Why Study Mathematics & Statistics?
Is math a subject you've enjoyed in high school? Is it something you do well at? Do you enjoy the challenge of working on math problems, and the feeling of accomplishment when you successfully solve them? You're certainly not alone, and many students find math and stats an excellent area for study at university. It's certainly challenging, and looked on with a great deal of respect. It's also very useful: the mathematical sciences are developing rapidly, providing many career opportunities and challenges both in traditional fields and in new exciting areas where mathematics and statistics turn out to be essential tools. By deciding to undertake mathematical studies at university, you will be choosing not only a fascinating and prestigious subject, but also a program which will give you excellent prospects for a rewarding career.
Did you know?
In many areas of current interest and research, methods and ideas from math and stats play a crucial role. For instance:
- In biological research, mathematics and statistics can be used to model and analyse everything from mite populations in orchards to complex biosystems. These models can be used to establish information about how populations of several species will interact in an environment, how disease or invasive species spread throughout an area, how different regions of the brain correspond to specific functions, and even how various cellular operations, such as cellular division and cell-to-cell communication work.
- Mathematics and Statistics have played a number of key roles in genetics research, in modelling DNA and its functions and replication, and in understanding and extracting the complex amount of information these helixes.
- Medical Research of course uses statistics heavily in studying diseases and treatments, for instance to determine the effectiveness of new treatments and whether these are improvements over the accepted ones. But research in medicine goes further. Models may be used to study the performance of organs and bodily functions, how diseases such as cancer, or other cells or molecules, spread throughout the body, and how viruses may be used to aid in healing. The models used simulate many possibilities, produce numerical data for each, and allow researchers to eliminate less successful approaches and find candidates for further study. This speeds up the research process dramatically, avoiding costly experimental work.
- Understanding our environment and climate represent a major focus of current scientific research, and again mathematics and statistics play an important role. Mathematicians use tools called partial differential equations to model such phenomena as the movement of oceans and the atmosphere, leading to models used to study and predict sea and weather behaviour, as well as to investigate the harnessing of power from wind and tides. Statistics may be used to study the vast amounts of data we have about these systems and look for patterns. Mathematical and Statistical models can be used to understand and make predictions about such diverse things as glacial movement, seismic events, and tsunamis.
- Industrial modelling involves using tools from math and stats to study problems in manufacturing and distribution of goods, and in service delivery. This includes such things as the design of barcodes to encapsulate information and for use in tracking, the analysis of complex delivery and shipment networks, the modelling of complex traffic patterns, and optimizing the scheduling of production processes.It also of course includes using modelling to design better products, such as cars and airplanes. Mathematicians even use origami methods to develop better ways to fold things, such as packaging, air bags, and equipment in space.
- The social sciences have also seen math and stats methods come in to play in many areas, including the use of geometry and modelling in architecture and structural design. These methods are also being used to study potential election cases, look for evidence of human rights abuses, suggest alternative election methods, study how electoral ridings should be designed, and even in crime-solving.
- Finance and Economics are two other heavy users of mathematics and statistics, in pricing of stocks, bonds, and especially of derivative securities, in analyzing and modelling complex financial systems or economies. Much of economics relies on companies and consumers and their decision making, and Game theory is used to model and study these decision processes. Statistical methods are also used very heavily by Actuaries and Risk Managers to study pension and insurance schemes and ensure that they remain solvent and viable.
- Modern physics is intimately connected to mathematics, so much so that virtually all modern theoretical physics work relies heavily on advanced mathematical ideas. Understanding Einstein's theories requires considerable mathematics background. And mathematics is a critical ingredient in designing and analyzing quantum computing devices. Modelling is an important tool in physics too. Modelling and simulation allow scientists to study new phenomena like colliding black holes. Numerical multi-scale algorithms are used to allow physicists to develop and study more accurate galactic models. Adaptive techniques in optics use mathematics to help astronomers eliminate atmospheric distortion and see further and more clearly. And mathematical transformation methods are now being used to study the potential of bending waves around objects like cylinders, reconstructing them on the other side. Could this really lead to invisibility?
- Computer science uses math and stats in all sorts of ways. Many computer algorithms are mathematical in nature, and many include randomness in order to speed things up. In many major computer graphics applications, from video games to recent action movies, mathematics is used heavily in order to increase realism. These days music and video have moved mainly into the digital realm, and mathematics has been used to create methods for efficiently encoding and compressing data into smaller sizes while maintaining quality, and even for enhancing sound and video. Fractal and statistical methods are also used in the analysis and compression of images. Statistical methods are also used to train computers to improve speech recognition capabilities. In robotics, mathematical and statistical methods are used to help robots work independently and yet still be able to navigate and make decisions. And security on computer networks, including the web, is based on cryptography, an area which takes techniques and ideas from number theory and algebra and applies them to create safe protocols for data transfer.
Incredibly, this list is only a very small sample of all of the places where mathematics and statistics are used! And the number of these applications grows every year.