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Mathematics
How many whole numbers can you squeeze in between 0 and 30 such that no two pairs of numbers are the same distance apart? In the picture to the right, the first two attempts fail but the third one is good. We managed to squeeze 4 numbers between 0 and 9 with this property, {0,2,5,9}. Here are some natural questions to ask: can you answer any?
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Statistics
How do you estimate or predict events when processes are random? Can you measure how likely is it that you will win the Irish Lottery? In the "Deal or No Deal" game show can you predict the banker's offer, or determine the likely winnings given the boxes already opened in the game? Many real world processes are random phenomena. Theory in probability and statistics helps us to make sense of randomness, through statistical modelling. By observing the process and modelling randomness we can estimate what is most probable taking into account variability. Reliable statistical modelling can be used for estimation and prediction and exploring relationships between variables. For example, the price of a "Big Mac" burger is often used as an index to compare economies between different countries. What factors may affect the price of a Big Mac burger? How would one identify which factors significantly affect the price and estimate its effect? Time series analysis attempts to assess past performance to predict what is likely to happen in the future, for example, to explore patterns in shares, economical indicators, birth rates, mortality rates, or athletic ability, over time. How would you design and analyse a survey or experiment, for example, in survey polls or clinical trials? Through probabilistic sampling we can weigh up the evidence from our sampled data and assess whether a hypothesis may be true or rejected.
"When it is not in our power to determine what is true, we ought to follow what is most probable" -- Rene Descartes |
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Computational MathematicsThis branch of mathematics was originally concerned with solving equations using computers, but has developed to encompass a broad range of activities from simulating mechanical and biological systems, to using computers to construct mathematical proofs, to building tools to help you find your friends using Google. As computers keep developing, becoming faster and more sophisticated, the need for new mathematical techniques becomes more immediate, demanding for example new algorithms to harness the power of cloud computing, or new encryption techniques that can survive attacks by powerful computers.
"The purpose of computing is insight, not numbers" -- Richard Hamming |
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BioinformaticsBioinformatics uses computational and statistical techniques to model and analyze large-scale biomolecular information. In an era in which biology has become swamped with amazing data from initiatives such as the Human Genome Project, and much larger projects that have succeeded it, bioinformatics is critical to realizing the potential of contemporary life-sciences research.Techniques and ideas from mathematics and statistics are now applied in almost all areas of molecular biology research, from tracking the emergence and spread of the recent H1N1 influenza pandemic to the development of drugs for major human diseases, such as cancer and HIV. Bioinformatics breaks down the boundaries between traditionally separate disciplines and seeks to harness the benefits of getting experts from different disciplines working together on some of the most important problems of our time. |
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Applied MathematicsApplied mathematics consists of mathematical techniques and results that are used to investigate problems in areas such as science, engineering, finance, industry and medicine. Applied mathematicians propose and study sets of equations called models that describe real-world phenomena. Traditionally, applied mathematicians tended to work in the area of the physical sciences and engineering, and many still do. However, applied mathematics is now an extremely broad subject, encompassing models describing, for example, the spread of infectious diseases, chemical reactions, cancer tumour growth, combustion in car engines, biological cells communication, the variation in the price of stocks and shares, the behaviour of drugs in the body, traffic flow, the operation of electronic devices, human evolution, and so on. Applied mathematicians find work in, for example, schools, universities, the financial sector, and industry. |
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