*

I quite enjoyed the fact that in the MOG the problems are longer and require more thought. I've felt that sometimes Maths can become detached from problems which can be materialised in real life, especially in the things we've been covering this year, but the problems in the MOG are refreshing in that often you don't need complicated Maths but instead you need to search and find an often simpler method which works.

*

It's a very different experience to other maths exams we take. Even SMC has far more questions, so the approach is different. It is less time pressured but requires a high level of concentration for an extended period of time. It's great when you think you can have a go at most/all of the questions but not so fun if you get stuck!

*

Doing such a long paper with so few questions..I think can be encouraging and discouraging at the same time. Encouraging in that it gives you enough time to think fully through how to go about answering questions/writing solutions, and then the end result is quite satisfying. But then again, because there are so few questions, I found that if I didn't know how to approach a question, I became quite stuck and then you're left with time which you could be using to answer another question...but you can't seem to get anywhere substantial!

*

Obviously if you do very well in the MOG, it gets you recognised for other maths competitions such as BMO. But I genuinely just enjoy that I can sit down for a few hours and do some maths questions and problem solving, especially considering how I well I perform doesn't matter. We often aren't given that luxury! I would say it was a combination of this and knowing I would be happy with a score higher than my 7 from last year that made me enjoy it and gain more points this year.

*

I guess the point of things like MOG could be to take a step back. Because we have to fully explain any steps we do or assumptions we make, it means we have to completely understand what we're talking about (whereas in other circumstances such as the SMC it's easier to approximate, make a guess, etc)

]]>

The second question was a classic geometry problem involving circles and triangles, using a number of circle theorems and spotting similar and congruent triangles. Unsurprisingly, having a good diagram was essential to finding and writing a good solution. I noticed that there were a number of different solutions, all equally valid but some much more elegant than others. Having written a fairly convoluted solution, I noticed from my diagram that a far simpler solution was possible and the published solution is different still. That is normally the fun with geometry questions!

The writers were keen on combinatorics this year with the last three questions all some sort of counting problem. The fourth question was about ways of painting 100 houses in a row in two colours. The second part was deceptive, leading us to think there were far fewer possible arrangements than there really were and culminating in most of us making the same error. Listing arrangements systematically was essential.

The final question, which was about a game involving coins arranged on a chequered square board, was cumbersome and I’m still not entirely sure why the last part was the same number of marks as the previous part (as it was completely dependent on trial and error and spotting an arrangement that worked), nor have I since found a more sensible way of approaching it… all I can say is hats off to everyone who persevered to find a solution.

As always, this year’s MOG was really fun, and not just because it went better than previous years and we got to miss lessons. I would highly recommend that keen mathematicians should have a go next year!

Heeral, Year 13]]>

by Mia, Year 12]]>

If you are interested further, check out Ursula Martin's book: Ada Lovelace: The Making of a Computer Scientist.]]>

It’s quite a different style of teaching to school: an hour’s lecture will give you lots of new concepts (methods for solving differential equations, proofs of set theory results) which you then spend time absorbing after the lecture. (I learnt that I didn’t expect to understand the finer points – or sometimes the main points – of every proof while sitting in the lecture hall.) Instead you become more familiar with the material by working through ‘problem sheets’ – exercises using concepts and methods from the lectures. This is where lots of problem solving comes in, because usually the questions require you to apply the lecture material in unfamiliar situations. Since this was one of the aspects of maths I really loved at NLCS, I was pleased that there was lots of opportunity to continue solving interesting problems while at university!

Now I am moving on to the big scary world outside of academia, I have more of a sense of how maths is used more widely. At the moment data analysis and machine learning seem to be everywhere, as well as more traditional opportunities around finance, for example. I think the other thing I have learnt is that you don’t necessarily need to know where you are going when you start – either in terms of what you specialise in at university or where you want to head afterwards. Instead you just need to enjoy doing maths. The Cambridge course allows you to experience many different types of maths in the first year or two, and then you can specialise lots in the third year. I chose mostly pure maths, which I didn’t necessarily see myself doing at the start.

