Quadractic equation

This equation I like more than the "beatiful" equation () mainly becaus it's not that mysterious. There is certain propoties of the quadractic equation that can be looked at and tested.
1st one is what shape will the equation be:

x^2x
Is the shape of:

And The second property you can get is directly from the quadractic equation, whether a equation has 2 roots, 1 root or it has imaginary roots

x^2x
b^2-4ac=
How many roots has this equation got?

Okay that was fun hope you enjoy.

OR careers, MSc project, Discrete Event Simulation

Apologies first. I have not been blogging in a long time mainly because I was caught up doing my MSc project website in which there is a heck of a lot of modules to go through and then check to make sure they display correctly. At the moment I have made all 27 modules of the website, now all I need to is sort out display, repeating JavaScript and the most labour-some task Testing. Or as I like to call it "Testing to destruction". The idea of making it fail is more harsh but sounds more fun.

Okay apologies done. On the 16th November 2011, it was a Wednesday (by the way) I attended a Operational Research Careers Open day. This was in Birmingham and started at 10:00 and went on to 15:30. There were a lot of stalls there so to name as many as I can:

• [dstl]
• BA
• GORS
• Tesco
• Hartley McMasters ltd
• RBS
• Atass Sports
• IBM UK
• Cardiff University
• University of Southampton

After browsing the stalls they had a lot of talks from a lot of different companies on what exactly they do. There was talks from Martin Slaughter from Hartley McMaster Ltd on what they did with Vodafone. It was on opening hours and rotas for staff i.e. whether to open on a Sunday or not? Also a talk from Mike Nicholson from IBM UK talking about a case study they did. Next up was GORS or Government OR Services. They talked about how the work is very varied, job security and an amazing pension (better than the average). Then Andrew Long from British Airways Where he talked about the code on an airway ticket and all the different sections which is put together to form British Airways. Then there was a Company I never heard of before that day Tata Steel I presume this is for engineers who describe themselves as mathematicians but I could be wrong. And the very last talk of the day was Tom Hibbert from Tesco who talks about the different problems Tesco faces like perishable good, how much to order etc.

The Careers day was very informative the only problem was travel costs for me to get there by 10.00 i had to pay £70 roughly and to get home i got the cheapest ticket which was around £18 pounds mark. If however they moved the starting time to nearly 12.00 then my forward journey would only cost £18 roughly. Thats the only thing that annoyed me, apart from that well done the OR Society.

For an assessment centre I have to study up on one of four Operational Research Topics namely "System Dynamics", "Discrete Event Simulation", "Bayes net or other decision tree type approach", "Multi- criteria Decision Analysis (or a specific technique from within this group of techniques)".

Having looked at the wiki pages of these I found out Discrete Event Simulation looks mainly like Queueing theory. So I have to brush up on this, luckily I did actually do this in my BSc whilst at Greenwich University with my favourite lecturer Professor Vitaly Strusevich. I have a lot of man love for this guy, a person who actually got me into OR and got me to join the OR society.

UPDATE 13th December
Some links I forgot about. Whilst at the career fair the first talk was from the chairman of the OR Society and he mentioned some projects he was working on they were Green Logistics and ITIS Holding.

Backing Samuel Hansen Relatively Prime

Right im backing it mainly because of his twitter updates which were summed up on Peter Rowletts blog. Some of them sound interesting

Wondering if you can musically represent a function? Support Relatively Prime and I will have the chance to answer

If you want to hear maths (or math if your from certain parts of the world) stories that aren't well known but deeply fascinating, go on and support Relatively Prime. Heres a video to wet your appetite.

IMA 14th Early Career Mathematician Conference

I went to this on Saturday mainly for the career talk which was held in the morning and bits of the afternoon. The conference was held at the University of Leicester. And during some of it people were twittering #ecm14. Adrian Hamilton took the talk on career planning workshop. We first looked at what to include on a CV, the very broad first:

1. Profile (Pen Picture of facts)
1. Management level
2. Business Areas
3. Functions carried out
4. skills, abilites, strenghts
2. Achievements
1. Some selected achievements
2. Excerpts from experience
3. Career Progression
1. Start from most recent
2. Dates, name of organisation, what it does
3. Key tasks and responsibilities
4. Other Relevant Facts
1. Education, qualifications, training
2. Outside work experience, interests, personal

He did mention that CV change over time, the format I mean but they should about 2 pages no more. Any more and the employer will get bored, as he/she has too see loads of these.
We then did a group discussion on identifying Achievements and then trying to get as many doing words as possible to show what you have accomplished. He also mentioned as a side note that apparently there a preconception that mathematicians aren't good with money, so if you can show you are good with money it will be no bad thing (nudge, nudge).
We also looked at the different ways to search and apply for jobs.

