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.

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

Part 2:
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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:

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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 | 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:

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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 | May 8th, 2018|Uncategorized|3 Comments

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

Review written by Henri Laurie.

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 | May 6th, 2018|Uncategorized|2 Comments

Mathematical Foundations of Quantum Mechanics – By John Von Neumann, edited by Nicholas A Wheeler, a review

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

I have to admit that I was rather embarrassed to encounter this book, as I had never heard of it, and given the topic, and the author, it seemed that it must be one of the canonical texts in the field. However, it turns out that although Von Neumann wrote this book in 1932 (full German text here), it was not translated until 1955 (by Robert Beyer), and this edition aged quickly, particularly with the limitations of typesetting the equations. It wasn’t until now that a modern edition has been put together, by Nicholas Wheeler, and the result is lovely.

The book is really a collection and expansion of Von Neumann’s previously published works, attempting to put quantum mechanics on a firm mathematical footing. The first chapter is dedicated to the equivalence of Matrix Quantum Mechanics, and Schrodinger’s Wave Mechanics.…

By | May 6th, 2018|Book reviews, Reviews|1 Comment

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

Reverse Mathematics – By John Stillwell, 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/9780691177175_1.png?resize=336%2C480&ssl=1

From Princeton University Press

I’m not sure I’ve read a mathematics book which was so hard to review, not because of the quality of the book (which is superb), but because the way of thinking is in some senses so different to the way we normally think about mathematics. This, indeed, is also the book’s best feature. This book gets you thinking about mathematics in ways which I have never explored before, and which have definitely given me a new, and I think, improved perspective on formal mathematics.

In general in mathematics we start with a set of assumptions (axioms), and explore the consequences of them. Within Euclidean geometry we start with ideas about lines, and points, and circles, and then see what other theorems can be proved from these. Within set theory too, we start with a set of ideas about equalities of sets, existence, pairings, unions etc which we hold to be true and then see what can be said of other properties of sets, which are not straightforwardly stated in the axioms.…

By | March 18th, 2018|Uncategorized|1 Comment

Singalakha’s guide to plotting rational functions

To sketch the graph of a function k(x)=\frac{f(x)}{g(x)}:

  1. Find the intercepts:
    1. X-intercepts, set y=0 (there can be multiple)
    2. Y-intercept, set x=0 (there can be only one)
  2. Factorise the numerator and denominator if possible:
    1. Sign table: determine where the function is negative and where it is positive
  3. Find the Vertical asymptotes:
    1. This occur if the function in the denominator is equal to zero, i.e g(x) = 0, AND that in the numerator must not be zero, i.e f(x)\ne 0.
  4. Find any Horizontal asymptote:
    1. If the degree of the function in the numerator, i.e f(x), is less than the degree of the function in the denominator, i.e g(x), then the horizontal asymptote is the line y = 0.
    2. If the degree of the function in the numerator, i.e f(x), is equal to the degree of the function in the denominator, i.e g(x), say for example, the degree of f(x) and g(x) is n for some non-negative n element of integers, then there is a horizontal asymptote.
By | March 15th, 2018|Uncategorized|1 Comment

My vlogging channel

Hi all, I’m not sure if it counts as vlogging, or making maths videos regularly fits into a slightly more niche category, but anyway, I wanted to advertise some videos that I’ve been putting up recently. I’m doing this in an attempt to find a different communication channel with my first year maths class, and so far the videos are getting reasonable feedback. I have a long way to go in terms of making them slick, and I goof up from time to time, but it’s an interesting experience. If you have specific questions that you would like me to discuss in a video. Let me know.

In this video I talk about a method for solving inequalities involving absolute values:

How clear is this post?
By | March 13th, 2018|Uncategorized|2 Comments

A quick introduction to writing mathematics in WordPress using LaTeX

Here are a couple of very useful links about writing mathematics, for new authors of this blog:

I will update this as I find more useful material.

  • Generally I like to use the Visual Tab on the editor here rather than the Text Tab, unless there is some sort of strange formatting in which case I will go in and alter the Text.
  • I usually like to put formulas centrally justified on their own on a line with blank lines above and below.
  • Add Media to upload pictures or gifs and use the Fusion Shortcodes button (to the left of the yellow star in the blue box), to embed Youtube content.

Please let me know if, as an author, there is anything which is unclear about posting here and I will update accordingly.…

By | February 28th, 2018|Uncategorized|0 Comments

Can you find a simple proof for this statement?

I thought more about the last question I added into the addendum of the Numberphile, Graph theory and Mathematica post

It can be succinctly stated as:

(\forall m\in\mathbb{Z}, m\ge 19) (\exists p,q\in\mathbb{Z}, 1\le p,q<m, p\ne q) such that \sqrt{p+m}\in\mathbb{Z} and \sqrt{q+m}\in\mathbb{Z} .

In words:

For all integers m, greater than 19, there are two other distinct positive integers less than m such that the sum of each with m, when square rooted is an integer.

What is the shortest proof you can find for this statement?

How clear is this post?
By | January 17th, 2018|Uncategorized|2 Comments