How Behavior Spreads: The Science of Complex Contagions, by Damon Centola, a review

NB. This book was sent to me as a review copy.

 

The idea of this book is relatively simple, but the consequences are huge, and in fact some of the ideas are far more subtle and complex than they may first appear.

Essentially this book is based on a series of experiments which Damon Centola has run, which are all related to changes in behaviour which can be tracked, and made to occur, through a social network (in the broadest sense of the word). This is the study diffusion in a network.

The fundamentals of the research lie on two distinctions: One in the complexity of a contagion/behaviour, meaning how many connections with others who have the contagion/behaviour do you need until you adopt it, and the other in the topology of the social network, meaning loosely, how much like a street where each person only talks to their neighbours, versus a small world-network where there are a lot of disparate connections does the network look like.…

By | August 21st, 2018|Book reviews, Reviews|2 Comments

Calculus for the ambitious, by Tom Korner, a review, by Henri Lauri

Amazon link

This is a lovely book: strong emphasis on ideas; a lively sense of humour; a sure logical touch; historical detail that is accurate, relevant, yet quirky (takes some doing!). What’s not to like?

Well, there’s this: it is not easy to decide whether to recommend the book to anybody who doesn’t already know calculus. I’ll return to that. Let me start by describing why this is such a good book.

Firstly, the light touch and the clarity, which together make it wonderfully accessible. Fans of Tom Korner, including yours truly, will be happy to hear that it it as good as his “The Pleasures of Counting” and “Fourier Analysis”, two of the best books on maths ever. Like them, it discusses applications, social context and history but always in a way that supports the maths, which remains the main focus.

Secondly, the balance between rigour and intuition is superbly judged and maintained.…

By | June 20th, 2018|Book reviews, Reviews|0 Comments

Music by the Numbers, From Pythagoras to Schoenberg – By Eli Maor, a review

NB. I was sent this book as a review copy.

Music by the numbers leads us on a journey, as stated in the title, from Pythagoras to Schoenberg. In many ways the endpoint is stated early on, giving us clues that a revolution in mathematical thinking about musical scales will be encountered in the early twentieth century. Indeed the journey through musical practice, mathematics, physics and the biology of hearing is woven rather beautifully together, giving the account of our step by step explorations of tonal systems and their links to the physics of vibration. The development of calculus and the triumph of Fourier take as from the somewhat numerological and empiric realms of musical experimentation to the age of a true understanding of timbre – the way different instruments express harmonics and their overtones in different admixtures. A lot of emphasis is placed on the development of scales based on subtly different frequency ratios, which were developed over the years (particularly within European music, non-European music being given only very brief comment) to balance the physical, mathematical and aesthetic qualities of the various possible tunings of instruments.…

By | June 2nd, 2018|Book reviews, Reviews|1 Comment

What can be computed? A practical guide to the theory of computation – by John MacCormick, a review

NB. I was sent this book as a review copy.

It’s not often that a textbook comes along that is compelling enough that you want to read it from cover to cover. It’s also not often that the seed of inspiration of a textbook is quoted as being Douglas Hofstadter’s Pulitzer prize-winning book Godel, Escher Bach. However, in the case of “What can be computed”, both of these things are true.

I am not a computer scientist, but I have spent some time thinking about computability, Turing machines, automata, regular expressions and the like, but to read this book you don’t even need to have dipped your toes into such waters. This is a textbook of truly outstanding clarity, which feels much more like a popular science book in terms of the journey that it takes you on. If it weren’t for the fact that it is a rigorous guide to the theory of computability and computational complexity, complete with a lot of well thought through exercises, formal definitions and huge numbers of examples, you might be fooled by the easy-reading nature of it into thinking that this book couldn’t take you that far.…

By | May 27th, 2018|Book reviews, Reviews|1 Comment

On Gravity, a brief tour of a weighty subject – By Tony Zee, a review

NB. I was sent this book as a review copy.

In the era when our eyes are being opened to the Universe in the gravitational spectrum via the recent gravitational wave observations, this book is exactly what is needed to communicate to the general public the beauty and depth of Einstein’s theory of gravity, as well as the interplay between gravity and quantum mechanics which takes place at the event horizon of a black hole.

Starting with the observations of merging black holes black in 2016, Tony Zee takes the reader on a clear and swift journey through the ideas of the incredible weakness of gravity, the basics of field theory, relativity, curved space-times, quantum weirdness, black holes and Hawking radiation, back, full circle to the consequences of General Relativity including the existence of gravitational waves and the detectors now observing them and those which will give us a far clearer picture of the gravitational universe in the near future.…

By | May 27th, 2018|Book reviews, Reviews|1 Comment

Mathematical Foundations of Quantum Mechanics – By John Von Neumann, edited by Nicholas A Wheeler, a review

NB. I was sent this book as a review copy.

