Reviews – Page 4 – Mathemafrica

Faith, Fashion and Fantasy in the New Physics of the Universe, by Roger Penrose – a review

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