Maths can lead to a career in anything... including fashion
My passion for the fusion of science and design developed at University. Although I learned to knit and crochet as a child, it was while at university studying maths that my interest in knitting really developed, and I started to design and make unusual and interesting clothes. Being self-taught, I was not restricted by any boundaries and felt I could translate any idea into knitting by working out a logical way of doing it.
This approach clearly owed something to my mathematical background, and for me, there was a natural relationship between the two. I often put many ideas and techniques together to create complex designs, many of which are are non-repetitive, and combine colour, texture and form so that the result appears totally natural. Even now as a research professor, knitting continues to be, for me, the perfect blend of creativity, craft and technology, which my education seemed to want to separate.
Knitting used to be the poor relation of textiles but has now grown to be properly recognized, and has a vital part to play in fashion. I built an international business in fashion knitwear and yarns, with my designs and knitting kits selling in major retail stores worldwide such as Liberty and Harrods in London, Saks on 5th Avenue in New York and Takashimaya in Tokyo. Innovative and experimental crafted knitwear have recently made a big splash on the London Fashion Week catwalk, with Mark Fast’s intricate designs.
But knitting is not the only textile that has been influenced by science and mathematics. My current work as director for the Centre for Fashion Science at the London College of Fashion aims for collaboration between scientists and designers to create new concepts, products and processes which harness innovations in science and technology. This will break new ground in fashion–related research and hopefully merge desirability and fashion with sustainability and well-being.
The convergence of digital technologies and disciplines such as nanotechnology, with materials and cognitive sciences has opened up unprecedented possibilities for these technologies to create fashion and textiles that can respond to the user and have a function which enhances other aspects of our lifestyles.
For example, some of the centre’s researchers are exploring applications of body scanning for made-to-measure fashion and accessories and virtual try-on developments for key retailers. This could allow consumers to see if trousers fit their figure without having the hassle of the changing rooms.
Other areas of research include the development personalised design. This includes projects in to bespoke bags, which are ergonomically designed to fit the body; research examining how new forms of textiles can be developed to conform to the body providing clothes that truly are the ‘perfect fit’; and the study of seamless garment knitting for comfort and personalised fit utilising advanced knitting technology. A team at London College of Fashion is also developing an online style advisor system for ‘mass customization’, allowing the consumer to make clothing to their own specification. This is part of a European collaborative research project involving manufacturers and institutions from Germany, France, Greece, Italy and the UK.
Wonderland, a research project funded by the EPSRC, is collaboration between Professors Helen Storey (co-director Centre for Fashion Science at LCF) and Prof Tony Ryan (a polymer chemist from Sheffield University) which is enabling fashion to create the seemingly impossible. For instance, the disappearing dress, made from dissolving textiles which disintegrate in water, creating vibrant underwater fireworks; bringing a whole new possibility for sustainable clothes development. There are also incredible extensions of this, using the technologies to explore intelligent packaging, which once finished with, can be dissolved under hot water to form a gel in which seeds can be grown. This concept could revolutionise the packaging industry and resolve the age old problem of waste plastic.
These are just a few examples of how science and technology will increasingly link up with textiles, fashion and the creative industries to both push the boundaries of useful new technology and create design-led and innovative product ideas. These are exciting times for fashion and science, and I am excited to be at the cusp of the research which could change our lives.
Sandy Black is supporting the Science: [So what? So everything] campaign, which aims to highlight the science behind our everyday lives and the exciting careers in science.
Monday, November 2, 2009
Mental Arithmetic
Being able to do calculations in your head has some obvious uses, like checking your change in the supermarket, or figuring out the scores on the cricket ground. But is it useful for anything else in this age of computers and calculators?
The most important thing mental arithmetic does is to give you a feel for numbers, relationships between them and the patterns they make. This is obviously essential if you want to do well in maths at school, or go on to take a job that uses a lot of maths. But even if you plan to move into a completely different field after school, you will need a good grip on numbers and the ability to solve simple maths problems in your head. It’s a bit like learning a language: even though you can resort to a dictionary whenever you don’t know a word, you will never be able to speak fluently unless you know a lot of the vocabulary off the top of your head.
A safety net
Doctors and nurses, for example, need to do complicated calculations to work out the doses of the drugs they have to give to their patients. Even if they do have a calculator to hand, they have to be able to spot if they have made a mistake – punching in an extra zero or forgetting a decimal point can lead to the dose being ten times too high or low, with disastrous consequences for the patient. Being good at mental arithmetic is like having a safety-net that will guard you against mistakes.
Visual imagination
People whose work is very visual, like designers, architects and artists, for example, need to be able to imagine the way three-dimensional objects move in space. A look at a fashion designer’s sketch pad will show you that he or she has an intuitive feel for proportions and perspective. Such a feel for space and the objects in it can only come through practice and experience. The mental arithmetic you learn at school helps you exercise your visual imagination.
