## Archive for August, 2014

I currently work at The University of Manchester in the UK as a ‘Scientific Applications Support Specialist’. In recent years, I have noticed a steady increase in the use of open source software for both teaching and research – something that I regard as a Good Thing.

Even though Manchester has, what I believe is, a world-class site licensed software portfolio, researchers, lecturers and students often prefer open source solutions for all sorts of reasons. For example, researchers at Manchester can use MATLAB while they are associated with the University but their right to do so ceases as soon as they leave. If all of your research code is in the form of MATLAB and Simulink models, you had better hope that your next employer or school has the requisite licenses.

This summer, a few people in the Control Systems Centre of Manchester’s Electrical and Electronic Engineering department asked the question **‘Is it possible to implement all of the simple MATLAB/Simulink examples we use in a second year undergraduate introduction to Control Theory using free software?’ **In particular, they chose the programs Scilab and Xcos.

Since the aim of this course is to teach control theory principles rather than any particular software solution, it would ideally be software agnostic. Students aren’t asked to develop models, they are just asked to play with pre-packaged models in order to improve their understanding of the material.

Student intern Danail Stoychev was tasked with attempting to port all of the examples from the course and in fairly short order he determined that the answer to their question was a resounding ‘Yes’.

For example, the model below is an example of **feedback with a first order transfer function and a dela**y. First in Simulink:

and now in xcos

Part of the exercise set for the students is to define all of the relevant parameters in the workspace: b,a,k and so on. If you attempt to download and run the above, you’ll have to do that in order to make them work. You’ll also need extract and plot the results from the workspace.

It can be seen that the two models look very similar and, for these examples at least, it really doesn’t matter which piece of software the students use.

The full set of MATLAB/Simulink examples along with Danail’s Scilab/Xcos conversions can be found at http://personalpages.manchester.ac.uk/staff/William.Heath/matlab_scilab.html

Welcome to the rather delayed Carnival of Mathematics for July. This is the 113th edition of the mathematical blogging tradition that’s organised by Katie and company over at The Aperiodical.

**Number Trivia and a challenge**

Long held tradition dictates that I find something interesting about this month’s edition number – 113 – and I turn to Number Gossip for help. It comes up with 3 very nice little prime tidbits:

- 113 is the smallest three-digit permutable prime
- 113 is the smallest three-digit Unholey prime: such primes do not have holes in their digits
- 113 is the smallest three-digit prime whose product and sum of digits is prime

**Walking Randomly Challenge**: Prove the above using the programming language of your choice and post in the comments section. Here’s a demonstration of the first statement using Mathematica.

(*Returns true if num is a permutable prime*) permutePrimeQ[num_] := AllTrue[PrimeQ[Map[FromDigits, Permutations[IntegerDigits[num]]]], TrueQ] (*prints all permutable primes from 1 to 1000*) Do[ If[permutePrimeQ[x], Print[x]] , {x, 1, 1000} ] 2 3 5 7 11 13 17 31 37 71 73 79 97 113 131 199 311 337 373 733 919 991

**On with the show**

**Mathematical software blogs**

A math carnival wouldn’t be a WalkingRandomly math carnival without some focus on mathematical software blogs. Loren of The Art of MATLAB brings us Analyzing Fitness Data from Wearable Devices in MATLAB which is a guest post by Toshi Takeuchi. The new computational programming language on the block is Julia and the Julia blog contains videos and code on mathematical Optimization in Julia. The Wolfram Blog has a video on how to Create Escher-Inspired art with Mathematica (Don’t forget that Mathematica can be had for free for the Raspberry Pi).

Sage is a free, open-source alternative to Mathematica, Maple and MATLAB and the SageMath blog recently published SageMathCloud — history and status. The Numerical Algorithms Blog, on the other hand, brings us Testing Matrix Functions Using Identities. Efficient linear algebra routines form one of the cornerstones of modern scientific computing and July saw the publication of a tutorial on how to write your own, super-fast Matrix-Matrix Multiply routine.

**Stamps, Making Change and Dealing Cards**

When was the last time you used a postage stamp? Even if it was a long time ago, you may have held in your hands a strip of stamps. Maybe you have even tried to fold it into a stack, one stamp wide, so that the strip was easier to store. Have you ever wondered how many ways there are to do so? This post reviews a recent research survey about the topic.

How many ways can you make change for a dollar? This post gives a Lisp program that solves the problem and an analytical solution based on generating functions.

Over at The Aperiodical, home of the math carnival, Dave Wilding has been Discovering Integer Sequences by dealing cards.

**Ninjas, Lord Voldemort and Hairy Hay Balls**

Colin Beveridge has written a delightful follow-up to Pat Ballew’s post which featured in CoM112 – Trigonometric Trick Secrets of the Mathematica Ninja.

Ben of Math with Bad Drawings fame has written a highly readable rant about a bit of syllabus design which will resonate with anyone teaching (or learning) mathematics in The Voldemort of Calculus Classes.

