First, the math can be intimidating at the start. Good news! You don't have to learn it all at the start. Take your time. If you can find a good teacher it will all be much easier. Most of the math in a US EE curriculum is taught in parallel with the EE stuff.
I am not familiar with the certificate levels in the UK, but the math involved in the various EE areas in a US undergrad program will cover a pretty fair range. The distinction is going to be how far you want to go, and whether we're talking about "gut" understanding (that looks like a low pass filter) or analytical chops (that's a low pass filter with a cutoff of X Hz).
Better folks than I can talk about the first. For the second category:
1) Algebra is pretty important for passive circuits. It can even get you through things like op-amps. Capacitors and inductors will be a bit of a trick, but Algebra is a good basic start. Nothing fancy -- up to solving quadratics, and enough to understand how to solve simple systems of a few variables.
Along the way, it is useful to gain some understanding of complex numbers and trigonometry. This will come in handy later on. But it won't be necessary for simple circuits without L and C.
Calculus is underneath most of the stuff that follows. (if not all of it). Lots of people get tied up in their shorts here. Calculus may come easy to you, it may not. But the basic notions that come out of it that are important:
- we can manipulate functions that tell us about "qualities" of the functions (ragged, smooth, growing, shrinking, perpetual...)
- we can relate thing A to thing B based on how B is changing
- we can use both of these ideas to understand circuits and systems
2) Linear differential equations is useful -- though there is a cruel joke that gets played on EEs where we learn a "short cut" through most of this. But familiarity with diff-eqs is a foundation that other things get built upon. It has been forty years, but I think I could still solve some simple diff-eqs without losing too much hair.
Diff-eqs come into play with analysis of L-C-R circuits (inductors and capacitors in particular). But then...
3) Laplace Transforms -- this is the punch line of the cruel joke: Laplace transforms are a really useful way to reason about and analyze circuits. They are often introduced after a semester or two of diff-eq based instruction in circuits, almost all of which are easier to analyze in the Laplace domain.
4) Vector Calculus -- this is about as sophisticated as it gets in the undergrad curriculum. The subject is central to really understanding electric and magnetic fields, wave propagation, and "life the universe and everything."
That's most of the trajectory. Some would add in Fourier analysis (useful in communications and other things), probability and statistics (useful in lots of things), and some others. But these seem to be the hammer, screwdriver, pliers kind of tools: algebra, diff-eq/calculus, transforms.
Some might argue that this is all obsolete in the era of simulators. I won't: the math fundamentals are important to the way I think about circuits.
In any case, take your time. For some of us, it took a couple of passes through the material before it really "clicked."
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