Book Review – Page 3 – Mathemafrica

Ten Great Ideas about Chance – By Persi Diaconis & Brian Skyrms, a review

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

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From Princeton University Press

This book straddles a tricky middle ground, given that it introduces topics from scratch and goes into some very specific details of them in a relatively few pages, before jumping onto the next. On starting to read it, I was skeptical of how this could possible work, but by the end of it I believe that I saw the real utility of a book like this. The audience is quite specific, but for them it will be a gem.

The book covers a huge range of ideas related to chance, from the underlying mathematics of probability, to the psychology of decision making, the physics of chaos and quantum mechanics, the problems inherent in induction and inference and much more besides.

The book is taken from a long-running course at Stanford which the authors taught for a number of years, and they have tried to condense down the most important aspects of it to a relatively light book.…

By Jonathan Shock| December 31st, 2017|Uncategorized|1 Comment

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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

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

Cover page taken from http://press.princeton.edu/titles/10664.html

Roger Penrose is unquestionably a giant of 20th century theoretical physics. He has been enormously influential in diverse areas of both mathematics and physics, from the nature of spacetime to twistor theory, to geometrical structures and beyond. His famous, but perhaps less well-accepted theories on quantum consciousness, the collapse of the wave function, and visible imprints of cyclic cosmologies on our universe are thought-provoking, to say the least.

I will premise this review of his latest book “Faith, Fashion and Fantasy in the New Physics of the Universe” (FFaFitNPotU) with a slight detour to talk about his book “The Road to Reality” (TRtR), as there are some interesting contrasts, and similarities. TRtR, I see as a fascinating attempt to teach a large swathe of mathematics and physics from the ground up (wherever the ground really is). The book is some 1000 pages long, and goes at quite a pace through a number of very complicated topics, but it is enough, I believe, for the keen high school student to get an idea of some of the most important areas of mathematical physics.…

By Jonathan Shock| November 5th, 2016|Book reviews, Reviews|1 Comment

Group Theory in a Nutshell for Physicists, by Tony Zee – A review

I studied group theory for the first time around 15 years ago at the beginning of my PhD. There were six of us in the class, and I found it both a magical, as well as a mysterious subject. We had a great lecturer, but the way that the course was set up, and as a course designed for theoretical physicists, where the tools were more important than the construction of the tools, a lot of ideas were left as mysterious boxes where the right answers were guaranteed so long as the algorithm was correctly followed.

Tony Zee is known for his incredible ability to lead the student on a path from little knowledge, to an intuitive understanding of a topic in a seemingly painless process. His books are not necessarily the most technically rigorous (note that this doesn’t mean that they are wrong, but that the appropriate level of detail is chosen for the new learner such that the overarching ideas aren’t fogged in unnecessarily complication), but they are, in my opinion some of the best texts for taking a learner from nothing, to a working knowledge with which they can perform calculations that I’ve ever come across.…

By Jonathan Shock| September 11th, 2016|Book reviews, Reviews|1 Comment

The Princeton Companion to Applied Mathematics – a review

Disclaimer – I was sent a review copy of this book, upon request.

(Image taken from here).

A detailed review of a book like this is almost impossible, given both the range of topics, as well as the number of authors involved. However, I can attempt to give an overview of the feel and breadth of the book.

As can be seen from the table of contents, this is a book of absolutely vast scope, and such scope has both advantages and disadvantages. Its advantages are simply that it covers so many topics, that almost every aspect of applied mathematics that you could think of is included, from numerical techniques, to cell biology, from the theory of solitons to cosmology, from how to write a book for the general public to science in the media, from complex analysis to graph theory, and so many more areas besides. As such it is an amazing reference to give very useful leads to go into the world of research in applied mathematics.…

By Jonathan Shock| January 5th, 2016|Book reviews, Reviews|1 Comment