- How to Solve It - by George Polya
- van Aubel's Theorem
- A Problem Halved: the Trouble with Fractions
- Revision tips for March
- Why Do Students Find AS-Level Maths So Difficult?
What can you do with your Maths?
I studied Maths at university because I was good at it, not because I had any idea of what career I wanted to do. People suggested accountancy, and indeed that was my first job on graduating. It was never really me, but I am forever glad of the taste of the business world and of industry that it gave me. I worked in audit, which involves checking over the accounts of businesses to ensure that they are accurate. I therefore visited many different companies and industries. My most memorable experience was of visiting an oil refining plant, where I climbed up and around some of their huge drums of oil, to verify their stock-taking exercise. Of course, some people do love this job. They enjoy the satisfaction of working as part of a team, of learning about different industries, and perhaps going onto give business financial advice. Many of our top managers qualified as accountants. Basic book-keeping is the name given to making sure all incomes and expenditures of the company are correctly accounted for. This requires some relatively straight-forward maths, most commonly simple addition. It also needs a logical mind and attention to details. Tax accountancy may be more appealing for those who like the problem solving element, and learning the many different rules of law. If you like the business financial world, and are drawn to a more mathematical job, then there are high-powered jobs in the city, modelling finances and risks, and there is the highly paid actuarial world. Actuaries assess risks, and therefore help to determine appropriate premiums for pensions and for insurance. If your inclination is more to management and business advice per se, then mathematical modelling can help with forecasting sales, revenues, cash flow and much more besides.
You may not feel inclined to a Maths career at all, but it is still possible that you may use some Maths. For instance, Medics, Biologists, Quantum Physicists, Psychologists, Economists all use Statistics. Even if you do not take the Statistics modules at A-level, then you will still find much use for the core Maths units, as a foundation for it. I personally found my mission for many years in the world of Medical Statistics. In this career, I enjoyed using my problem solving abilities, and combined this with a sense of fulfilling a useful function (collaborating in Medical research), team working, and learning about Medicine. So what do I think about the old adage, “There are lies, damn lies and Statistics”!! Well, how dare you insult me!! Surely we all believe some-one who quotes proper statistics to back up their arguments? I do feel that we are more inclined to believe them, despite the saying. However, when some people quote statistics, they are putting a spin on them to support their chosen view of reality, quoting them in a way which may confuse, where many people may misunderstand. When we have some knowledge of Statistics ourselves, it is easier to spot this, and come to our own conclusions. There is a lot of Statistics quoted by politicians and in the media, so it is great to be able to understand these more fully.
Mathematical modelling can be used in the field of finance, biology, medicine, social sciences. You may not want to work professionally in finance, but it is good to understand the implications of interest rates on your mortgage repayments, and on your investment opportunities. Is it worth your while buying the sofa on credit, or are the interest rate payments exorbitant?
Of course, Physics and Maths overlap a lot. If you are taking the Mechanics options, then this could be described as Physics. Engineering is applied Physics, so again a lot of Maths is used. Architects also use Maths, to ensure that their buildings stand up, and they might need some geometry. Geometry is helpful if some-one wants to build a fancy show-off hexagon room, or to build a bridge. A tree surgeon friend uses geometry to calculate the height of a tree, based on the length of its shadow and the angle from the top of the shadow to the top of the tree. My brother-in-law used a simple technique to make his lawn oval shaped (using 2 pegs a shortish distance apart in the middle and a very large piece of string).
Learning about prime numbers might not seem very exciting or useful. However, they are used in some codes. In the Second World War, it was some clever pure mathematicians, working with prime numbers and similar, who managed to crack the German Enigma code. This code was used in transmitting messages on war tactics between German politicians and fighter pilots. British knowledge of this information was a huge boost in winning the war. Some estimates suggest that the war ended two years sooner as a result ( http://www.bbc.co.uk/history/worldwars/wwtwo/enigma_01.shtml ). There are still some jobs available in similar areas.
For more detailed career advice, see http://www.mathscareers.org.uk/ .