I have to admit that I was rather embarrassed to encounter this book, as I had never heard of it, and given the topic, and the author, it seemed that it must be one of the canonical texts in the field. However, it turns out that although Von Neumann wrote this book in 1932 (full German text here), it was not translated until 1955 (by Robert Beyer), and this edition aged quickly, particularly with the limitations of typesetting the equations. It wasn’t until now that a modern edition has been put together, by Nicholas Wheeler, and the result is lovely.

The book is really a collection and expansion of Von Neumann’s previously published works, attempting to put quantum mechanics on a firm mathematical footing. The first chapter is dedicated to the equivalence of Matrix Quantum Mechanics, and Schrodinger’s Wave Mechanics.…

By | May 6th, 2018|Book reviews, Reviews|1 Comment

An Introduction to analysis – By Robert G Gunning, a review

NB. I was sent this book as a review copy.

While this book is called An Introduction to Analysis, it contains far more than one might expect from a book with such a title. Not only does it include extremely clear introductions to algebra, linear algebra, intregro-differential calculus of many variables, as well as the foundations of real analysis and beyond, building from their topological foundations, the explanations are wonderfully clear, and the way formal mathematical writing is shown will give the reader a perfect guide to the clear thinking and exposition needed to go on to further areas of mathematical study and research. I think that for an undergraduate student, taking a year to really get to grips with the content of this book would be absolutely doable and an extremely valuable investment of their time. While a very keen student would, I think, be able to go through this book by themselves, as it truly is wonderfully self-contained, if it were used as part of a one year course introducing mathematics in a formal way, I think that this really would be the ideal textbook to cover the foundations of mathematics.…

By | May 5th, 2018|Book reviews, Reviews|2 Comments

The Probability Lifesaver – by Steven J. Miller, a review

NB. I was sent this book as a review copy. In addition, I lent this book to a student studying statistics, as I thought that it would be more interesting for them to let me know how much they get out of it. This is the review by Singalakha Menziwa, one of our extremely bright first year students.

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From Princeton University Press

All the tools you need to understand chance, the insight of statistics at base, and more complex levels. Statistics is not just about substituting into the correct formulae but requires understanding of what the numbers mean. Counting rules and Statistical inference were two of the topics I struggled with, especially the logic behind statistical inference, but this book provided great insight and explanations regarding these topics with a step by step procedure and gave enough interesting exercises. Miller’s goal when writing the book was to introduce students to the material through lots of accurately done, in depth worked examples and some fascinating coding for those who want to get more practical, to have a lot of conversations about not just why equations and theorems are true, but why they have the form they do.…

By | October 20th, 2017|Book reviews, Reviews|1 Comment

The Mathematics of Various Entertaining Subjects, Volume 2- edited by Jennifer Beineke and Jason Rosenhouse, a review

NB. I was sent this book as a review copy.

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From Princeton University Press

I tell my first year students that whether or not they will use their first year maths directly in the future, taking a course in mathematics is like going to a gym for your brain. Unless you are doing some good mental sweating, you are not benefiting from the study. It should be a subject in which you grow by gently (or not) applying more and more intellectual pressure to your thought patterns, and over time you will find that you can understand more complicated, or more abstract concepts than you ever thought that you could before. This translates into solving problems which may not have anything to do with maths, but require a similar pattern of logical juggling.

This book (The Mathematics of Various Entertaining Subjects, Volume 2) feels like Crossfit for the mathematics world. It’s a book filled with strength, endurance, flexibility and power exercises, each of which will stretch you in different ways.…

By | October 15th, 2017|Book reviews, Reviews, Uncategorized|3 Comments

The Seduction of Curves – by Allan McRobie, a review

NB. I was sent this book as a review copy.

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From Princeton University Press

This is a beautiful book, it is a thought-provoking books and it is an informative book.  It really is the intersection of mathematics, nature and art, and explores the three themes via the language of Catastrophe Theory, the theory by René Thom which aims to classify the possible folds in the solution space of natural systems and their two dimensional projections.

The book starts by introducing the alphabet of curves from the image of the human body, its curves and crevasses, its osculations and puckerings and from this alphabet it branches out to study the universe of catastrophes in the natural world.

As a fan/devotee/obsessive of atmospheric optics, the fold catastrophe which occurs in the production of the rainbow was bound to appeal to me. As Rene Descartes said in 1673:

A single ray of light has a pathetic repertoire, limited to bending and bouncing (into water, glass or air, and from mirrors).

By | October 1st, 2017|Book reviews, Reviews|1 Comment