Maths in music
If you play a musical instrument, you will already have learnt how maths is important in music. Certain combinations of sounds are pleasing to us, because of the mathematical relationships between their frequencies. This is all about fractions, and musicians and sound engineers need an intuitive understanding of the relationships between numbers.
These are just three examples of how a good understanding of maths and numbers helps even in areas which, on the face of it, have nothing to do with maths. But also in your private life such an understanding is essential. When you open the paper or switch on the TV, you are bombarded by statistics, issued by politicians to get you to vote for them or by companies to get you to buy their products. When you open your mail, you will find bank statements and bills. You won’t always have the time to sit down and check them with a calculator and a maths book. But if you understand numbers, a quick glance can give you a good indication as to whether what is presented to you makes sense or not. If you’re good at mental arithmetic, you’ll glide much more smoothly through a world that is, after all, made up of numbers and patterns.
The most important thing mental arithmetic does is to give you a feel for numbers, relationships between them and the patterns they make. This is obviously essential if you want to do well in maths at school, or go on to take a job that uses a lot of maths. But even if you plan to move into a completely different field after school, you will need a good grip on numbers and the ability to solve simple maths problems in your head. It’s a bit like learning a language: even though you can resort to a dictionary whenever you don’t know a word, you will never be able to speak fluently unless you know a lot of the vocabulary off the top of your head.
A safety net
Doctors and nurses, for example, need to do complicated calculations to work out the doses of the drugs they have to give to their patients. Even if they do have a calculator to hand, they have to be able to spot if they have made a mistake – punching in an extra zero or forgetting a decimal point can lead to the dose being ten times too high or low, with disastrous consequences for the patient. Being good at mental arithmetic is like having a safety-net that will guard you against mistakes.
Visual imagination
People whose work is very visual, like designers, architects and artists, for example, need to be able to imagine the way three-dimensional objects move in space. A look at a fashion designer’s sketch pad will show you that he or she has an intuitive feel for proportions and perspective. Such a feel for space and the objects in it can only come through practice and experience. The mental arithmetic you learn at school helps you exercise your visual imagination.
Maths in music
If you play a musical instrument, you will already have learnt how maths is important in music. Certain combinations of sounds are pleasing to us, because of the mathematical relationships between their frequencies. This is all about fractions, and musicians and sound engineers need an intuitive understanding of the relationships between numbers.
These are just three examples of how a good understanding of maths and numbers helps even in areas which, on the face of it, have nothing to do with maths. But also in your private life such an understanding is essential. When you open the paper or switch on the TV, you are bombarded by statistics, issued by politicians to get you to vote for them or by companies to get you to buy their products. When you open your mail, you will find bank statements and bills. You won’t always have the time to sit down and check them with a calculator and a maths book. But if you understand numbers, a quick glance can give you a good indication as to whether what is presented to you makes sense or not. If you’re good at mental arithmetic, you’ll glide much more smoothly through a world that is, after all, made up of numbers and patterns.
The Universal Language
Mathematics is the only language shared by all human beings regardless of culture, religion, or gender. Pi is still approximately 3.14159 regardless of what country you are in. Adding up the cost of a basket full of groceries involves the same math process regardless of whether the total is expressed in dollars, rubles, or yen. With this universal language, all of us, no matter what our unit of exchange, are likely to arrive at math results the same way.
Very few people, if any, are literate in all the world's tongues—English, Chinese, Arabic, Bengali, and so on. But virtually all of us possess the ability to be "literate" in the shared language of math. This math literacy is called numeracy, and it is this shared language of numbers that connects us with people across continents and through time. It is what links ancient scholars and medieval merchants, astronauts and artists, peasants and presidents.
With this language we can explain the mysteries of the universe or the secrets of DNA. We can understand the forces of planetary motion, discover cures for catastrophic diseases, or calculate the distance from Boston to Bangkok. We can make chocolate chip cookies or save money for retirement. We can build computers and transfer information across the globe. Math is not just for calculus majors. It's for all of us. And it's not just about pondering imaginary numbers or calculating difficult equations. It's about making better daily decisions and, hopefully, leading richer, fuller lives.
Very few people, if any, are literate in all the world's tongues—English, Chinese, Arabic, Bengali, and so on. But virtually all of us possess the ability to be "literate" in the shared language of math. This math literacy is called numeracy, and it is this shared language of numbers that connects us with people across continents and through time. It is what links ancient scholars and medieval merchants, astronauts and artists, peasants and presidents.
With this language we can explain the mysteries of the universe or the secrets of DNA. We can understand the forces of planetary motion, discover cures for catastrophic diseases, or calculate the distance from Boston to Bangkok. We can make chocolate chip cookies or save money for retirement. We can build computers and transfer information across the globe. Math is not just for calculus majors. It's for all of us. And it's not just about pondering imaginary numbers or calculating difficult equations. It's about making better daily decisions and, hopefully, leading richer, fuller lives.
