## Screencasting with Macs and PCs

The videos below were made a few years ago to support a Science Communication and Group Project module at the School of Physics Astronomy and Mathematics at the University of Hertfordshire. The work was supported by the Institute of Physics and the HE STEM programme. I also got support from the Institute of Mathematics and its Applications. The tools are probably a bit dated now, but I hope the principles still help some students trying to get their work seen.

Students were asked to prepare a short video to present the results of their project and share it with the world. To support them, the videos below were prepared.

Students were also encouraged to prepare technical documentation and the videos for using LaTeX and structuring their documents with LaTeX were very useful.

### Screencasting with a Mac

In this video we will see some tools to capture video from your screen using a Mac. The tools are Quicktime Player, MPEG Streamclip and iMovie.

Screencasting with a PC

In this video we will see some tools to capture video from your screen using a PC. The tools are CamStudio and Freemake Video Converter.

In this tutorial we will see how to set up an account in Vimeo and how to upload your screencast. Also you will be able to send a link to your video to you friends and other people.

## Structured Documents in LaTeX

This is a video I made a few years ago to encourage my students to use better tools to write dissertations, thesis and reports that include the use of mathematics. The principles stand, although the tools may have moved on since then. I am reposting them as requested by a colleague of mine, Dr Catarina Carvalho, who I hope will still find this useful.

In this video we continue explaining how to use LaTeX. Here we will see how to use a master document in order to build a thesis or dissertation.
We assume that you have already had a look at the tutorial entitled: LaTeX for writing mathematics – An introduction

## Byrne’s Euclid

This is pure magic: Byrne’s Euclid by Nicholas Rougeux

BYRNE’S EUCLID

THE FIRST SIX BOOKS OF THE ELEMENTS OF EUCLID WITH COLOURED DIAGRAMS AND SYMBOLS

A reproduction of Oliver Byrne’s celebrated work from 1847 plus interactive diagrams, cross references, and posters designed by Nicholas Rougeux – Explore﻿

Learn about Byrne’s original publication and how this site was made including design, typography, and more.

## POSTERS.

Decorate your walls with a colorful detailed poster of every geometric illustration from Oliver Byrne’s colorful 1847 edition of Euclid’s Elements.2

See the poster

## The Year in Math and Computer Science

A reblog from Quanta Magazine:

https://www.quantamagazine.org/quantas-year-in-math-and-computer-science-2018-20181221/

Several mathematicians under the age of 30, and amateur problem-solvers of all ages, made significant contributions to some of the most difficult questions in math and theoretical computer science.

Youth ruled the year in mathematics. The Fields Medals — awarded every four years to the top mathematicians no older than 40 — went out to four individuals who have left their marks all over the mathematical landscape. This year one of the awards went to Peter Scholze, who at 30 became one of the youngest ever to win. But at times in 2018, even 30 could feel old.

Two students, one in graduate school and the other just 18, in two separate discoveries, remapped the borders that separate quantum computers from ordinary classical computation. Another graduate student proved a decades-old conjecture about elliptic curves, a type of object that has fascinated mathematicians for centuries. And amateur mathematicians of all ages rose up to make significant contributions to long-dormant problems.

But perhaps the most significant sign of youth’s rise was when Scholze, not a month after the Fields Medal ceremony, made public (along with a collaborator) his map pointing to a hole in a purported proof of the famous abc conjecture. The proof, put forward six years ago by a mathematical luminary, has baffled most mathematicians ever since.

## At the Norwegian Embassy for the Abel Committee Reception

At the Norwegian Embassy for the Abel Committee Reception.

The Abel Prize was established on 1 January 2002. Its purpose is to recognise outstanding scientific work in the field of mathematics. The prize amount is 6 million NOK (about 750,000 Euro) and was awarded for the first time on 3 June 2003.

Each year, in anticipation of the prize announcement, an afternnon of lectues showcases previous winners and member of the Committee. This year the event WAS be held in Oxford on Monday 15th January. Andrew Wiles, John Rognes and Irene Fonseca were the the speakers and a reception was held in the Norwegian Embassy in London. I had an opportunity to attend the reception as a member of the London Mathematical Society.

The 2018 Abel Prize recipient will be announced on March 20th by Ole M. Sejersted, President of the Norwegian Academy of Science and Letters.

The Abel Prize Laureates 2003-2016

2017: Yves Meyer
2016: Sir Andrew J. Wiles
2015: John F. Nash Jr. & Louis Nirenberg
2014:Yakov G. Sinai
2013: Pierre Deligne
2012: Endre Szemerédi
2011: John Milnor
2010: John Torrence Tate
2009: Mikhail Leonidovich Gromov
2008: John Griggs Thompson
and Jacques Tits
2006: Lennart Carleson
2005: Peter D. Lax
2004: Sir Michael Francis Atiyah
2003: Jean-Pierre Serre

## Probably more likely than probable – Reblog

This is a reblog from here Probably more likely than probable // Revolutions

What kind of probability are people talking about when they say something is “highly likely” or has “almost no chance”? The chart below, created by Reddit user zonination, visualizes the responses of 46 other Reddit users to “What probability would you assign to the phase: <phrase>” for various statements of probability. Each set of responses has been converted to a kernel destiny estimate and presented as a joyplot using R.

Somewhat surprisingly, the results from the Redditors hew quite closely to a similar study of 23 NATO intelligence officers in 2007. In that study, the officers — who were accustomed to reading intelligence reports with assertions of likelihood — were giving a similar task with the same descriptions of probability. The results, here presented as a dotplot, are quite similar.

For details on the analysis of the Redditors, including the data and R code behind the joyplot chart, check out the Github repository linked below.

Github (zonination): Perceptions of Probability and Numbers

## A new “Mathematician’s Apology” – Reblog

In the two and a half years (or so) since I left academia for industry, I’ve worked with a number of math majors and math PhDs outside of academia and talked to a number of current grad students who were considering going into industry. As a result, my perspective on the role of the math research […]

## Bessel series for a constant

Fourier series express functions as a sum of sines and cosines of different frequencies. Bessel series are analogous, expressing functions as a sum of Bessel functions of different orders.

Fourier series arise naturally when working in rectangular coordinates. Bessel series arise naturally when working in polar coordinates.

The Fourier series for a constant is trivial. You can think of a constant as a cosine with frequency zero.

The Bessel series for a constant is not as simple, but more interesting. Here we have:

$1=J_0(x)+2J_2(x)+2J_4(x)+2J_g(x)\cdots$

Since $J_{-n}=(-1)^n J_n(x)$ we can write the series above as the following infinite series:

$1=\sum_{n=-\infty}^{\infty} J_{2n}(x)$

Cool, right?