Jonathan Shock – Page 6

About Jonathan Shock

I'm a lecturer at the University of Cape Town in the department of Mathematics and Applied Mathematics. I teach mathematics both at undergraduate and at honours levels and my research interests lie in the intersection of applied mathematics and many other areas of science, from biology and neuroscience to fundamental particle physics and psychology.

The Recamán sequence

In case you have watched the following video about the Recamán sequence.

and want to play around with it in Mathematica. Here is my code for doing so:

nums = {0};

For[i = 1, i < 66, i++,
If[nums[[-1]] – i > 0 && Position[nums, nums[[-1]] – i] === {}, nums = Append[nums, nums[[-1]] – i],
nums = Append[nums, nums[[-1]] + i]]
]

{{#[[1]], 0}, #[[2]]} & /@ Partition[Riffle[Mean[#] & /@ Partition[Riffle[nums, nums[[2 ;;]]], 2],
Abs[Differences[nums]]/2], 2];

Show[Show[
Table[Graphics[Circle[%[[i, 1]], %[[i, 2]], {(i) \[Pi], (i + 1) \[Pi]}]], {i, Length[%]}], ImageSize -> 1000], Plot[0, {x, 0, 91}],
Axes -> True]

(You may have to copy this by hand rather than copy/paste.)

This produces the following rather beautiful graphic (and answers the question posed in the video):

Evidence away my dear Watson…evidence away.

How clear is this post?

…

By Jonathan Shock| June 14th, 2018|Uncategorized|0 Comments

Music by the Numbers, From Pythagoras to Schoenberg – By Eli Maor, a review

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

From Princeton University Press

Music by the numbers leads us on a journey, as stated in the title, from Pythagoras to Schoenberg. In many ways the endpoint is stated early on, giving us clues that a revolution in mathematical thinking about musical scales will be encountered in the early twentieth century. Indeed the journey through musical practice, mathematics, physics and the biology of hearing is woven rather beautifully together, giving the account of our step by step explorations of tonal systems and their links to the physics of vibration. The development of calculus and the triumph of Fourier take as from the somewhat numerological and empiric realms of musical experimentation to the age of a true understanding of timbre – the way different instruments express harmonics and their overtones in different admixtures. A lot of emphasis is placed on the development of scales based on subtly different frequency ratios, which were developed over the years (particularly within European music, non-European music being given only very brief comment) to balance the physical, mathematical and aesthetic qualities of the various possible tunings of instruments.…

By Jonathan Shock| June 2nd, 2018|Book reviews, Reviews|1 Comment

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Kovalevskaia research grants for female mathematicians in Southern African region

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Kovalevskaia research grants for female mathematicians in Southern African region

How clear is this post?

…

By Jonathan Shock| May 28th, 2018|Advertising|0 Comments

What can be computed? A practical guide to the theory of computation – by John MacCormick, a review

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

From Princeton University Press.

It’s not often that a textbook comes along that is compelling enough that you want to read it from cover to cover. It’s also not often that the seed of inspiration of a textbook is quoted as being Douglas Hofstadter’s Pulitzer prize-winning book Godel, Escher Bach. However, in the case of “What can be computed”, both of these things are true.

I am not a computer scientist, but I have spent some time thinking about computability, Turing machines, automata, regular expressions and the like, but to read this book you don’t even need to have dipped your toes into such waters. This is a textbook of truly outstanding clarity, which feels much more like a popular science book in terms of the journey that it takes you on. If it weren’t for the fact that it is a rigorous guide to the theory of computability and computational complexity, complete with a lot of well thought through exercises, formal definitions and huge numbers of examples, you might be fooled by the easy-reading nature of it into thinking that this book couldn’t take you that far.…

By Jonathan Shock| May 27th, 2018|Book reviews, Reviews|1 Comment

On Gravity, a brief tour of a weighty subject – By Tony Zee, a review

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

From Princeton University Press

In the era when our eyes are being opened to the Universe in the gravitational spectrum via the recent gravitational wave observations, this book is exactly what is needed to communicate to the general public the beauty and depth of Einstein’s theory of gravity, as well as the interplay between gravity and quantum mechanics which takes place at the event horizon of a black hole.

Starting with the observations of merging black holes black in 2016, Tony Zee takes the reader on a clear and swift journey through the ideas of the incredible weakness of gravity, the basics of field theory, relativity, curved space-times, quantum weirdness, black holes and Hawking radiation, back, full circle to the consequences of General Relativity including the existence of gravitational waves and the detectors now observing them and those which will give us a far clearer picture of the gravitational universe in the near future.…

By Jonathan Shock| May 27th, 2018|Book reviews, Reviews|1 Comment

Advice for MAM1000W students from former MAM1000W students – part 5

While I resisted Mam1000W every single day, I even complained about how it isn’t useful to myself. Little did I know when it all finally clicked towards the end that even though I wasn’t going to be using math in my life directly, the methodology of thinking and applying helps me to this day.