Population Growth
In the last few centuries, the number of people living on Earth has increased many times over. By the year 2000, there will be 10 times more people on Earth than there were 300 years ago.
How can population grow so fast? Think of a family tree. At the top are 2 parents, and beneath them the children they had. Listed beneath those children are the children they had, and so on and so on, down through each generation. As long as the family members continue to reproduce, the family tree continues to increase in size, getting larger with each passing generation. This same basic idea applies to the world's population.
Exponential growth
Population grows in the same way that money grows when it's left to compound interest in a bank. With money, growth comes through accumulating interest upon interest. The interest payments you accumulate eventually earn interest, increasing your money. With population growth, new members of the population eventually produce other new members of the population. The population increases exponentially as time passes.
--------------------------------------------------------------------------------
WORLD POPULATION
Year Population
1700 600,000,000
1800 900,000,000
1900 1,500,000,000
2000 6,000,000,000
--------------------------------------------------------------------------------
A crucial difference between money and population is that money can increase without limits while population can't. Any population of living creatures is constrained by the availability of food, water, land, or other important resources. Once those resources are depleted, a population won't continue to grow exponentially. It will plateau, or even decline, as a result of disease or malnutrition. Unlike calculating interest, calculating population growth is an imprecise business.
How fast will it grow?
To arrive at a reasonable estimate of how the world's population will grow in the next 50 years, you need to look at birth and death rates (the rates at which people are being born and dying in any given period). If birth and death rates stayed the same across the years in all parts of the world, population growth could be figured with a fairly simple formula much like the one used to figure compound interest. Birth and death rates aren't constant across countries and through time, however. Disease or disaster can cause death rates to increase for a certain period. A booming economy might mean higher birth rates for a given year.
The rate of Earth's population growth is slowing down. Throughout the 1960s, the world's population was growing at a rate of about 2% per year. By 1990, that rate was down to 1.5%, and by the year 2015, it's expected to drop to 1%. Family planning initiatives, an aging population, and the effects of diseases such as AIDS are some of the factors behind this rate decrease.
Even at these very low rates of population growth, the numbers are staggering. By 2015, despite a low expected 1% growth rate, experts estimate there will be 7 billion people on the planet. By 2050, there may be as many as 10 billion people living on Earth. Can the planet support this population? When will we reach the limit of our resources?
How can population grow so fast? Think of a family tree. At the top are 2 parents, and beneath them the children they had. Listed beneath those children are the children they had, and so on and so on, down through each generation. As long as the family members continue to reproduce, the family tree continues to increase in size, getting larger with each passing generation. This same basic idea applies to the world's population.
Exponential growth
Population grows in the same way that money grows when it's left to compound interest in a bank. With money, growth comes through accumulating interest upon interest. The interest payments you accumulate eventually earn interest, increasing your money. With population growth, new members of the population eventually produce other new members of the population. The population increases exponentially as time passes.
--------------------------------------------------------------------------------
WORLD POPULATION
Year Population
1700 600,000,000
1800 900,000,000
1900 1,500,000,000
2000 6,000,000,000
--------------------------------------------------------------------------------
A crucial difference between money and population is that money can increase without limits while population can't. Any population of living creatures is constrained by the availability of food, water, land, or other important resources. Once those resources are depleted, a population won't continue to grow exponentially. It will plateau, or even decline, as a result of disease or malnutrition. Unlike calculating interest, calculating population growth is an imprecise business.
How fast will it grow?
To arrive at a reasonable estimate of how the world's population will grow in the next 50 years, you need to look at birth and death rates (the rates at which people are being born and dying in any given period). If birth and death rates stayed the same across the years in all parts of the world, population growth could be figured with a fairly simple formula much like the one used to figure compound interest. Birth and death rates aren't constant across countries and through time, however. Disease or disaster can cause death rates to increase for a certain period. A booming economy might mean higher birth rates for a given year.
The rate of Earth's population growth is slowing down. Throughout the 1960s, the world's population was growing at a rate of about 2% per year. By 1990, that rate was down to 1.5%, and by the year 2015, it's expected to drop to 1%. Family planning initiatives, an aging population, and the effects of diseases such as AIDS are some of the factors behind this rate decrease.
Even at these very low rates of population growth, the numbers are staggering. By 2015, despite a low expected 1% growth rate, experts estimate there will be 7 billion people on the planet. By 2050, there may be as many as 10 billion people living on Earth. Can the planet support this population? When will we reach the limit of our resources?
Sunday, November 1, 2009
Maths in everyday life - 3
Market research
Have you ever been stopped by someone in the street wanting you to complete a questionnaire? If yes, have you thought about what happens to these answers?
All the data collected will be analysed by market researchers and statisticians, who then work out what people actually want. This could be something like finding out what people think about a new mobile phone, the look of a new MP3 player, anything really.
