"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.
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.