Overall I’d say that doing maths at university has been hard work, but lots of fun. Every course will be different, but if you enjoy doing maths, are interested in exploring the huge amount of maths out there, and solving interesting problems along the way, then I highly recommend it!

]]>

The team’s work is a testament to remarkable perseverance (that hallmark of the NLCS spirit), and cross-curricular collaboration at the highest level. Click here to download the app!

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It is widely recognized among scientists that mathematics is an essential accessory in scientific studies, and that mathematical models are employed to predict future trends and sometimes to infer information about our past. For example, it is possible to use logarithms to estimate roughly how long ago the most recent common ancestor of everyone on Earth today appeared; or we could also use differential equations to predict the infection development spread of a particular disease. This article will discuss the applications of one of the most commonly known and used mathematical models in Biology - dynamical systems - and give some very simplified examples of them.

Dynamical system is commonly defined as an evolution rule which determines how things change or behave over time, and examples of such application is in modelling the drug resistance in malaria, auto-regulation in kidney, anti-coagulation therapy and Ebola outbreaks. All of these involved extremely long and complex modelling and are therefore beyond the scope of this article. However, we can use a very simple example to help ourselves understand the principles of dynamical systems. For a population of rabbits, the area in which they live in might only support a population size of 1500. If the population is small enough, the population size will increase 1.5 times from current time to next period. Let’s use the well established logistic equation to model the population:

A(n+1) = A(n) + r (1-A(n)/L) x A(n), where A(n) represents population of the rabbits at time n, L represents the carrying capacity of the area (which in this case, is 1500) and r is the restricted growth rate (I.e. 1.5). These values could be found from consistent analysis of experimental data during fieldwork investigations. If A(n)<1500, then 1 - A(n)/L > 0, so at time n+1 the population A(n+1) will increase from A(n) at time n+1 E.g. if A(n) = 500 < 1500, A(n+1) = 1000 and the population has grown by 500. Using this to calculate A(n+2) we find the value is 1500, but if we calculate A(n+3), A(n+4) etc, we find that the value will remain constant at 1500. If we have a population of exactly 1500 rabbits, then A(n)/L = 1 and therefore A(n+1) - A (n) will be 0, and thus there would be no change in population from one period to the next, and we have reached an equilibrium point. In contrast, if A(n) > 1500, (1- A(n)/L) < 0 so population would decrease.

This is an oversimplified general model for some populations where adults often survive after reproduction, and is obviously not suitable for all populations. For example, when it comes to insect populations, it is often the case that they have non-overlapping generations, meaning all adults lay eggs in a specific time of year and then die, leaving only their offspring. To understand the modelling of insect populations we must first understand the

However, you may have realized that this is not a realistic model, as it is unlikely that all offspring will survive to give births to the next generation due to factors such as larvae predation and both intra and inter-specific competitions for limited resources. S(N), the fraction of offspring that survives, is therefore important, and the equation changes to Nn+1 = Nn x S(N) x R0, which for simplicity is generally rewritten as Nn+1 = F(N) x Nn = f(N)

If we hypothesize that insect populations are solely affected by intra-specific competitions only, then some further refinement could be done on the model. If there were no competition, then S(N)=1 as all offspring survive. In the second case, if the resources present are not sufficient to support the whole population, then some individuals obtain the units of resources they would need to survive and reproduce, and others die without producing any offspring. Thus in this case S(N) = 1 for Nn < Nc, (where Nc is the critical value above which it would no longer be the case that all individuals survive) and for Nn > Nc, S(N) = Nc/Nn - this type of competition is usually known as contest competitions. The other type of a commonly-known competition is called scramble competition, where every individual is given an equal share of the resources and if Nn < Nc, the critical value, S(N)=1 as all individuals obtain sufficient resources. If Nn > Nc, S(N) = 0 as the amount of resources gained by each individual is not enough to help them survive til the next generation. It is nevertheless very rarely the case that a population, especially a large one, would crash to 0, therefore the behaviour of S(N), and consequently F(N), is always treated as asymptotic.