Market research is carried out by almost every business to make sure the products or services fulfil the consumer’s wants and needs. This helps the company stay ahead of the competition.
Our planet and us
At the end of a long day you finally go to bed. The Sun has gone down and you know for certain that it will rise again tomorrow, and so does every other living thing on Earth. The life of every animal and plant is governed by the movement of the Earth around the Sun, and every animal and plant is perfectly adapted to the environment it lives in.
We humans try to understand the natural world around us using sciences like physics and biology. These sciences are written in the language of maths. Physicists and astronomers use mathematical formulae to express the secrets of the universe and to send humans into space. Biologists believe that the secret of life lies in the genes and mathematical processes determine how genes get passed on and cause animals and plants to evolve so that they fit their environment perfectly. Our brains work because of the complicated interaction of neurons — so complicated that only maths has a chance to describe it. Even the way the patterns form on a Leopard’s coat is best understood using maths.
Just a day like any other. And like any other day, one where mathematics has played a major part.
Have you ever been stopped by someone in the street wanting you to complete a questionnaire? If yes, have you thought about what happens to these answers?
All the data collected will be analysed by market researchers and statisticians, who then work out what people actually want. This could be something like finding out what people think about a new mobile phone, the look of a new MP3 player, anything really.
Market research is carried out by almost every business to make sure the products or services fulfil the consumer’s wants and needs. This helps the company stay ahead of the competition.
Our planet and us
At the end of a long day you finally go to bed. The Sun has gone down and you know for certain that it will rise again tomorrow, and so does every other living thing on Earth. The life of every animal and plant is governed by the movement of the Earth around the Sun, and every animal and plant is perfectly adapted to the environment it lives in.
We humans try to understand the natural world around us using sciences like physics and biology. These sciences are written in the language of maths. Physicists and astronomers use mathematical formulae to express the secrets of the universe and to send humans into space. Biologists believe that the secret of life lies in the genes and mathematical processes determine how genes get passed on and cause animals and plants to evolve so that they fit their environment perfectly. Our brains work because of the complicated interaction of neurons — so complicated that only maths has a chance to describe it. Even the way the patterns form on a Leopard’s coat is best understood using maths.
Just a day like any other. And like any other day, one where mathematics has played a major part.
Maths in everyday life - 2
Transport
You wait for the bus. Maths is used to timetable buses, trains and planes, taking into account the limited stocks of vehicles, the cost of fuel and the number of people wanting to use them for various journeys across the day. It is used to decide the timing of traffic lights, and to understand traffic flow and congestion. This is another application of operational research (see planning).
Maths also affects the designs of these vehicles, particularly planes, cars and boats. Aerodynamics, another application of fluid dynamics, is obviously vital in designing a plane that can actually fly, but is also important in designing any sort of vehicle to move as smoothly through the air as possible so that it can go faster and take less fuel.
Understanding chance and risk
You get off the bus and someone is selling tickets in a raffle for a new car. Should you buy one? What are the chances of you winning in this, or in any other, lottery? All games of chance are governed by probabilities of events happening. If you understand probability, you have a much better chance of coming out on top, or in deciding that it's not worth spending your money at all.
The bus got stuck in traffic, and you arrived at your destination really late. Should you ride your bike next time, you wonder. But is that too risky? And, if you do, should you wear a helmet?
Your friend calls you to say she has had some negative test results from the doctor. Is she definitely sick, or what are the chances that the test is wrong and she is not sick at all? There are a number of treatment options available, but all have different rates of success and different side effects. To decide which one to take, she will need to weigh up the risks of side effects of each treatment against the chances of success, using the probabilities of each of these.
Business and industry also need to make decisions about risk and chance and need mathematicians - or operational researchers - to help them with this.
Communicating
Finally you get home and get a chance to check your email. Computers store all information as binary numbers, and use mathematical operations to manipulate this information, whether you are editing an email, resizing a photo or setting preferences in your web browser.
Computers communicate digitally, sending packets of information across networks or wires, fibre optic cables and phone lines. The way this information is encoded uses maths. Maths is also used to create better compression methods, so that you can download mp3s faster, or that movie makers can fit longer movies and more special features on DVDs.
You wait for the bus. Maths is used to timetable buses, trains and planes, taking into account the limited stocks of vehicles, the cost of fuel and the number of people wanting to use them for various journeys across the day. It is used to decide the timing of traffic lights, and to understand traffic flow and congestion. This is another application of operational research (see planning).
Maths also affects the designs of these vehicles, particularly planes, cars and boats. Aerodynamics, another application of fluid dynamics, is obviously vital in designing a plane that can actually fly, but is also important in designing any sort of vehicle to move as smoothly through the air as possible so that it can go faster and take less fuel.
Understanding chance and risk
You get off the bus and someone is selling tickets in a raffle for a new car. Should you buy one? What are the chances of you winning in this, or in any other, lottery? All games of chance are governed by probabilities of events happening. If you understand probability, you have a much better chance of coming out on top, or in deciding that it's not worth spending your money at all.
