be an "engineer in theory only" if you want to perform on a job.

Learning from mistakes in a class setting is much easier, and c͟h͟e͟a͟p͟e͟r͟ than casually failing a USD $1M design in a very simply way, but a way not taught in any textbook.

Not to disparage you, I know many people who were similarly dragged into electronics engineering by necessity, and got to the level of degreed engineers over many years. COB But those guys had years, and years to perfect their skills in a time when the industry was more forgiving, and was growing with their skill.

I would say that today, nobody will hire a 18 year guy who was just an electronics hobbyist to a factory, that was not the case 12-10 years ago.

What I can say against modern electronics engineering education is that excessive focus on producing "workplace ready" cadres makes for worse workers past the basic level.

I know people who are quite adept with digital electronics, but can't even understand how anything but textbook versions of SMPS power supplies work because of universities thought that analog circuits are now what people pay for. This the same for many more fields in electronics.

I believe properly taught EE can figure out just anything with the right approach, and time, and this attitude is the best what education can give you, unlike mass produced engineers who keeping find lame excuse "I'm not a logic/power/high speed/rf/motion control/asynchronos circuit/metrology/network/audiovideo engineer! I did not study this at school!"

My main concern with EE is that once I'll get to the brain-computer interfaces, I'll be in a situation where there aren't many off-the-shelf components/solutions available, and at the same time I'll likely need to know how I can push physics closer to the edge. I suspect I may need a better theoretical foundation to do that.

That said, I definitely like the idea of focusing a lot on hands-on projects.