In praise of Truss …

Praise not for our new Prime Minister, about whom the less said the better, but for her admirable logician father John Truss.

By chance, I had occasion recently to dip into his 1997 book Foundations of Mathematical Analysis (OUP) which I didn’t know before and which is excellent. It is my sort of book, in that there is a lot of focus on conceptual motivation and Big Ideas, and a relatively light hand with detailed proofs. E.g. if you want just a very few pages on Gödelian incompleteness, his treatment in the first chapter is exemplary. Or jumping to the end of the book, there is e.g. a really helpful broad-brush section on the ingredients of Gödel’s and Cohen’s independence proofs in set theory, and a very good chapter on constructive analysis and choice principles. In between, we get a story that takes us from the naturals to the integers to the reals to metric spaces and more (e.g. a nice chapter on measure and Baire category). OK, this is a tale which is often told, but I think John Truss’s version is particularly insightful and good at bringing out the conceptual shape of the developing story. So, recommended!

OUP have disappointingly let the book go out of print. A Djvu file can, however, be found at your favourite file depository.

3 thoughts on “In praise of Truss …”

  1. I bought this book during my A-levels and still love it to this day. i actually got Truss to sign my copy when he visited Cambridge!

    It’s an excellent book. I learnt so much from it

  2. I think this is a great book for reasons similar to yours (focus on conceptual motivation and Big Ideas, relatively light hand with detailed proofs).

    OUP seems quite poor at spotting maths / logic books that could attract enough readers that it would be worth making more people aware of their existence, keeping them in print, and issuing them in paperback at a reasonable price — or what passes as a reasonable price these days (£30-40 or thereabouts).

    There are several examples in the Logic Guides series. Some books somehow get through. Awodey’s Category Theory is a £38 paperback; Nies’s Computability and Randomness is £35; Shapiro’s Foundations without Foundationalism is £36.99; Bell’s Set Theory: Boolean-Valued Models and Independence Proofs, £33.49. Bell’s book is quite technical and narrowly focused, though. Why is it available at such a price when Smullyan’s Godel’s Incompleteness Theorems, his Diagonalization and Self-Reference, McLarty’s Elementary Categories, Elementary Toposes, and Hallett’s Cantorian Set Theory and Limitation of Size aren’t?

    Some of the prices are insane! Smullyan’s Godel book is £169.41 on Amazon UK. That’s bad enough. It’s RRP, though, is £225! (Diagonalization and Self-Reference is slightly less expensive.) Hallett’s book is at least available in paperback. At £140. McLarty’s is a paperback at a mere £96.

    What are they thinking?

    It’s especially strange when the hardcovers are print-on-demand technology, not the nicer books there were originally.

    Meanwhile, Smullyan and Fitting’s Set Theory and the Continuum Problem, originally a Logic Guide, is available from Dover at £11.99

    1. I have the Hallett and the Smullyans and very glad I am that I bought them at publication time (or did I get desk copies? can’t remember). I wish they’d sell all of their back catalogue to Dover.

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