The bus got stuck in traffic, and you arrived at your destination really late. Should you ride your bike next time, you wonder. But is that too risky? And, if you do, should you wear a helmet?
Your friend calls you to say she has had some negative test results from the doctor. Is she definitely sick, or what are the chances that the test is wrong and she is not sick at all? There are a number of treatment options available, but all have different rates of success and different side effects. To decide which one to take, she will need to weigh up the risks of side effects of each treatment against the chances of success, using the probabilities of each of these.
Business and industry also need to make decisions about risk and chance and need mathematicians - or operational researchers - to help them with this.
Communicating
Finally you get home and get a chance to check your email. Computers store all information as binary numbers, and use mathematical operations to manipulate this information, whether you are editing an email, resizing a photo or setting preferences in your web browser.
Computers communicate digitally, sending packets of information across networks or wires, fibre optic cables and phone lines. The way this information is encoded uses maths. Maths is also used to create better compression methods, so that you can download mp3s faster, or that movie makers can fit longer movies and more special features on DVDs.
Maths in everyday life
Maths is everywhere. Without realizing, we use maths every day, and it plays a part in nearly all our daily activities. Every time we pick up the phone, use the internet, manage money, decide to take a risk, check the weather report, go to the doctors or travel anywhere, maths plays its part.
The weather
You wake up in the morning and get ready to go out. You check the weather report to decide what to wear and what to take - an umbrella? Sunglasses? A hat? The forecasts you read in the paper are a result of solving complicated equations involving the way air, clouds and water move around the planet - part of an area of mathematics called fluid dynamics.
Long-term weather trends can affect our whole environment. For instance, climate change might lead to more storms and more floods. These problems are part of the work of environmental statisticians who study data received from around the world and try to predict what might happen over the next several years. For more information related to this subject please visit the RSS guide to environmental statistics link below.
Buildings and construction
If it is rainy and cold outside, you will be happy to stay at home a while longer and have a nice hot cup of tea. But someone has built the house you are in, made sure it keeps the cold out and the warmth in, and provided you with running water for the tea. This someone is most likely an engineer. Engineers are responsible for just about everything we take for granted in the world around us, from tall buildings, tunnels and football stadiums, to access to clean drinking water. They also design and build vehicles, aircraft, boats and ships. What's more, engineers help to develop things which are important for the future, such as generating energy from the sun, wind or waves. Maths is involved in everything an engineer does, whether it is working out how much concrete is needed to build a bridge, or determining the amount of solar energy necessary to power a car.
Money
Once out the door you walk past a newsstand where the headline "house prices boom again" scream from the front pages. House prices are determined by supply and demand, and the one thing anyone buying a house needs is money. Most people get a loan from a bank to buy a house, and then have to pay back the money they borrowed plus some interest and fees. To choose which bank to borrow from, and to decide if you can afford to borrow at all, you need to understand compound interest.
The housing market is part of the bigger economic picture. How the economy is doing affects how much things cost, how much we are paid and how much the government spends - and maths is used to monitor the economy and predict how it will change. A large part of the world's economy is invested in the stock market, and highly skilled mathematicians are employed to try to understand, and even predict, movements in the stock market.
Planning
Whether you are managing money (trying to save for a gap-year holiday), resources (trying to make those Easter eggs last) or time (deciding how much time to spend on studying for each subject), you are doing calculations, sometimes automatically in your head, trying to optimise your outputs (money saved, grades achieved) given your inputs (pay from part-time job, hours in the day). In industry this is called operational research, and is used to improve the processes used in manufacturing, in how businesses are run, and in making the best use of resources such as beds in a hospital or police on the beat.
The weather
You wake up in the morning and get ready to go out. You check the weather report to decide what to wear and what to take - an umbrella? Sunglasses? A hat? The forecasts you read in the paper are a result of solving complicated equations involving the way air, clouds and water move around the planet - part of an area of mathematics called fluid dynamics.
Long-term weather trends can affect our whole environment. For instance, climate change might lead to more storms and more floods. These problems are part of the work of environmental statisticians who study data received from around the world and try to predict what might happen over the next several years. For more information related to this subject please visit the RSS guide to environmental statistics link below.
Buildings and construction
If it is rainy and cold outside, you will be happy to stay at home a while longer and have a nice hot cup of tea. But someone has built the house you are in, made sure it keeps the cold out and the warmth in, and provided you with running water for the tea. This someone is most likely an engineer. Engineers are responsible for just about everything we take for granted in the world around us, from tall buildings, tunnels and football stadiums, to access to clean drinking water. They also design and build vehicles, aircraft, boats and ships. What's more, engineers help to develop things which are important for the future, such as generating energy from the sun, wind or waves. Maths is involved in everything an engineer does, whether it is working out how much concrete is needed to build a bridge, or determining the amount of solar energy necessary to power a car.
