Saturday, 22 July 2017

Michael Spivak: Calculus (1967)

Edition: Addison-Wesley (World Student Series)
Review number: 1506

Calculus was the very first textbook I read for my university degree. As well as being a fine description of the basics of analysis (mostly real, with a toe in the deep water of complex functions), it is an excelent book to ease the transition from mathematics as taught at school level to the rigours of university mathematics.

Unlike many writers of textbooks in mathematics, Spivak makes a big effort to give more than a dry exposition: theorem - proof - next theorem etc. Considerable attention is paid to motivating the discussion, showing why each result is important (though mainly in the pure mathematics context, applications of calculus being mainly found in the problems at the end of each chapter). Of especial use to the budding mathematician are the points where Spivak discusses potential proof strategies for the theorems, often explaining the pitfalls that student taking a naive approach could fall into. There are even occasional jokes, both in the text and the index.

For students with an interest in how analysis can be used in apparently unrelated parts of mateematics, a number of advanced sections give proofs of such topics as the transcendence of the number e, and a construction of the real numbers from set theoretic principles.

Calculus was not just the first university textbook I read, but one of the best.

My rating: 10/10.

Monday, 30 January 2017

Alexander Broadie: Introduction to Medieval Logic (1993)

Edition: Oxford University Press, 1993
Review number: 1505

The title is perhaps somewhat misleading. I would expect that a book introducing medieval logic should be fairly easy to follow for someone like myself, with a doctorate in modern mathematical logic and an interest in medieval philosophy. But the first few chapters assume a fair amount of prior understanding of the form of logic used in the middle ages, i.e. one based on natural language rather than symbolic representation of carefully pre-defined and abstract ideas of such ideas as truth, implication, proof and so on (this, the basis of modern mathematical logic, being the legacy of Frege and others such as Russell, Tarsky, and Gödel).

In fact, what is eventually revealed is a way to relate the arguments of medieval logicians, which can seem weird and monumentally pedantic, to a process which moves from the potential ambiguities of natural language towards more abstract understanding of the processes of logic. No matter how interesting that might be to me, though, the path travelled through mainly fourteenth century logical arguments is one I found hard to follow. For me, the best part of the book is the concluding chapter, in which Broadie discusses the transition from scholastic logical thought to humanistic ideas of proof, more based on rhetoric and Ciceronian legal arguments, and the relation of scholasticism to the ideas of modern mathematics.

I would have welcomed a lot more historical context, and also some way to connect the thematically organised discussion to that context

My rating: 5/10.

Tuesday, 3 January 2017

Patrick Dennis: Auntie Mame (1955)

Edition: Pan, 1958
Review number: 1504

I'm a big fan of Patrick Dennis, although the difficulty of finding his books nowadays means I haven't read all that many of them - three out of sixteen (all published under various pseudonyms, his real name being Edward Everett Tanner III). Even the normally reliable Fantastic Fiction only lists the two Auntie Mame books.

This is the third of his books, the first under this name, and was hugely successful in the fifties, made into a play and then an Oscar nominated film with Rosalind Russell as the title character. The trailer for the film describes it as "the one you've been waiting for", and expects the watcher to guess the name of the title character. So this was a huge phenomenon at the time, and yet it seems to be almost forgotten today. (It later became a stage musical and another film.)

It is a parody of an autobiography, scenes from a bizarre Bohemian childhood. The narrator, named as Patrick Dennis, is sent as a nine year old to be brought up by his aunt after the death of his father. This catapults the boy into a completely different world - one which many today would still consider unsuitable for the raising of a child. In her company, he expands his vocabulary, meets a lot of strange people, and gets involved in many scrapes, as he becomes an integral part of his vivacious aunt's life. The last scene in the book depicts Patrick, now married and respectable, being persuaded by Mame to let his seven year old son join her on a trip to India: although the book's chronology would indicate that she was by this point in her seventies, she had not changed a bit. This also sets up Dennis' second novel, Around the World with Auntie Mame.

Auntie Mame and its sequel are lit up by the  larger than life character of Mame. I can easily imagine that she would be tiresome in the long term in real life. Indeed, the portrayal by Rosalind Russell in the film is wearingly strident to me, even in the short dose of the trailer. The literary version of the character has a lot more charm, and her dominance of the book makes liking Mame crucial to enjoyment of the humour.

It's easy to see why it was so popular. It's still immensely funny, and bears comparison with the best comic fiction ever written. Why, then, is it so much less well known today? Dennis himself stopped writing and became a butler before his death in 1976, but already by then his books were out of print. It is possible that revelations about the author's lifestyle (he was bisexual and was involved in the Greenwich Village gay community) made publishers less keen to promote his work. Indeed, a number of publishers rejected Auntie Mame, presumably because of its endorsement of an unconventional lifestyle, tame though much of it seems today. Maybe it was the opposite: in the liberated 1970s, did people no longer feel shocked enough by Dennis' writing to want to read it? I don't know what happened, but whatever it was, Patrick Dennis was too good a writer to deserve it.

My rating: 10/10.