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?

The navigability of Mathemafrica isn’t ideal, so I have created this post which might guide you to what you are looking for. Here are a number of different categories of post which you might like to take a look at:

• First year mathematics notes and resources (particularly for the University of Cape Town MAM1000W)
• MAM1019H – Fundamentals of mathematics
• Book reviews
• Posts in languages other than English
• Conference write-ups
• Animations
• Basic Graph Theory
• Some slightly more advanced mathematics
• Computational complexity
• The South African Maths Olympiad problems

Always write in a comment if there is anything you would like to see us write about, or you would like to write about.

• On Convergent Sequences and Prime Numbers

• An integral expression for n!

• Welcome to Reproducing Kernel Hilbert Space

• Fibonacci and the Golden Ratio

• Fibonacci and Binet

• Fibonacci and induction

• Pi and the Mandelbrot set

• Quantum computing

• Dependent types

• Type theory, logic and programming

• Ishango, Nyakubereka Svomhu (Shona)
• Mathematics or dreams, which is more real (Sepedi)
• Mathematics or dreams, which is more real (IsiXhosa)
• Your post?

• Calculus Reordered: A History of the Big Ideas, by David M. Bressoud – a review
• Prime Suspects – The anatomy of integers and permutations, by Andrew Granville and Jennifer Granville, illustrated by Robert Lewis – a review
• Relativity, The Special and General Theory, 100th anniversary edition – by Albert Einstein – a review
• How to Fall Slower Than Gravity And Other Everyday (and Not So Everyday) Uses of Mathematics and Physical Reasoning – by Paul J. Nahin, a review
• Millions, Billions, Zillions – Defending Yourself in a World of Too Many Numbers – by Brian W. Kernighan, a review
• The Mathematics of Secrets – by Joshua Holden, a review
• How Behavior Spreads: The Science of Complex Contagions, by Damon Centola, a review
• Calculus for the ambitious, by Tom Korner, a review, by Henri Laurie
• Music by the Numbers, From Pythagoras to Schoenberg – By Eli Maor, a review
• What can be computed?

Attendance: The mismatch between academics and students. Who is right?

R. Nazim Khan, University of Western Australia

Presentation at the 11th Southern Hemisphere Conference on the Teaching and Learning of Undergraduate Mathematics and Statistics (‘Brazil Delta 2017 for short)

Students don’t attend from the 1^st lecture – how do they know if the lecturer is good or not? Something else is afoot.

Lectures are recorded, students watch the recordings rather than attending.

Low attendance is correlated to high failure rate.

Reasons for low attendance:

• Maths is not their major
• Lecturing is not done well
• Students believe they can pass without attending
• When students have jobs and work comes up, they prioritise work over attendance
• Attendance is higher when there is assessment in class
• Research on attendance …

This study:

Does attendance affect performance? Who attends class? Attitudes on attending, staff and students?

Business statistics course, records of attendance, survey, marks, demographics, high school marks.…

A tale of two journeys

Barbara Miller-Reilly and Charles O’Brien

Presentation at the 11th Southern Hemisphere Conference on the Teaching and Learning of Undergraduate Mathematics and Statistics (‘Brazil Delta 2017 for short)

20 years ago Charles was a young business man with a fear of maths; Barbara was a teacher of mathematics-avoident adults and working on a PhD.

Recently Charles asked Barbara for help with maths again. They decided to co-author a paper on their journeys.

Barbara:

• Left teaching to look after her 3 children
• Did part-time teaching, e.g. course on Maths Anxiety, where she learnt many skills
• Started job-share university work
  • Developed maths and statistics learning
  • Researched programmes encouraging girls in STEM
  • Started PhD in early 50’s

Charles

• Lower stream in maths at aged 13
• Failed all maths tests in high school
• Left his brokering job due to fear of maths
• Wondered if he has a maths version of dyslexia
• Said maths was like skiing on blue ice with no edges, blindfolded.