Money
Once out the door you walk past a newsstand where the headline "house prices boom again" scream from the front pages. House prices are determined by supply and demand, and the one thing anyone buying a house needs is money. Most people get a loan from a bank to buy a house, and then have to pay back the money they borrowed plus some interest and fees. To choose which bank to borrow from, and to decide if you can afford to borrow at all, you need to understand compound interest.
The housing market is part of the bigger economic picture. How the economy is doing affects how much things cost, how much we are paid and how much the government spends - and maths is used to monitor the economy and predict how it will change. A large part of the world's economy is invested in the stock market, and highly skilled mathematicians are employed to try to understand, and even predict, movements in the stock market.
Planning
Whether you are managing money (trying to save for a gap-year holiday), resources (trying to make those Easter eggs last) or time (deciding how much time to spend on studying for each subject), you are doing calculations, sometimes automatically in your head, trying to optimise your outputs (money saved, grades achieved) given your inputs (pay from part-time job, hours in the day). In industry this is called operational research, and is used to improve the processes used in manufacturing, in how businesses are run, and in making the best use of resources such as beds in a hospital or police on the beat.
Why keep on studying maths?
Mathematics is one of the most general, and one of the most fundamental subjects that you can study. Although it may sometimes be difficult to see immediately the relevance of maths to a future career, and perhaps to subjects you intend to study later, maths in fact gives you an excellent grounding for any subject and is itself a prerequisite for many.
Why take A level maths?
Deciding which A levels to take can be difficult. Sometime it is a conflict of what you really like or are good at and what you want to do in order to be successful in your career or even something that your parents are doing. If you are thinking of going on to university, your first step should be to look at all the courses you might possibly want to take and see what the requirements are. Some courses specify particular subjects at A level and obviously this should be your first consideration.
For a degree in maths, statistics, physics, engineering or actuarial science, for example, you will almost certainly have to have a good maths A level and possible a further maths A level. However, there are many degrees which do not specify any particular subjects they wish you to have taken and, for many of these, maths will be an excellent choice.
If you are thinking of looking for a job straight after A levels, maths is a great "core" subject - in fact, it is one of the most important subjects you can take. This is because the ability to understand and manipulate numbers and mathematical concepts is extremely useful for almost any job.
There is always a demand for employees who can think logically and process information accurately - skills which an A level in maths will teach you.
Further maths?
If you enjoy doing maths, you might want to consider taking Further Maths at A/S or A level. The problems you are faced with in further maths are more challenging that the ordinary mathematics problems. They can also be more applicable in real case situations and have applications in physics, chemistry or biology. You can do this even if your school or college does not offer it.
Scientists need maths and stats!
Maths is the language of the physical sciences, and many of the quantitative parts of the social sciences as well. It also enables you to communicate complicated concepts. These more general skills that will be useful no matter what you want to do in the future.
Practically any course in the social or laboratory sciences will include a module on statistics, and students who stopped studying maths at GCSE often find this very difficult. If you have A level maths, even if this was not a required subject for admission, you will be ahead of the game!
Practically any course in the social or laboratory sciences will include a module on statistics, and students who stopped studying maths at GCSE often find this very difficult. If you have A level maths, even if this was not a required subject for admission, you will be ahead of the game
Engineering
If you study engineering you will use maths for most of your courses. Whether you are doing civil, mechanical, electrical or materials engineering, you will need to use geometry, calculus, and algebra to work with mathematical formulas for physical forces, electrical currents and other phenomena. For example, when studying civil engineering you will have to calculate the force distribution for different structures, such as truss bridges. This involves a combination of trigonometry and solving the equations of forces on the bridge. On other occasions you need to use integration to calculate the centre of mass of an object, or use differential equations to understand the flow of water through pipes.
Economics
Studying economics requires you not only to be able to handle data and work with figures, but to understand the concepts underlying economic questions as well. You will use maths to calculate compound interest, and arithmetic series to calculate growth of investments. You will need to use calculus to optimise cost-and-profit calculations, and to use maths to express and analyse supply and demand problems.
Medicine
Medical students have to take courses in statistics, which is not surprising given that much of today's medical knowledge is evidence-based. You will need to critically interpret data, such as the results of trials of new medical practise, judge the reliability of tests and assess the risks of treatments. Maths is also used in medical research for modeling tumour growth and the effects of therapy, planning treatment and understanding and interpreting medical scans.
Archaeology
Mathematics is even necessary in many of the social sciences, such as psychology and archaeology. Archaeologists use a variety of mathematical and statistical techniques to present the data from archaeological surveys and try to distinguish patterns in their results that shed light on past human behavior. Statistical measures are used during excavation to monitor which pits are most successful and decide on further excavation. Finds are analyzed using statistical and numerical methods to spot patterns in the way the archaeological record changes over time, and geographically within a site and across the country. Archaeologists also use statistics to test the reliability of their interpretations.
