As RL points out, the maths is just high school level algebra until page 13. From then on he gets into partial differentiations, which in themselves are only first year undergrad stuff. Of course, once that stuff is developed and builds on itself as in here, then it looks pretty hairy. But it's not when you know the basic rules

The point is that the test of a scientific communicator is his abliity to put the hardest stuff into everyday terms. I am SURE Einstein believed this too - I can't find the reference to back me up right now. But I remember reading his views on teaching and communication and having this viewpoint impressed on me. And, if this means culling the math for the sake of simplicity, so be it. In more advanced stuff like General Rel, the math can't be all discarded, but can in itself be simplified into words for the sake of lay clarity. Jeez, Maths in itself is just highly condensed language, with operational 'buttons to press' for doing clever stuff. General Rel seems to be built up from heaps of partial differentiations connected and developed. These are for getting exact pictures of how the universe looks to you if you move to a very different type of place in the universe - and how you in turn will look to the guy you left behind in your original place.

Teaching Special Rel does NOT need advanced maths, and in fact IS part of the high school physics syllabus. (The more advance partial differentations can be bypassed for teaching purposes). It's always the concepts that are the tough bits to accept in Rel. Here's Special Rel in a nutshell:

1) The speed of light is absolutely constant in flat space only ( ie. away from gravitational sources which distort space and complicate things - General Rel deals with that). It's constant for all observers regardless of how fast or slow they're moving (so long as they're not accelerating or decelerating - again, that comes under GR)

Again, everyday language helps clarify this. Speed of light being absolutely constant means for instance, that any number of people moving at DIFFERENT speeds with respect to each other (even in different directions as well) will still measure the SAME speed for a given light beam. This is completely different from everyday experience, where if for instance we replace the light beam with a moving train, then the train will appear to move at a DIFFERENT speed wr to people depending on whether they're on the ground, or on another train moving in the opposite direction, or in the original train itself (which will then be stationary wr to you). All of those observers are regarded as having equally valid points of view BTW - you can't specifiy an absolutely 'correct' frame of reference, you can only measure the train's motion RELATIVE to some specified observer. That's called Galilean-Newtonian relativity.

Light doesn't work that way - it's a different animal whose motion DOES serve as an absolute reference regardless of the observer's motion (in flat space anyway). The reason for this comes out of Maxwell's work on electromagnetism, which Einstein understood deeply. And yes, it is a good question as to what this implies for the universe as a whole. The immediate result is:

2) If lightspeed is an absolute constant for all (non accelerating) observers, AND the physics of motion must still make sense for all these people regardless of their state, THEN there it must follow that time and space itself can vary for each observer. Why? :

basic physics of motion says speed equals distance travelled divided by time taken. If we have the bizarre case that lightspeed is constant for everyone regardless of their own motion, then we must accept the equally bizarre conclusion that space (or distance travelled) and time taken, will be seen differently by different people. Otherwise they will end up getting different values for lightspeed, which is unacceptable.

So we already see how the nature of light - an ephemeral energy - is connected to things of which we have more direct experience: space and time. Special Rel extends these connections to matter itself, coming up then with E = mc squared. Another bizarre result (a favorite of mine) is that magnetism isn't really a force at all, but actually an effect seen by US, relative to moving electricity (hence, 'electrodynamics'). I can't elaborate on those right now as I don't have the time - and also, because I don't understand them fully well enough to put them into simple English. As I said at the top of this post, THAT is a very good way for a scientist to gauge his familiarity with a topic. And Einstein would definitely agree .. he was a kind man ..