Idealized contest competition exhibits exact compensation, where the increase in mortality compensates exactly for any increase in population between time n and time n+1. This occurs if F(N)-->c/N as N -->infinity, (where c is a constant) and consequently f(N) -->c, according to

These are just a few small glimpses into how populations are monitored. Obviously, there are still limitations to these models, as they do not take into account other factors such as inter-specific competitions, presence of predators etc., however, scientists do hope that the models correspond roughly with real-life data. If that were the case, the models could then become very useful tools when monitoring and predicting the scale of species population trends in the future.

Computer algorithms are the maths from which computer programs were made. Algorithm comes from the name of the man who also named algebra. It comes from the medieval version of the name of a man called Aljabr. It is now specifically used to mean a mathematical process to solve a problem. Mathematicians considered a problem to be solved if they could write and algorithm to solve it. Appyling an algorithm wasn’t important because the formula already was the answer but computers changed that view because complicated formulas could easily be solved. An algorithm was like a formula that would lead you to the answer and it could also estimate the time it would take to solve a problem.

An example of a fast algorithm is knowing if a number is odd or even:

Is the last digit 0? If yes then STOP. The number is even.

Is the last digit 2? If yes then STOP. The number is even.

Is the last digit 4? If yes then STOP. The number is even.

Is the last digit 6? If yes then STOP. The number is even.

Is the last digit 8? If yes then STOP. The number is even.

STOP. The number is odd.

So in conclusion an algorithm is a process or set of rules to be followed in calculations or other problem-solving operations, especially by a computer.

By Tia, 8L

]]>An example of a fast algorithm is knowing if a number is odd or even:

Is the last digit 0? If yes then STOP. The number is even.

Is the last digit 2? If yes then STOP. The number is even.

Is the last digit 4? If yes then STOP. The number is even.

Is the last digit 6? If yes then STOP. The number is even.

Is the last digit 8? If yes then STOP. The number is even.

STOP. The number is odd.

So in conclusion an algorithm is a process or set of rules to be followed in calculations or other problem-solving operations, especially by a computer.

By Tia, 8L

Teachers are writing positive comments in the maths books of all pupils at a top girls’ schools to improve their confidence in the subject.

Outstanding results are already achieved by pupils at North London Collegiate but positive comments must now be included on all pieces of work to increase self-confidence and promote a “can-do” attitude.

The decision was inspired by research from Harvard, which showed that confidence was critical to success. The school also sends postcards to pupils to celebrate small achievements and teachers are asked to email students, and copy in form tutors, when small milestones are reached.

One pupil said: “During class, teachers constantly provide positive reinforcement which really helps to keep us motivated and push through the tough and seemingly impossible parts.

“Whenever we get tests and homework back, our sheets are always showered with stickers and this adds another incentive to keep on top of homework and makes the experience of receiving marks a much less uneasy experience.”

The school has introduced “low-stakes” testing to build pupils’ resilience to exam conditions. Regular ten-minute assessments have been introduced, to help to reward pupils with small victories and to track their progress.

According to an international study of gender equality in schools by the Organisation for Economic Co-operation and Development, girls lack confidence in their ability to solve maths and science problems and achieve worse results than they otherwise would, despite outperforming boys overall.

At A level more than 60 per cent of maths candidates are boys and only 14 per cent of people working in science, technology, engineering and maths are women, short of the goal of 30 per cent.

The school is adopting a number of maths initiatives to inject the subject with fun. These have included “maths-off” contests and musical talent shows.

Girls also mentor pupils two years below them in advanced mathematics and sixth-formers have been trying to make maths clubs more appealing. Teachers have given lectures on the philosophy of science, the links between maths and art, and the maths of*Alice’s Adventures in Wonderland*.