And best of all...
Obviously, if you want to go on to study mathematics or statistics, all the maths and stats you have done in the past will play its part. If you enjoy and even love these subjects, this is the greatest help in doing well. But even if this isn't exactly you, building up your mathematical toolbox will come in handy whatever you intend to study.
Why take A level maths?
Deciding which A levels to take can be difficult. Sometime it is a conflict of what you really like or are good at and what you want to do in order to be successful in your career or even something that your parents are doing. If you are thinking of going on to university, your first step should be to look at all the courses you might possibly want to take and see what the requirements are. Some courses specify particular subjects at A level and obviously this should be your first consideration.
For a degree in maths, statistics, physics, engineering or actuarial science, for example, you will almost certainly have to have a good maths A level and possible a further maths A level. However, there are many degrees which do not specify any particular subjects they wish you to have taken and, for many of these, maths will be an excellent choice.
If you are thinking of looking for a job straight after A levels, maths is a great "core" subject - in fact, it is one of the most important subjects you can take. This is because the ability to understand and manipulate numbers and mathematical concepts is extremely useful for almost any job.
There is always a demand for employees who can think logically and process information accurately - skills which an A level in maths will teach you.
Further maths?
If you enjoy doing maths, you might want to consider taking Further Maths at A/S or A level. The problems you are faced with in further maths are more challenging that the ordinary mathematics problems. They can also be more applicable in real case situations and have applications in physics, chemistry or biology. You can do this even if your school or college does not offer it.
Scientists need maths and stats!
Maths is the language of the physical sciences, and many of the quantitative parts of the social sciences as well. It also enables you to communicate complicated concepts. These more general skills that will be useful no matter what you want to do in the future.
Practically any course in the social or laboratory sciences will include a module on statistics, and students who stopped studying maths at GCSE often find this very difficult. If you have A level maths, even if this was not a required subject for admission, you will be ahead of the game!
Practically any course in the social or laboratory sciences will include a module on statistics, and students who stopped studying maths at GCSE often find this very difficult. If you have A level maths, even if this was not a required subject for admission, you will be ahead of the game
Engineering
If you study engineering you will use maths for most of your courses. Whether you are doing civil, mechanical, electrical or materials engineering, you will need to use geometry, calculus, and algebra to work with mathematical formulas for physical forces, electrical currents and other phenomena. For example, when studying civil engineering you will have to calculate the force distribution for different structures, such as truss bridges. This involves a combination of trigonometry and solving the equations of forces on the bridge. On other occasions you need to use integration to calculate the centre of mass of an object, or use differential equations to understand the flow of water through pipes.
Economics
Studying economics requires you not only to be able to handle data and work with figures, but to understand the concepts underlying economic questions as well. You will use maths to calculate compound interest, and arithmetic series to calculate growth of investments. You will need to use calculus to optimise cost-and-profit calculations, and to use maths to express and analyse supply and demand problems.
Medicine
Medical students have to take courses in statistics, which is not surprising given that much of today's medical knowledge is evidence-based. You will need to critically interpret data, such as the results of trials of new medical practise, judge the reliability of tests and assess the risks of treatments. Maths is also used in medical research for modeling tumour growth and the effects of therapy, planning treatment and understanding and interpreting medical scans.
Archaeology
Mathematics is even necessary in many of the social sciences, such as psychology and archaeology. Archaeologists use a variety of mathematical and statistical techniques to present the data from archaeological surveys and try to distinguish patterns in their results that shed light on past human behavior. Statistical measures are used during excavation to monitor which pits are most successful and decide on further excavation. Finds are analyzed using statistical and numerical methods to spot patterns in the way the archaeological record changes over time, and geographically within a site and across the country. Archaeologists also use statistics to test the reliability of their interpretations.
And best of all...
Obviously, if you want to go on to study mathematics or statistics, all the maths and stats you have done in the past will play its part. If you enjoy and even love these subjects, this is the greatest help in doing well. But even if this isn't exactly you, building up your mathematical toolbox will come in handy whatever you intend to study.
Mathematics education
Mathematics education is the practice of teaching and learning mathematics, as well as the field of scholarly research on this practice. Researchers in mathematics education are in the primarily concerned with the tools, methods and approaches that facilitate practice or the study of practice. However mathematics education research, known on the continent of Europe as the didactics of mathematics, has developed into a fully fledged field of study, with its own characteristic concepts, theories, methods, national and international organisations, conferences and literature. This article describes some of the history, influences and recent controversies concerning mathematics education as a practice.
History
Elementary mathematics was part of the education system in most ancient civilisations, including Ancient Greece, the Roman empire, Vedic society and ancient Egypt. In most cases, a formal education was only available to male children with a sufficiently high status, wealth or caste.
