Measuring up

The paucity of original mathematics books in a country famed for its mathematicians is something that we have learned (with some sadness) in the few years that SwB has been in operation. Its not just mathematics- in the sciences, the situation is just as bad. Or maybe worse. The reasons are many- prime among them being that journal articles- and not books- are the usual mode of transmission of original research in the sciences, as opposed to, say, history or economics or philosophy. Be that as it may, the lack of good texts is both undeniable and worrisome...

It is not all bleak, though. There is a tremendously good series of high level, high quality books in Mathematics published by the Hindustan Book Agency in Delhi. Texts and Readings In Mathematics or TRIM has Rajendra Bhatia as managing editor, and in the ten or so years that they have been publishing, have brought out over 50 books of superb quality, both in the mathematics as well as the production value.

One area where there have been a number of rather good books is Measure Theory. An outstanding text is K R Parthasarathy's Introduction to Probability and Measure, 33 in the TRIM series. (According to a remark attributed to Mark Kac, probability theory is measure theory with a soul!) Those who have had the fortune to be taught by KRP will know that this book captures his meticulous style: it is a masterly exposition by a master.

Also in the same series is Measure Theory by Krishna Athreya and Soumendra Lahiri, both professors in the US. The book is written with the MSc or PhD student in India in mind, though- presenting measure and integration theory in a self-­contained and step by step manner. A modern presentation of the subject, this book includes a large number of exercises that should prove very useful to teachers and students in mathematics, statistics and related fields.

Universities Press in Hyderabad, is another publishing house that does something to alleviate the problem of the lack of original texts. Addressing, along the way, the lack of a strong University press tradition in the country (when, if ever, will we have the likes of an Oxford or Cambridge University Press? Probably when we have the likes of Oxford or Cambridge....) they have been bringing out a number of publications in the sciences, both original books as well as reprints. (We did a post about their Maths Olympiad books some time ago.)

Recently they published Measure and Probability by Siva Athreya and V Sunder, another fine addition to the field from two of the best. Among the highlights of the book are a thorough coverage of the fundamentals, a discussion of real as well as complex measures, Lp spaces, Radon–Nikodym theorem and the Riesz representation theorem. The elements of probability theory (random variables, distributions, independence, product measures spaces), discrete time Markov chains, the Riesz representation theorem and the law of large numbers and the central limit theorem are presented.

All in our Mathematics section. Great value.