A very good account of algebraic-number theory, a branch of mathematics whose genesis was motivated by the search for a proof of Fermat’s last theoremA very good account of algebraic-number theory, a branch of mathematics whose genesis was motivated by the search for a proof of Fermat’s last theorem, as well as a brief discussion of the ideas used by Andrew Wiles for his Wolfskehl Prize winning proof. I thought the theory of ideals could be developed a bit further, but I understand that the central theme of the book is on FLT....more
An introduction to the life and teachings of Shakyamuni Buddha, supplemented by the author’s personal experiences of the spirit world – highly absorbiAn introduction to the life and teachings of Shakyamuni Buddha, supplemented by the author’s personal experiences of the spirit world – highly absorbing....more
A little boy meets a convict on the run in the marshes. Feeling sorry for the starving man, he brings him some food. Little does little Pip know thatA little boy meets a convict on the run in the marshes. Feeling sorry for the starving man, he brings him some food. Little does little Pip know that this little act of kindness is to shape the entire course of his life as he grows up, comes into a mysterious fortune, falls in love with the beautiful but distant Estella, and learns all sorts of valuable lessons that life as a young gentleman has to teach him....more
An excellent introduction to a fascinating area of abstract algebra. The style is somewhat unconventional but the treatment is rigorous. The crucial tAn excellent introduction to a fascinating area of abstract algebra. The style is somewhat unconventional but the treatment is rigorous. The crucial theme throughout is uniqueness of factorization: it holds for the rational integers (a subring of the rational numbers) and the Gaussian integers (a subring of the rational complex numbers), but for which other algebraic integers – subrings of other algebraic-number fields – does it also hold? The journey takes the reader to the fundamental theorem of ideal theory and culminates with Kummer’s proof of Fermat’s last theorem (still only a conjecture at the time of publication of the book) in certain special cases....more
It may be everybody’s favourite children’s book. Not mine, I’m afraid. The author himself described his work as “a book of nonsense” – and I totally aIt may be everybody’s favourite children’s book. Not mine, I’m afraid. The author himself described his work as “a book of nonsense” – and I totally agree. But there may be something behind all the nonsense. In one episode of the J series of QI XL, Stephen Fry proposes the “dubious theory” that “Alice in Wonderland is not a children’s fantasy story, but a satire on Victorian mathematicians. … Carroll disliked the way maths was becoming more abstract,” and a number of scenes in the book “typified modern mathematics as nonsense.” (https://www.comedy.co.uk/tv/qi/episodes/10/13/) Even if this is true, I must say – as a mathematician myself – that the whole satire is lame: I just do not see any resemblance between the nonsense in the book and the abstract mathematics that Lewis Carroll didn’t like....more
Excellent treatment of the subject, very comprehensive for such a small volume. Though may be a bit technically demanding for the complete beginner toExcellent treatment of the subject, very comprehensive for such a small volume. Though may be a bit technically demanding for the complete beginner to existentialism, it is a richly rewarding read for those who already know something about this rather underrated area of philosophy and wish to know more....more
Well written, with excellent material being discussed in understandable language, but not very well presented in layout. The long chapters (each aboutWell written, with excellent material being discussed in understandable language, but not very well presented in layout. The long chapters (each about thirty pages) could have been broken down into bite-sized sections, making material easier to digest....more
Most well planned, with all plots slotting into place and no loose ends to tidy up, Bleak House is among Dickens’s novels what Hamlet is among ShakespMost well planned, with all plots slotting into place and no loose ends to tidy up, Bleak House is among Dickens’s novels what Hamlet is among Shakespeare’s plays....more