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.
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Book reviews

 

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By | January 17th, 2018|Uncategorized|0 Comments
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The Strength in Numbers: The New Science of Team Science – By Barry Bozeman & Jan Youtie, a review

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

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From Princeton University Press

If you want insights into what makes a good collaboration dream-like and a bad collaboration nightmarish, this is the book for you.

In short, The Strength in Numbers details an extremely important piece of research, with reference to many other studies, which aims to analyse collaborations within STEM, and figure out not only measures of collaboration effectiveness, but also ways to make your own collaborations more likely to succeed.

Academia is a funny old game, where there is extensive training in certain aspects of the job (the fundamental tools of science, for instance), and others are left to the researcher to try and piece together as they go along. Some obvious and frequent examples of these are:

  • How to write and give talks effectively
  • How to mentor young researchers
  • How to best disseminate your own knowledge

and perhaps most importantly, how to create an effective collaboration.…

By | January 16th, 2018|Uncategorized|1 Comment
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Graph Theory, Numberphile and Mathematica

Edit: I made a mistake with some of the language here. A comment from a true graph theorist:

“Hamiltonian” usually means there’s a hamilton/hamiltonian cycle. Graphs with a hamilton path are “traceable”. Hamiltonian implies traceable, but not conversely.

Thus, I have edited below accordingly.

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There was a nice video up on Numberphile about a problem which could easily be explained to a school student, and yet we don’t yet know the answer to it. See the videos here:

and

The game is the following: Given a sequence of consecutive integers, draw a graph where the nodes are the integers and there is an edge between each integer if their sum is a square number.

If we take the numbers from 1 to 12, then the following would be the associated graph (note that there are three disconnected pieces of it).

graph12Note that this is a disconnected, undirected graph. Looking at some of the edges.…

By | January 15th, 2018|Uncategorized|1 Comment
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Welcome to Mathemafrica

If you’re here from Juan Klopper’s YouTube channel, then welcome! If you’re not, then welcome!

I wanted to point new readers to a few of the different types of posts that we have here on Mathemafrica. Please, if there are some topics that you would like us to write about, let us know. We’re always happy to produce new content and especially to have new writers (if you enjoy writing about mathematics and are in Africa or have links to Africa, then let us know in a comment and we can sign you up as a contributor).

Here are some links to some of the types of posts that you will find on Mathemafrica:

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By | January 8th, 2018|Uncategorized|0 Comments
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Ten Great Ideas about Chance – By Persi Diaconis & Brian Skyrms, a review

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

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From Princeton University Press

This book straddles a tricky middle ground, given that it introduces topics from scratch and goes into some very specific details of them in a relatively few pages, before jumping onto the next. On starting to read it, I was skeptical of how this could possible work, but by the end of it I believe that I saw the real utility of a book like this. The audience is quite specific, but for them it will be a gem.

The book covers a huge range of ideas related to chance, from the underlying mathematics of probability, to the psychology of decision making, the physics of chaos and quantum mechanics, the problems inherent in induction and inference and much more besides.

The book is taken from a long-running course at Stanford which the authors taught for a number of years, and they have tried to condense down the most important aspects of it to a relatively light book.…

By | December 31st, 2017|Uncategorized|1 Comment
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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.

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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
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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
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Missing lectures after writing a challenging test – thoughts from a recent MAM1000W student

The following is by one of the current undergraduate tutors for MAM1000W, Nthabiseng Machethe, who has been providing me with extremely useful feedback and her thoughts on the course from the perspective of a recent student of it. She wrote this to me after a lot of students were disappointed with their marks from the last test.

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This is based on my perspective as a student. I always plan to attend lectures, however as the work load increases and exhaustion kicks in, it is difficult to keep up with the plan.

It is easy to think of the things one may want (like excelling in MAM1000W) but realistically, it is hard to achieve them. In most instances, you find that students are studying a certain concept with a short term vision (passing a test), which can give one instant gratification but may not sustain in the long run (exam). Hence, one tends to quarrel about the time spent studying for the test not equating to the marks.…

By | October 1st, 2017|Courses, First year, MAM1000, Undergraduate|1 Comment
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The Seduction of Curves – by Allan McRobie, a review

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

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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).

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By | October 1st, 2017|Book reviews, Reviews|1 Comment
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2017 2/3rds numbers game

This is the fourth year that I’ve played the 2/3rds numbers game with my first year maths class. I’m always interested to see how, knowing previous results will affect this year’s results. Of course I am sure that a great deal depends on exactly how I explain the game, and so I imagine that this is the largest confounding factor in this ‘study’.
If you don’t know about the 2/3rds numbers game, take a look at the post here.

Here are the histograms from the last three years:

gametheory

This year I told the class the mean results from the previous years to see if it would make a difference (as it seemed to last year). This year, the results are somewhat lower:

numbersgame2017The winner was thus the person who got closest to 2/3 of 24.4=16.3. This year one person guessed 16, and one person guessed 16.2. Because everyone was asked to write down an integer, unfortunately I can’t claim that 16.2 is the winner, but they will get a second prize.…

By | September 22nd, 2017|Courses, First year, MAM1000, Undergraduate|0 Comments
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