Foundations
Everything else in this vault rests on what is here. Before power systems, machine learning, and control theory, there is mathematics, programming, and engineering fundamentals.
These are not prerequisites to be checked off and forgotten. They are living references. The deeper the specialization, the more often you return to the foundation.
Subdisciplines
Programming Foundations
The implementation layer. Data structures, algorithms, software design, and systems programming. Fluency here means being able to build, simulate, and automate anything in the technical stack above it.
Mathematical Foundations
The shared language of every engineering discipline. Calculus, linear algebra, differential equations, probability, complex analysis, and discrete math — each one appears directly in power systems, control theory, machine learning, and signal processing.
Engineering Foundations
The physical principles underlying all of electrical engineering. Circuit theory, electromagnetics, thermodynamics, and systems thinking. Understanding at this level means understanding why the specialized tools work, not just how to apply them.
How These Three Connect
Mathematics
├── Models dynamic systems (ODEs, Laplace)
├── Describes signals and spectra (Fourier, complex analysis)
├── Analyzes networks (linear algebra, graph theory)
└── Quantifies uncertainty (probability, statistics)
Engineering Foundations
├── Applies mathematics to physical systems
├── Translates physics into circuit and field models
└── Establishes the first-principles basis for all EE
Programming Foundations
├── Implements mathematical models computationally
├── Automates analysis and simulation
└── Bridges theory and deployed systems
A Note on Depth
Foundational knowledge has no ceiling. An undergraduate circuit analysis course and a graduate research paper on power system stability both draw from the same circuit theory — at vastly different depths.
Notes here are marked with #status tags to indicate maturity:
#status/seedling— introduced, not yet internalized#status/growing— actively developing, being applied#status/evergreen— stable, reliable, worth referencing
The goal is to keep pushing concepts from seedling to evergreen.
Connects To
Every domain in this vault. Start here, return often.