A mathematical physics degree in paperback form.

Specifically, it's a dense, epic, 1000+ page tome by the physicist Roger Penrose, covering not just the evolving ideas and theories composing our current physical understand of the universe, but the mathematics behind them.

Yes, that's right. The mathematics behind them. Stephen Hawking's A Brief History Of Time famously included just one equation. This is...about as far in the opposite direction as you can go and not call the result a textbook. You'll battle through 400 pages of hyperfunctions, Riemann surfaces, tensor algebra, calculus on manifolds, Lie groups, and fibre bundles, with gratuitous amounts of foreign letters, before you even get to the physics.

On the other hand, this makes it very comprehensive. I was moderately serious about the degree-in-paperback-form thing. Aside from the maths, it covers advanced classical physics with the Lagrangian and Hamiltonian formalisms, Maxwell's electromagnetism, all of relativity and quantum mechanics. It then goes on to cutting edge developments in physics such as superstring theory, supersymmetry, loop quantum gravity, and Penrose's own pet research topic Twistor theory.

I am definitely not qualified to comment on how well all this stuff is presented. Penrose states that "as an expert you may find that there is something to be gained from my perspective on a number of topics, which are likely to be somewhat different (sometimes very different) from the usual ones". As an electrical engineering student, I definitely did learn some new things about Fourier series (a Fourier expansion is equivalent to the Laurent series expansion of an analogous complex function defined on the unit circle!? That's deep. Why don't they teach us this shit?) and electromagnetism (which was presented in tensor or gauge theory form or something which I don't really understand yet...definitely not your traditional Maxwell).

I really don't know how this ended up as a Top Ten Bestseller in The Sunday Times. No one can actually finish this book. I haven't, I'm bogged down in the middle somewhere. My friend who's majoring in mathematical physics claims to have finished it, over the course of a mere five years. His differential geometry lecturer admitted that he couldn't finish it. That's the level we are talking about here. I mean, you might think that A Brief History Of Time or Godel Escher Bach or a Daniel Dennett book on consciousness is hard going...but this is another level.

A lot of people must have bought it, gotten three pages in to where he talks about fractions as equivalence classes of ordered pairs, realised that this book is in fact the opposite of light reading, and placed it permanently on the shelf, where it can look hefty and impart an air of intellectualism on the owner. Just like A Brief History Of Time.

Having said this, I think it's an excellent addition to the library of a curious and mathematically-minded person. You're not going to read it cover-to-cover, but whenever you want to chew on something difficult and profound, it will be there. Makes good reading on the dunny. And if you do, in fact, manage to finish it, you will earn my eternal respect.

Now, where was I up to: "Here R is some compact (p+1) dimensional (oriented) region whose (oriented) p-dimensional boundary (consequently, also compact) is denoted by dR..."