Last year 98 per cent of pupils at the school achieved an A or A* at International GCSE maths.

]]>Outstanding results are already achieved by pupils at North London Collegiate but positive comments must now be included on all pieces of work to increase self-confidence and promote a “can-do” attitude.

The decision was inspired by research from Harvard, which showed that confidence was critical to success. The school also sends postcards to pupils to celebrate small achievements and teachers are asked to email students, and copy in form tutors, when small milestones are reached.

One pupil said: “During class, teachers constantly provide positive reinforcement which really helps to keep us motivated and push through the tough and seemingly impossible parts.

“Whenever we get tests and homework back, our sheets are always showered with stickers and this adds another incentive to keep on top of homework and makes the experience of receiving marks a much less uneasy experience.”

The school has introduced “low-stakes” testing to build pupils’ resilience to exam conditions. Regular ten-minute assessments have been introduced, to help to reward pupils with small victories and to track their progress.

According to an international study of gender equality in schools by the Organisation for Economic Co-operation and Development, girls lack confidence in their ability to solve maths and science problems and achieve worse results than they otherwise would, despite outperforming boys overall.

At A level more than 60 per cent of maths candidates are boys and only 14 per cent of people working in science, technology, engineering and maths are women, short of the goal of 30 per cent.

The school is adopting a number of maths initiatives to inject the subject with fun. These have included “maths-off” contests and musical talent shows.

Girls also mentor pupils two years below them in advanced mathematics and sixth-formers have been trying to make maths clubs more appealing. Teachers have given lectures on the philosophy of science, the links between maths and art, and the maths of

Last year 98 per cent of pupils at the school achieved an A or A* at International GCSE maths.

All are welcome to have a go! Click here for the paper.

Answers to mcopin@nlcs.org.uk by the end of the weekend.

Family efforts are encouraged!]]>

Many thanks to the many teachers from both the Junior and Senior School who volunteered to man the stations and help run this event. We hope the Y5s enjoyed their maths with a twist!

1. Mathematics never hurt anyone, except when it did. It is incomparably powerful when trying to understand the modern world, but mathematical ideas need to exist alongside thinking from other disciplines.

2. Miss Buss made NLCS so that young women would be able to play the same games as their brothers, and with the same advantages.

Though today's society is fairer than ever before, it has been a man's world since the beginning of time and women are still woefully under-represented in public life and leadership roles. Society teaches women to underestimate their powers. You have the opportunity to lead the way.

3. Don't play life as though it is a game of Monopoly. Monopoly makes you a bad person. Furthermore, Mathematics tells us that cooperation is better for individuals as well as for the collective. Why not think of upcoming exams as an opportunity to work together?

Individual lives are full of struggle: "success is going from failure to failure with no loss of enthusiasm." So you should learn to rejoice - to

This week, we were delighted to see 25 enthusiastic girls turn up to the session, and their insight and ingenuity impressed us all! Letting them indulge in the maths society chocolate fountain is therefore a perfect way to reward them for their hard work and a sweet way of finishing off!

The poem read out in assembly is below:

**A notice from Kureha, Saachi and Mengyao in the Maths Society. **

Hey there middle school you better listen to this

It’s Maths Soc news that will fill you with bliss.

In 223 every Wednesday, first half of lunch

It’s how-to-solve it sessions with the loveliest bunch

For year 7 and 8 of ALL maths abilities

To develop your Junior Maths Challenge capabilities

Getting Bronze, Silver, Gold is really very easy

If you use all our tricks from the proper to the sleazy.

So bring a pen and a friend and be brave, don’t be shy

And this April we’ll beat the school’s all-time high

Of 90% getting medals because

We’ve got a chocolate fountain and some jokes about cos.

223. Every Wednesday, during lunch (the first half)

For some maths and some food, and a bit of a laugh.

]]>Hey there middle school you better listen to this

It’s Maths Soc news that will fill you with bliss.