Cold Approach
It's simple, one letter. Useful if growing company. But there may be no job available. Also the chances of success are small.

The other methods most people know:
Contact Networks
Response to Adverts
Recruitment Agencies

The Contact Network seemed to be the best way of getting a job you want. We also looked at Referral Interviews. This was completely new to me. If you have some one in a contact network and you ask them about getting a job in a particular sector, they can refer you to someone who may have more knowledge about the goings on.

The first step is to get referred to someone. Next write them a letter about what you want to get out of it, these referrals are not for you to ask them for a job but talk to them your career plan in general sense, also send them your CV. Next to phone them to confirm a meeting. This is where you mention your letter and make clear that you are not after a job. Mention that it will not take long and you know their time is valuable. If they say they can't help you, stroke their ego tell them they have vast knowledge about this particular field.
If it all goes well hold the meeting, then send a thank you letter for meeting that person.

We also spent some time looking a questions that may be asked i.e.
What recruitment agencies specialise in this sector?
What sort of papers or source should I look at for job advertisement?
Realistic Salary?
Do you other people that could help me out and me more information in these sort of areas we have discussed?
Is my cv okay?
can I hear about your experience.

We then looked at responding to to job adverts, difficult interview questions, do and don't of interviews. Then each person was given a snippet from Mathematics Today (February 2011). This featured a bit about job options and describing where certain people work. One option some one mentioned was Transportation planner. Then a list of website to find jobs:

1. Datatech Recruiment
2. DSTL- Defence science and Technology Laboratary
3. Government Actuary's Department
4. Government Communications Headquarters GCHQ
5. Government Operational Research Service
6. Government Statistical Service GSS Jobs
7. Matchtech Group
8. Met Office
9. Statisticians in the Pharmaceutical Industry PSI
10. Office for National Statistics
11. The inside career guide to Actuarial Work
12. The institute of Actuaries
13. Transport Planning Opportunities

At the end of this there was a talk by Peter Rowlett about mathematics teaching and learning. Aperiodic tiling by Edmund Harris and a talk by Steve King on something to do with Rolls Royce.

As a side note they did say for students you can join the ima for free or £5 fee.

Paradoxial games

This was a free lecture to anyone in Greenwich or out. The Greenwich MathSoc set this up with help from @NoelAnn and @Tony_Mann. When I was doing my last year at Greenwich Eduardo Cuntin did a project on paradoxical games giving the history off it and interviewing the man himself. So a couple of months later MathSoc asks him to come and then we have an event. A couple of people on twitter and facebook spread the word of the event. Then we are brought to the day of the event.

WARNING: if you are going to attend a lecture by Juan M.R. Parrondo do not read any further, if your interested in the maths contine.

The man who everyone came to see is Juan M.R. Parrondo was introduced by Noel-Ann Bradshaw and Eduardo Cuntin. This problem is apparently 10 years old. The idea is there is 2 games which if played individually will end up with you losing money (gambling is easier to visualise) but if you alternate between the 2 games randomly then you will win. Confused? read on.
He gave an example, Game A is a simple game you win with probability p1 and lose with p2. The second game Game B is more complicated if your capital is divisible by 3 then you win with prob p3 and lose with p4, if your capital is not divisible by 3 then you win with prob p5 and lose with p6. This should help visualise it

This is what happens when you play the games randomly or the games separate

As you can see playing randomly turns to be profitable (The above was the game being played 5000 times).

Apparently the trick to working out this paradox comes from something called Brownian motor and the probability of each game.

Game A has a small positive gradient and Game B is a mixture of 2 gradients 1 big positive gradient and one shallow negative gradient. Switching between the 2 games means you increase your profits. This website may explain the Brownian motor better.

There was some criticism of the paradox in 2004. They questioned the paper and said if it was not random but they got to pick which game they chose then their odds and profit would go up. This is true but if you deal with more than one person choosing between which game to play i.e. democracy then you will end up losing but random still triumphs.

The lecture ended.
Parrondo's paradoxical games homepage

Unstructured Meshes

Last term for me I was studying meshes and the physics of what goes on when the radiator is on. The most common mesh is structured meshes, like calendars, all squares all evenly distributed. i.e.

