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.

http://i1.wp.com/press.princeton.edu/sites/default/files/styles/large/public/covers/9780691149547.png?resize=336%2C480&ssl=1

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.

http://i2.wp.com/press.princeton.edu/sites/default/files/styles/large/public/covers/9780691171920_1.png?resize=316%2C480&ssl=1

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.

http://i0.wp.com/press.princeton.edu/sites/default/files/styles/large/public/covers/9780691175331.png?resize=384%2C480&ssl=1

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

Philosophy of Mathematics, by Øystein Linnebo – A review, by Henri Laurie

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 | August 21st, 2017|Book reviews, Reviews|3 Comments

Unsolved!: The History and Mystery of the World’s Greatest Ciphers from Ancient Egypt to Online Secret Societies by Craig P. Bauer – A review

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 | 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.

http://press.princeton.edu/images/j10953.gif

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 | April 3rd, 2017|Book reviews, Reviews|1 Comment

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

 

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 | 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 | 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 | January 5th, 2016|Book reviews, Reviews|1 Comment