In 223 every Wednesday, first half of lunch

It’s how-to-solve it sessions with the loveliest bunch

For year 7 and 8 of ALL maths abilities

To develop your Junior Maths Challenge capabilities

Getting Bronze, Silver, Gold is really very easy

If you use all our tricks from the proper to the sleazy.

So bring a pen and a friend and be brave, don’t be shy

And this April we’ll beat the school’s all-time high

Of 90% getting medals because

We’ve got a chocolate fountain and some jokes about cos.

223. Every Wednesday, during lunch (the first half)

For some maths and some food, and a bit of a laugh.

Gaya, Year 9

We video-called Jeju and everyone sat around a desk ready to win. It as tough and everyone was under pressure. The first question was given and straight away everyone began working fast. Throughout, everyone was tense. London and Jeju were side by side then suddenly London took the lead. Many year groups participated to keep us four points ahead. Soon the harder questions kicked in and Jeju were confident. They took the lead and eventually took the crown.

They won but London will be back! We put a lot of effort in and it was fun to talk and compete with our sister school.

Tia, 8L

]]>They won but London will be back! We put a lot of effort in and it was fun to talk and compete with our sister school.

Tia, 8L

On the Tuesday 12th December 2017, Mr Linscott accompanied the three of us to the Institute of Mechanical Engineering in Westminster, London.

We set of from North London Collegiate at 5pm and took the Jubilee line to Westminster station. When we got there, we were amazed by the sight before us. There were so many people inside and the building looked beautiful. Inside, it had intricately carved wood paneling and a very elaborate staircase.

During the evening, we had the opportunity to partake in a range of activities including: building and racing models of the 1000 mph Bloodhound World Land Speed record car and a model of a Rolls Royce jet engine, designing a robot hand and talking to engineers. We were also able to debate cutting-edge research ideas with engineers from Imperial College and Kingston University, explore aerodynamics in a special wind tunnel with model aeroplanes and drones and chat to RAF Cadets.

Two lectures took place throughout the evening; one on aerospace engineering and the other on robotics engineering from Imperial College, which we really enjoyed.

In addition, we won a competition of who could create the fastest and most efficient model of a car using certain materials in order to travel the furthest after being launched using pressurised gas. Our design theory was that we should create the car with the most streamline, least amount of mass, reinforced foundations, strong bonding and eventually a triangle shape. When we won, we were very surprised as we were not sure our design theory would pay off, but it did, and we were awarded our certificates and a kit to build our own Bloodhound World Land Speed record car.

Overall, the evening was very interesting and we feel like we gained more of an insight into the world of engineering and especially mechanical engineering. We would definitely recommend it to anyone interested in engineering, not just mechanical engineering, and maths.

By Isabella Menéndez, Alyssa Quinney and Visharlya Vijayakumar.

]]>We set of from North London Collegiate at 5pm and took the Jubilee line to Westminster station. When we got there, we were amazed by the sight before us. There were so many people inside and the building looked beautiful. Inside, it had intricately carved wood paneling and a very elaborate staircase.

During the evening, we had the opportunity to partake in a range of activities including: building and racing models of the 1000 mph Bloodhound World Land Speed record car and a model of a Rolls Royce jet engine, designing a robot hand and talking to engineers. We were also able to debate cutting-edge research ideas with engineers from Imperial College and Kingston University, explore aerodynamics in a special wind tunnel with model aeroplanes and drones and chat to RAF Cadets.

Two lectures took place throughout the evening; one on aerospace engineering and the other on robotics engineering from Imperial College, which we really enjoyed.

In addition, we won a competition of who could create the fastest and most efficient model of a car using certain materials in order to travel the furthest after being launched using pressurised gas. Our design theory was that we should create the car with the most streamline, least amount of mass, reinforced foundations, strong bonding and eventually a triangle shape. When we won, we were very surprised as we were not sure our design theory would pay off, but it did, and we were awarded our certificates and a kit to build our own Bloodhound World Land Speed record car.

