Jonathan Shock – Page 10

Finding Fibonacci, by Keith Devlin – a review

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

I have a terrible admission to make. I came to this book with a paltry knowledge of Fibonacci (Leonardo of Pisa). The knowledge that I thought that I had was quickly shown in fact to be incorrect, so I was largely starting with a blank slate (Fibonacci did not discover the Fibonacci sequence, nor would he be terribly happy to know that in the popular psyche, this is what he is famous for).

In fact, this book is not really about Fibonacci (Devlin has another book about him). This is a book about the writing of a book, and about Devlin’s process of uncovering the history and importance of what Fibonacci had accomplished. It is a book about the research of the history of mathematics, and as such, it is a lovely tale: one of fortuitous moments of discovery, and of frustrations of searching for manuscripts.…

By Jonathan Shock| April 28th, 2017|Uncategorized|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

Group Theory (lecture 2) by Robert de Mello Koch

As promised in the previous post, here is the second lecture by Prof Robert de Mello Koch on Group Theory.

Please comment if you have thoughts or questions from this video.

How clear is this post?

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By Jonathan Shock| February 8th, 2017|English|0 Comments

Group Theory (lecture 1) by Robert de Mello Koch

Some ten (and change) years ago, the African Summer Theory Institute (ASTI) took place in Cape Town at UCT. This was a course designed for students to give them a taste of a number of topics related to theoretical physics. These lectures were all recorded, and I watched them at the time, never of course thinking for a moment that I would end up lecturing in the same venue a decade or so later. In particular, I remembered that the lectures by Robert de Mello Koch on Group Theory were some of the most pedagogically clear that I had ever seen. Sadly, the old ASTI website seems to be defunct, but the lectures can all be found on YouTube.

I wanted to start posting some of them here and see if people seem enthusiastic about me posting more. It would be great to have some comments on this post to let me know if you would like more of these, or of course if you have any questions or comments about the material itself.…

By Jonathan Shock| January 19th, 2017|Uncategorized|4 Comments

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

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Checking direction fields

Courses, First year, MAM1000, Undergraduate

Checking direction fields

I was recently asked about how to spot which direction field corresponds to which differential equation. I hope that by working through a few examples here we will get a reasonable intuition as to how to do this.

Remember that a direction field is a method for getting the general behaviour of a first order differential equation. Given an equation of the form:

$\frac{dy}{dx}=f(x,y)$

For any function of x and y, the solution to this differential equation must be some function (or indeed family of functions) where the gradient of the function satisfies the above relationship.

The first such equation that we looked at was the equation:

$\frac{dy(x)}{dx}=x+y(x)$ .

We are trying to find some function, or indeed family of functions y(x) which satisfy this equation. We need to find a function whose derivative (y'(x)) at each point x is equal to the value of the function (ie. y(x)), plus that value of x.…

By Jonathan Shock| October 11th, 2016|Courses, First year, MAM1000, Undergraduate|1 Comment

Cellular Automaton

How clear is this post?

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By Jonathan Shock| October 4th, 2016|Uncategorized|0 Comments

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

Radius of convergence of a series, and approximating polynomials

I hinted today that there were sometimes issues when you did a polynomial approximation, that if you tried to find the value of a function a long way from the region about which you’re approximating, that sometimes you wouldn’t be able to do it. This is related to an idea called the radius of convergence of a series. In the following we are just plotting polynomials, but you can see that whereas in the polynomial approximation for sin(x) (on the right), as we get more and more terms, we approximate the function better and better far away from the point x=1 (which is the point about which we are approximating the function). However, for the function $\sqrt{1+x}$ , after x=3, the approximations are nowhere near the function itself. This is because that function has a radius of convergence of 2, when expanded about x=1. This is due to the behaviour of the function at x=-1, which is a distance 2 away.…