This was taken from my iCal on my mac. (note sure who I ask permission to use this image, if you know can you reply in the comments)

Structured meshes are good for rectangle type of shapes but what if they are not rectangle? For this type of problem we can triangles and view this as an unstructured mesh.
An example would be a rectangle split into triangles (because i can claim its my own work and its easy to draw)

This image was made by the software Paintbrush
Now before we get into the how a computer works with unstructured meshes we first need to know each triangles neighbour.
1: has neighbours 2 & 3.
2: has neighbours 1 & 4.
3: has neighbours 1 & 6.
4: has neighbours 2 & 5.
5: has neighbours 4, 6 & 7.
6: has neighbours 3 & 5.
7: has neighbours 5 & 8.
8: has neighbour 7.

Now we create three vectors, one will be the neighbours so something like
Neigh=[2,3,1,4,1,6,2,5,4,6,7,3,5,5,8,7]
The second will be to determine how many where the neighbours finish for that triangle i.e. for triangle 3 it would be 6, the vector will look like:
NeighPos=[2,4,6,8,11,13,15,16]
The last matrix will be the coefficients for those triangles so something like:
Coeff=[15,16,16,17,18,17,19,19]

Then you can use Successive over relation or Gauss Seidel or even the Jacobi method. Other iterative methods are available.

One last bit of advice do not use my triangle arrangement to solve problems mainly because it is not evenly spread out and so any results you get will be wrong or at least not very accurate.

This should be pre dated to 30th January 2011

Math/Maths Live at University of Greenwich

Math/Maths podcast is hosted by Pulse Project starring Peter Rowlett (@PeterRowlett) and Samuel Hansen (@Samuel_Hansen).
I was Meant to upload this sooner, but coursework got in the way. Anyway on Pulse Project website you can listen to the audio of the podcast, but you never get to see them, so I recorded them doing their thang (<--deliberately spelt wrong).



At the start of this event they gave a talk of Peters and Samuels trip to Nottingham and mathematicians that lived there. After the Math/Maths recording a group of us went up to explore the Greenwich Observatory and came across a unique sundial:

This should be pre dated to 4th of December 2010

Recreational Mathematics

At Greenwich today the maths society (MathSoc) arranged a lecture on the subject of "Recreational Mathematics" which was given by David Singmaster. Unfortunately after my first picture my iPhone lost internet connection. Here is my first pic:

If you did read his wiki article, you would know he is famous for his Rubik cube solution, so I was glad when he brought that out:

Unfortunately my memory sucks so I can only recoil memories from the pictures. So somehow we managed to get to a bit about labyrinths and he found one underground, this was him getting into the cave:

And the he presented the cave itself and a drawing of the labyrinth

We then moved on to the Fibonacci series and there was a weird pattern in there:

Its a bit hard to see but if you look at the 15th line where it begins 14,1,....., 1001, 2002, 3003.... Huh this is weird but wait, because of this the 16th line reads 15, 1,.....,3003,5005..... and again on the 17th line we get 16,1,...., 8008,..... Strange phenomenon, its uncommon and doesn't happen often.

He then showed us fibonacci work (I believe) and the numbers we now use today which he got when he travelled abroad.

We then looked at another bit of Fibonacci's work, which included work that showed how to use the numbers for adding and multiplying. No picture here as it seemed a bit boring.

Now we looked at problems and teapots. I'll get to the teapots in a minute. One problem we looked at was:

If you can't read it, it says

"As I was going to St. Ives, I met a man with seven wives, each wife had seven sacks, each sack had seven cats, each cat had seven kits. Kits, cats, sacks and wives. How many were going to St. Ives?"

The answer wonderfully is none. Or one if you count the man himself.
There was other puzzles but I forgot them and forgot to take a picture of the puzzles. Shame apparently those puzzles perplexed even the greatest mathematicians.

Okay now the teapot. David Singmaster brought one with him:

As you may notice although the picture isn't that good, it has no lid to speak of, so how do you use it I hear you ask. Well glad you did, because I wondered as well and here's how:

You fill it up from the bottom and then flip it over, wonderful.

Next we had a problem:

"Can you draw three rabbits with three ears between them and that each rabbit looks like they have two ears each"

Easy enough draw them in a triangle formation like so:

This is all well and good but this image has been used in loads of different places:

Then the lecture finished:

for the next hour or so any people who were left got to play around with some stuff he brought along i.e. teapot, rubik cube (3*3*3), rubik cuke (7*7*7), Rubik cube (1*3*3), bolts that were together, sheet of paper that looked like it had space in side of it and some more things I can't remember.
Actually one thing i did remember was a magic trick (apparently it actually something to do with physics) which was cool here is the 10 sec video:
Wordpress wants me to upgrade to put video on here so hello Twit Vid

This should be back dated to 10th of November 2010