New math blogger, Grace, recently had an experience in which her math education intersected with her everyday life in Hay Ball Meets the Hairy Ball Theorem.

**Tweeting bots, 3D Printed Geometry and Hair ties**

*(/begin shameless plug)* I spend a lot of time on twitter posting as @walkingrandomly *(/end shameless plug)* and have discovered quite a few mathematical twitter bots in my time. Evelyn Lamb has discovered many many more and has posted reviews of them all over at Roots of Unity.

James Tanton posts fun problems on twitter all the time. One particular problem caught the attention of Mike Lawler because of how 3D printing could help younger children see the geometry.

If you’ve ever wondered what a 120-cell would look like if it were made out of hair ties, wonder no longer because Andrea Hawksley has made one – Hair Tie 120-Cell (By the way, hold your mouse of the title of her blog – it’s cool!)

**More Ninjas, Dots and Mandelbrots**.

A round-up of fun stuff from Colin Beveridge’s “Flying Colours Maths” – a kind of @icecolbeveridge carnival for Mathematics Carnival.

Have you ever wondered what mathematics is behind those pretty Mandelbrot posters that are all over the place? Find out over at Grey Matters: Blog – Mandelbrot Set: What Exactly Are We Looking At, Anyway?

Did you know that dots have power? To see how much power, check out Keith Devlin’s article The Power of Dots.

**Football, drugs and underwear**

Since I’m not a big fan of football at the best of times, the football world cup is a distant memory for me (England’s dismal performance didn’t help much either). Fortunately, there’s more than one way to enjoy a world cup and Maxwell’s Demon and The Guardian helped me enjoy it in a data science way: How shocking was Brazil’s 7-1 defeat, mathematically speaking? and Data Visualization, From The World Cup To Drugs In Arkansas.

At this time of year, many of us turn our thoughts to vacations. If you are a math geek, you owe it to yourself to optimise your underwear and pack like a nerd.

**Puzzles, Games and playing like a mathmo**

When I’m on vacation, I often take a notebook with me so I can do a little mathematics during downtime. My wife and friends find this extremely odd behaviour because mathematics looks like hard work to them..in short, they don’t know how to play like a mathematician.

My job at The University of Manchester is wonderful because it often feels like I am being paid to solve puzzles. While on vacation, however, I have to find some unpaid puzzles to solve and this concentric circles puzzle is an example of one thats fun to solve.

I think that one of the best ways to learn is through play and games and, in a new post over at Math Frolic, a Li’l Game From Martin Gardner introduces mathematical “isomorphism.”

**Cartoons and Limits**

Mathematics is everywhere, it’s even in the voice bubbles used in web comics! As an added bonus, this blog post contains a little Python programming too.

Next up, we have Part 2 of Bressoud’s masterful investigation (Part I featured in Carnival 112) of how students understand limits.

**Resources, Exams and Books**

Colleen Young brings us a great set of Standard Form Resources.

Patrick Honner continues his long-running evaluation of New York State math Regents exams, the high school required exams there. In this post, he looks at a multiple choice question that asks the student to identify the graph of an “absolute value equation”.

The Maths Book Club gives details of their most anticipated maths books for the rest of 2014.

**Bad Mnemonics and a Dislike of Mathematics **

Andrea Hawklsey muses on why some people dislike mathematics when they have interests that suggest they should. Perhaps it has something to do with poorly executed mnemonics when students are taught mathematics, or perhaps its just because they had dull math teachers? Most of my math teachers were awesome and I’ve always felt that this was a major factor in me enjoying the subject.

**Skirts, Snow globes and Mathematical Mind Hacking **

This edition of the carnival is in danger of becoming the Carnival of Andrea Hawksley since so many of her great posts were submitted! In one of her July posts, she manages to combine fashion and hyperbolic geometry – which is quite a feat!

The author of cavmaths has been musing over the dynamics governing snow globes. Can anyone help out?

Hacking your mind sounds like it might be dangerous but it turns out that it’s really quite safe. Head over to Moebius Noodles to see an example of a mathematical mind hack.

**That’s all folks**

Thanks to Katie for inviting me to host this month’s carnival, thanks to everyone for submitting so many great articles and thanks to you for reading. Carnival #114 will be hosted over at SquareCirclez.

I work at The University of Manchester as part of IT Service’s Research Support department. This month, I was given the task of editing the newsletter that we send out to the academics we serve.

For me, this month’s highlights include the fact that our Condor Pool (which I help build and run) has now delivered over 20 million CPU hours to academics at Manchester by making use of desktop PCs around campus. Another HPC system we have at Manchester is our Computational Shared Facility which is jointly funded by the University and all of the research groups who use it. This system has just seen the installation of its 6000-th CPU core.

Other news includes the Greater Manchester Data Dive, an AGM for Research Software Engineers, Image based modelling and more.

If you are interested in seeing the sort of thing we get up to, check out this months newsletter at http://documents.manchester.ac.uk/DocuInfo.aspx?DocID=20995