In Plato's division of the liberal arts into the trivium and the quadrivium, the quadrivium included the mathematical fields of arithmetic and geometry. This structure was continued in the structure of classical education that was developed in medieval Europe. Teaching of geometry was almost universally based on Euclid's Elements. Apprentices to trades such as masons, merchants and money-lenders could expect to learn such practical mathematics as was relevant to their profession.
The first mathematics textbooks to be written in English and French were published by Robert Recorde, beginning with The Grounde of Artes in 1540.
In the Renaissance the academic status of mathematics declined, because it was strongly associated with trade and commerce. Although it continued to be taught in European universities, it was seen as subservient to the study of Natural, Metaphysical and Moral Philosophy.
This trend was somewhat reversed in the seventeenth century, with the University of Aberdeen creating a Mathematics Chair in 1613, followed by the Chair in Geometry being set up in University of Oxford in 1619 and the Lucasian Chair of Mathematics being established by the University of Cambridge in 1662. However, it was uncommon for mathematics to be taught outside of the universities. Isaac Newton, for example, received no formal mathematics teaching until he joined Trinity College, Cambridge in 1661.
In the eighteenth and nineteenth centuries the industrial revolution led to an enormous increase in urban populations. Basic numeracy skills, such as the ability to tell the time, count money and carry out simple arithmetic, became essential in this new urban lifestyle. Within the new public education systems, mathematics became a central part of the curriculum from an early age.
By the twentieth century mathematics was part of the core curriculum in all developed countries.
During the twentieth century mathematics education was established as an independent field of research. Here are some of the main events in this development:
• In 1893 a Chair in mathematics education was created at the University of Göttingen, under the administration of Felix Klein
• The International Commission on Mathematical Instruction (ICMI) was founded in 1908, and Felix Klein became the first president of the organization
• A new interest in mathematics education emerged in the 1960s, and the commission was revitalized
• In 1968, the Shell Centre for Mathematical Education was established in Nottingham
• The first International Congress on Mathematical Education (ICME) was held in Lyon in 1969. The second congress was in Exeter in 1972, and after that it has been held every four years
In the 20th century, the cultural impact of the “electric age” (McLuhan) was also taken up by educational theory and the teaching of mathematics. While previous approach focused on "working with specialized 'problems' in arithmetic", the emerging structural approach to knowledge had "small children meditating about number theory and 'sets'."
History
Elementary mathematics was part of the education system in most ancient civilisations, including Ancient Greece, the Roman empire, Vedic society and ancient Egypt. In most cases, a formal education was only available to male children with a sufficiently high status, wealth or caste.
In Plato's division of the liberal arts into the trivium and the quadrivium, the quadrivium included the mathematical fields of arithmetic and geometry. This structure was continued in the structure of classical education that was developed in medieval Europe. Teaching of geometry was almost universally based on Euclid's Elements. Apprentices to trades such as masons, merchants and money-lenders could expect to learn such practical mathematics as was relevant to their profession.
The first mathematics textbooks to be written in English and French were published by Robert Recorde, beginning with The Grounde of Artes in 1540.
In the Renaissance the academic status of mathematics declined, because it was strongly associated with trade and commerce. Although it continued to be taught in European universities, it was seen as subservient to the study of Natural, Metaphysical and Moral Philosophy.
This trend was somewhat reversed in the seventeenth century, with the University of Aberdeen creating a Mathematics Chair in 1613, followed by the Chair in Geometry being set up in University of Oxford in 1619 and the Lucasian Chair of Mathematics being established by the University of Cambridge in 1662. However, it was uncommon for mathematics to be taught outside of the universities. Isaac Newton, for example, received no formal mathematics teaching until he joined Trinity College, Cambridge in 1661.
In the eighteenth and nineteenth centuries the industrial revolution led to an enormous increase in urban populations. Basic numeracy skills, such as the ability to tell the time, count money and carry out simple arithmetic, became essential in this new urban lifestyle. Within the new public education systems, mathematics became a central part of the curriculum from an early age.
By the twentieth century mathematics was part of the core curriculum in all developed countries.
During the twentieth century mathematics education was established as an independent field of research. Here are some of the main events in this development:
• In 1893 a Chair in mathematics education was created at the University of Göttingen, under the administration of Felix Klein
• The International Commission on Mathematical Instruction (ICMI) was founded in 1908, and Felix Klein became the first president of the organization
• A new interest in mathematics education emerged in the 1960s, and the commission was revitalized
• In 1968, the Shell Centre for Mathematical Education was established in Nottingham
• The first International Congress on Mathematical Education (ICME) was held in Lyon in 1969. The second congress was in Exeter in 1972, and after that it has been held every four years
In the 20th century, the cultural impact of the “electric age” (McLuhan) was also taken up by educational theory and the teaching of mathematics. While previous approach focused on "working with specialized 'problems' in arithmetic", the emerging structural approach to knowledge had "small children meditating about number theory and 'sets'."
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