Overall, the evening was very interesting and we feel like we gained more of an insight into the world of engineering and especially mechanical engineering. We would definitely recommend it to anyone interested in engineering, not just mechanical engineering, and maths.

By Isabella Menéndez, Alyssa Quinney and Visharlya Vijayakumar.

The Year 12s who went on this trip have reflected on their day...

"It was a very interesting and informative - I am a mathematician and I am proud of it!"

"A truly fun day! Bobby Seagull and Dr Rock were entertaining and inspirational. I had a great time!"

"It was really inspirational and interactive"

"Maths in Action was educational and thought provoking."

"I really enjoyed Maths in Action as the speakers were so lively and engaging. Listening about problems and theories I had never heard about before was very inspiring."

"A day planned with a variety of fascinating talks by very different teachers."

]]>"It was a very interesting and informative - I am a mathematician and I am proud of it!"

"A truly fun day! Bobby Seagull and Dr Rock were entertaining and inspirational. I had a great time!"

"It was really inspirational and interactive"

"Maths in Action was educational and thought provoking."

"I really enjoyed Maths in Action as the speakers were so lively and engaging. Listening about problems and theories I had never heard about before was very inspiring."

"A day planned with a variety of fascinating talks by very different teachers."

The course involved building a substantial autonomous robot, capable of navigating its way around an arena, collecting objects and avoiding confrontation with rival robots in the process. It required a great deal of electrical, structural and mechanical engineering, through which we were able to learn about rapid prototyping, soldering, circuit design and fabrication, debugging, and wood-working. Programming was most challenging for me, as although I had some experience with coding on the Arduino in C++, I was yet to programme a Raspberry Pi in Python. After teams had miraculously scrambled together a functioning robot in less than 5 days, we put them to the test in an arena appropriately named “The Cube” to compete against other teams. Some robots had speed but displayed no signs of intelligence, others were blessed with amazing code yet lacked stealth. In the practice round, my team’s robot did a lap clockwise only to reverse anticlockwise, erasing any points gained in the first lap. What followed was an intense 10 mins of tremendous team-work to modify our code, which subsequently ensured our success in the tournament rounds (at least until the semi-finals!).

During the course, we also gained first-hand experience of university life, mingling with academics and students from the Electronics and Computer Science department at the University of Southampton; had the opportunity to visit ECS’ nanofabrication cleanrooms and an impressive High Voltage Laboratory; and took part in engaging talks on computer vision, cyber security and robotics.

I learnt so many things during this course, including the importance of simplicity in design and coding, and was lucky enough to meet the most amazing people who all shared the same love of engineering as me. I strongly recommend the Smallpeice Trust courses to any aspiring scientist reading this because it’s an amazing opportunity to explore your passion through hands-on learning.

By Kureha Yamaguchi (13MFW)]]>

Most part of the competition was spent one to one which means that I was up against the year 12 student in the opponent team on my own. To answer each question within 30 - 90 seconds was definitely a challenge for me. Not only should I spot a quick way of solving the questions, but I also needed to be familiar with all topics so that the time taken to solve the question can be significantly reduced.

For example, one of the year 12 questions was:

‘Given that 0° < x < 90° and 13 sin x = 5, find the value of 5/tan x.’

To obtain the answer, 12, one must be aware of trigonometry functions and their use on a right-angled triangle. Additionally, having the knowledge of the side lengths of 5, 12, 13 of a right-angled triangle would greatly decrease the time taken to work out the solution of the question.

Overall, I am really glad that I took part in such a fun and exciting experience (including little disappointment when I made a stupid mistake). Our team members have all done an amazing job which results in the victory. Good luck with Round 2!

]]>

Thanks for having us Art Department!

The talk, given by an Oxford lecturer on the gaps between prime numbers, was extremely interesting and insightful. The girls also had the opportunity to hear about those who had competed for the United Kingdom at international maths competitions, inspiring a drive to join them on the teams. Thank you to the Maths Department for organising such a great trip, it was extremely enjoyable for all involved.