Surviving Mam1000W isn’t really a miraculous thing. While everyone tends to make it seem like it’s impossible, it is challenging (Not hard) and I said that because I have seen first-hand that practice makes it better each time. Getting to know the principles by actually doing the tuts which is the most important element of the course in my opinion will make sure that even though you feel like you aren’t learning anything when the time comes (usually 2nd semester) it will all click on how you actually are linking the information together.

Another important aspect is playing the numbers game.

…

By Jonathan Shock| May 14th, 2018|Courses, First year, MAM1000, Undergraduate|1 Comment

Advice for MAM1000W students from former MAM1000W students – part 4

In high school, as I believe was the case for many students, there wasn’t much incentive to work very hard regularly on math – concepts were easy to grasp first hand in class. That’s the kind of attitude I brought towards MAM1000W last year (2017). Unfortunately things didn’t turn out as anticipated…by as early as April I had already started playing “catch-up” for I hadn’t been putting in any practice on the staff done in class. Tests were nightmares. With every course demanding its share of my attention, I found myself crying the other day alone in my room, asking myself, “what went wrong?”. Well, the answer was pretty simple – EVERYTHING.

Eventually, I figured a way to potentially get back on my feet – I became a very good friend of my WebAssign voluntary quizzes. In combination with past papers (WHICH I HIGHLY RECOMMEND) and the daily uploaded ‘practice questions and solutions’, I was able to gain back some bit of confidence.

…

By Jonathan Shock| May 9th, 2018|Uncategorized|0 Comments

Advice for MAM1000W students from former MAM1000W students – parts 2 and 3

Part 2:

——-

So one thing that really helped me was having a partner in tuts. We would do the tuts as far as we could and we would then try to help one another in the tuts and ask the tutors for help if there was a difference in opinion.

Another thing that helped studying, going through past papers and tuts were so important.

If I was ever stuck and couldn’t really understand the textbook I would go on YouTube and watch a guy named Professor Leonard. He’s videos are super long but extremely helpful and worth your time.

And last but not least, it’s important that you try your best to work everyday with maths because once you fall behind its difficult to catch up. Even if you do just one problem a day I promise it will help In the future.

and part 3:

——

I would suggest to MAM1 students that they should not fall behind the maths syllabus if they have tests in other subjects because it is very difficult to catch it up and requires much more effort than one thinks.…

By Jonathan Shock| May 8th, 2018|Uncategorized|1 Comment

Advice for MAM1000W students from former MAM1000W students – part 1

This is the first in a series of posts where I will be putting up the sage words of advice of former MAM1000W. Often, these students struggled their way through the course, before making a breakthrough in their study methods. I hope that maybe it will be easier to listen to students who have been through the struggle, than the advice of lecturers who seem to know it all (though I promise you, we do not!).

Here is the first:

——-

As an Actuarial Science student I was aiming for 70% last year. I clearly remember that at orientation I asked some of the older ActSci students at orientation what they had done when they scored below what they needed to. I was so shocked, and a little scared when the group I asked said they never had. I wasn’t worries at this stage though because I thought I’d done well at maths at school, and I’d do well at maths here.…

By Jonathan Shock| May 8th, 2018|Uncategorized|4 Comments

Hypatia, The Life and Legend of an Ancient Philosopher – by Edward J. Watts, a review by Henri Laurie

Review written by Henri Laurie.

From Oxford University Press

This is an important book for anybody interested in the history of mathematics and in the history of women intellectuals.

To recap very briefly: Hypatia is well-known as the mathematician/philosopher who was murdered by a Christian mob in 415 CE in Alexandria. She is one of the best-attested woman philosophers in the Greek tradition.

Watts turns this on its head: he tells the story of a life, one of singular achievement, and one in which the manner of death is not the most important part. The picture he paints is of a very remarkable woman, who became the head of her father’s school at a relatively young age and came to dominate the scholarly activity of her city, at the time one of the three most important centres of learning in the Mediterranean.

It is important to realise that although women did study philosophy at the time, and therefore also mathematics, which was seen as preparation for philosophy, very few of them were able to continue well into adulthood.…

By Jonathan Shock| May 6th, 2018|Uncategorized|2 Comments

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