Reviews – Page 3 – Mathemafrica

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 Jonathan Shock| 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.

From Princeton University Press

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 Jonathan Shock| 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.

From Princeton University Press

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 Jonathan Shock| 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.

From Princeton University Press

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 Jonathan Shock| May 5th, 2018|Book reviews, Reviews|2 Comments

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

Book reviews, Reviews

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 Jonathan Shock| 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 Jonathan Shock| 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 Jonathan Shock| October 1st, 2017|Book reviews, Reviews|1 Comment

From http://press.princeton.edu/titles/11024.html

This book was sent to me by the publisher as a review copy.

PHILOSOPHY OF MATHEMATICS OR PHILOSOPHY FOR MATHEMATICS? By Henri Laurie.

Review of Øystein Linnebo’s “Philosophy of Mathematics”, Princeton University Press, 2017. (This one is impressionistic; I hope to present a more conventional summary-of-contents review in due course).

I’ve just read Øystein Linnebo’s superb book on the philosophy of mathematics. It is very, very good. Superbly clear, concise, well organised, it gives not only a very accessible introduction but also takes the reader all the way to the cutting edge of what philosophers are doing in the philosophy of mathematics. Above all, Linnebo writes as a fully engaged philosopher and makes his preferred choice of philosophical position clear. But this is no mere polemic: I felt he clearly and forcefully presents the strengths and weaknesses of all the philosophical positions he discusses.

That said, even an introductory text in philosophy these days is not always easy reading.…

By Jonathan Shock| August 21st, 2017|Book reviews, Reviews|4 Comments

from Princeton University Press.

This book was sent to me by the publisher as a review copy.

This is a book of some impressive magnitude, both in terms of the time span that it covers (being millennia), as well as the ways in which it discusses the context and content of the ciphers, most of which, as the title suggests, are unsolved. The book starts with perhaps the most mysterious of all unbroken ciphers: The Voynich Manuscript (the entirety of which can be found here). This story in itself is perhaps the most fascinating in the history of all encrypted documents, and that we still don’t know if it truly contains anything of interest, or is just a cleverly constructed (though several hundred year old) hoax makes it all the more intriguing.

The writing rather effortlessly weaves between the potential origin stories, the history of the ownership of the manuscript and the attempts to decode it.…

By Jonathan Shock| July 29th, 2017|Book reviews, English, Level: Simple, Reviews|1 Comment

The best writing on mathematics 2016, edited by Mircea Pitici – a review

This book was sent to me by the publisher as a review copy.

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It is not easy to write a review for an anthology of writings, but I think that in such cases what is best discussed is the choice of writing and its range, both topically and in terms of level. In this case we have some 30 short essays, covering a huge range of topics, as well as a real breadth of complexity. I will highlight some of my particular favourites, though I should say from the outset that I really enjoyed reading just about everything in this book. There were perhaps two or three posts which didn’t resonate with me, but out of 30, that is pretty good, given my personal tastes.

The collection starts with a lovely essay discussing the interplay between the teaching, and the practice of mathematics, and in particular the role of rigour, formality and proof in these two somewhat separate directions.…

By Jonathan Shock| April 3rd, 2017|Book reviews, Reviews|1 Comment

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