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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

Prime Suspects – The anatomy of integers and permutations, by Andrew Granville and Jennifer Granville, illustrated by Robert Lewis – a review

NB I was sent this book as a review copy.

From Princeton University Press.

What a spectacular book! I am rather blown away by it. This is a graphic novel written about two bodies discovered by cops in an American city some time around the present day, and the forensic investigation which goes into solving the case, and somehow the authors have managed to make the whole book about number theory and combinatorics.

I have to admit that when I started reading the book I was worried that it was going to have the all-too-common flaw of starting off very simple and then suddenly getting way too complicated for the average reader, but they have managed to somehow avoid that remarkably well.

It is however a book that should be read with pen and paper, or preferably computer by one’s side. As I read through and mathematical claims were made, about prime factors of the integers and about cycle groups of permutations, I coded up each one to see if I was following along, and I would recommend this to be a good way to really follow the book.…

By Jonathan Shock| July 9th, 2019|Book reviews, Reviews|1 Comment

p-values: an introduction (Part 1)

The starting point

This is the first of (at least) 3 posts on p-values. p-values are everywhere in statistics- especially in fields that require experimental design.

They are also pretty tricky to get your head around at first. This is because of the nature of classical (frequentist) statistics. So to motivate this I am going to talk about a non-statistical situation that will hopefully give some intuition about how to think when interpreting p-values and doing hypothesis testing.

My New Car

I want to buy a car. So I go down to the second hand car dealership to get one. I walk around a bit until I find one that I like.

I think to myself: ‘this is a good car’.

Now because I am at a second-hand car dealership I find it appropriate to gather some data. So I chat to the lady there (looks like a bit of a scammer, but I am here for a deal) about the car.…

By Dean Bunce| August 21st, 2019|English, Level: Simple, Undergraduate|0 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

Review: Calculus Reordered

Book title: Calculus Reordered: A History of the Big Ideas
Author : David M. Bressoud

Princeton University Press
Link to the book: Calculus Reordered: A History of the Big Ideas

Discussions on the history of different fields are usually dry, wordy and generally, when you are studying the field, hard to read. This is because they are usually geared towards the general audience, and in doing so most authors tend to strip away the very exciting technical details. I expected the same treatment from the author, but I was pleasantly surprised.

The book contains $5$ chapters, which are the following:

1) Accumulations
2) Ratios of Change
3) Sequences of Partial Sums
4) The Algebra of Inequalities
5) Analysis

Each of these chapters has a central theme that is being covered, but they are not at all disjoint. For instance, the last three contain the history of concepts that would normally be found in a first course for Real Analysis, while the first two are essentially the more applied spectrum to serve as some form of motivation for going through all this trouble, although they can certainly stand on their own.…

By Siphelele Danisa| August 4th, 2019|Uncategorized|1 Comment

First week of lectures

So the first week of lectures has ended. In MAM1000 we have only dealt with sets and functions thus far, but in great detail using set builder and interval notation. In our first tutorial we have even started using parametric equations. The Modulus(Absolute value) Function had been added by the end of the week as well. Modulus function is nice to work with as the answer coming out of it must always be positive. If a variable (x) is shown in modulus it must be its non-negative version for example: if x in itself has a negative value then the value of x after modulus has been applied will be -x as this will then be a positive number. Similarly if x is positive then the output will be x. |x| is how modulus is written. We have now also learned that |x+y|<=|x|+|y|, this is called the Triangle inequality and is very important for future use.…

By Francois Kruger| February 20th, 2016|Uncategorized|2 Comments

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

The best writing on Mathematics, 2021, Edited by Mircea Pitici – a review

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

From Princeton University Press

I’ve been reading this series every year now for the last five years or so, and it never disappoints. Mircea does an amazing job each time at collecting such a diverse ideas, voices, and areas of mathematics, that I usually find the vast majority of them to be exceptional. This year is no different.

The book came out during Covid, and rather aptly starts off talking about the effects on mathematicians of involuntary confinement of one form or another. In fact the very first chapter talks of the work of Poncelet, who was involved in Napoleon’s failed campaign, and subsequently imprisoned in Russia, and of his teacher’s Monge, who studied aspects of projective geometry. It just so happened that the diagram of Monge’s published in the essay was precisely what I had needed for a particular problem that I was working on (though in higher dimensions).…

By Jonathan Shock| October 6th, 2022|Book reviews, Reviews|0 Comments

When least is best, by Paul Nahin – a review

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

From Princeton University Press

For my review of Nahin’s superb book “How to fall slower than gravity”, see here.

While not often taught as a topic with such wide-ranging uses in maths classes, finding the maxima or minima of functions is one of the most important areas in all of applied mathematics. I say this as a practitioner of machine learning, where most of what we do is trying to find the minimum of a loss function, and as a physicist where in quantum field theory, the dynamical equations come from trying to extremise an action. While these areas aren’t discussed in the book (the closest it gets is looking at the classical Euler-Lagrange problem), to get students to think about how useful it is to find the maxima and minima of a function is really a powerful thing.

Nahin takes on this challenge and succeeds in the same way that he succeeded in making the problems in the previous book of his that I reviewed both fascinating and easy to follow.…

By Jonathan Shock| April 23rd, 2022|Book reviews, 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 Jonathan Shock| April 3rd, 2017|Book reviews, Reviews|1 Comment

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