A Career in Applied Mathematics

by Greg Lewis, Associate Professor of Mathematics, UOIT

Would you like to work in the "best" profession? If you were thinking that would mean being a doctor or a lawyer, you would be wrong. In fact, you would be a mathematician, according to a study that compared 200 occupations based on five criteria: environment, income, employment outlook, physical demands and stress. The study, carried out by Les Krantz, author of "Jobs Rated Almanac", was released on www.careercast.com/, and was the topic of an article that appeared in the Wall Street Journal (http://online.wsj.com/article/SB123119236117055127.html?mod=yhoofront).

Perhaps you are wondering what work you would be doing in the best profession. It turns out that the answer to this requires a little explanation, as mathematicians can be found in a wide variety of companies, in a number of different sectors.

For instance, many mathematicians work in the financial sector, in particular for banks and investment firms. They may have a variety of responsibilities, including evaluating the risk associated with the purchase of a certain stock, or determining the price of various financial products, such as stock options, or other financial ‘derivatives’.

There are also many mathematicians who work in the pharmaceutical industry. Their jobs can involve creating and solving mathematical models to aid in the development of new drugs, or applying algorithms that search through large sets of data to determine, for instance, which chemical compounds tend to have the desired effect on a given disease. The last of these activities, which is referred to as 'data mining', is a procedure that involves extracting the important information from very large sets of data; essentially it is an efficient way of looking for a needle-in-a-haystack. Data mining is also used in other biomedical applications, as well as other areas, such as marketing.

In the manufacturing sector, you may find mathematicians in teams that develop products and processes, that find ways of improving the quality and efficiency of the manufacturing process, and that solve the ‘supply-chain problem’, which attempts to optimize the entire process that takes a product from the manufacturer to the customer. Mathematics can be particularly useful for saving a company time and money in product development, because mathematical models can be used to evaluate ideas before an often very expensive physical prototype is constructed and tested. This is particularly important in, for example, the automotive, aircraft, or aerospace sectors.

You will also find mathematicians in software development, creating software that, for instance, robustly and efficiently solves problems of interest for a variety of companies and/or individuals, or you’ll find them in government agencies studying the potential effects of, and potential methods for the mitigation of, a bioterrorism attack, or studying the dispersion of radio-active material after an nuclear attack or an accident at a nuclear power plant. Mathematicians are also found in hospitals developing medical imaging techniques, or modeling the growth of tumours. As a mathematician, you could also work in climate modeling or weather prediction, because these fields involve the numerical computation of large-scale mathematical models.

With the emergence of the critical need to develop renewable energy sources, many companies have begun to see that they can help society while creating a successful business. The skills of a mathematician are particularly suited to contribute in this area. You will find many mathematicians, for instance, helping to develop fuel cells that could be used to make automobiles run on an efficient renewable fuel source.

If your ambition has always been to work in the Hollywood film industry, enrolling in a math degree might actually help you get there! Have a look at the internet page of Rhythm & Hues (www.rhythm.com), a company that produces visual effects for Hollywood block-busters; you can also look them up on the Internet Movie Data Base (www.imdb.com). The specialists in visual effects and computation working for this California-based company have produced scenes for films like Superman Returns and X-Men. Who founded this company and who makes the graphics that keep millions on the edge of their seats? The founders are an engineer, a computer scientist and ... a mathematician.

There are many companies who require the use of mathematicians, but do not hire them directly. This is the domain of the consulting companies, which perform many of the tasks discussed above, but work on a contract basis with a given company. Working for a consulting company will sometimes involve changing areas of application many times.

These are just a few of the possibilities. In fact, mathematics is used, and thus there is a need for mathematicians, in almost every sector. For more examples and information, you can see the Society for Applied and Industrial Mathematics (SIAM) Careers Page (www.siam.org/careers/).

Although mathematicians can be found in a variety of sectors, generally, there is a commonality in the kind of work they do. In particular, a mathematician’s job often involves the development and numerical computation of mathematical models that are formulated using (partial, ordinary or stochastic) differential equations, combinatorics, and graph theory, and often involves the use of various types of statistical, dynamical and optimization analysis techniques. Problem-solving is usually an important part of the job, and often, if not usually, the use of computers is required.

Another commonality is that positions that require mathematics training are often intellectually stimulating. Two of the fundamental skills that mathematicians develop as they obtain their degrees are their problem-solving ability and the ability to think abstractly. Because these skills are often very useful for a company, mathematicians are often hired specifically for these intellectual attributes. Therefore, the jobs usually require the application of these skills, and thus involve continuous learning and creative thinking. It might be said that the tool that is most important to mathematicians is their brain.

For the most part, companies do not have large groups of mathematicians working together, but mathematicians tend to work as members of multidisciplinary groups. Furthermore, many of the jobs, for which mathematicians are hired, are not titled ‘mathematician’. As the SIAM Careers Page states, “applied mathematicians and computational scientists … often hold jobs with titles such as statistician, scientific programmer, electrical engineer, computer scientist, operations researcher, systems engineer, analyst, research associate, or technical consultant.” Perhaps this has led to the idea that there are fewer jobs for mathematicians than is the case.

Of course to become a mathematician you have to go to university and be taught by a mathematics professor. The job of a professor, however, is not only to teach mathematics courses, but also to mentor students in research projects, and to conduct research of their own. The research that you could undertake as an applied mathematics professor spans a stunning range of possibilities. You could work on the cutting edge of research, and, in the process, develop the methods necessary to solve problems in any of the above areas, and perhaps many more yet to be integrated. You could work in applications spanning all of the above fields, but also in other, more academic areas, such as, among many others, neuroscience, which is the science dedicated to understanding how the brain works.

Many people would say that the problems of the future lie at the boundaries between disciplines, and thus will be solved using an interdisciplinary approach. Because mathematics is the language of all quantitative analysis, it, perhaps more than any other single field, will be necessary for the solution of these problems. Applied mathematicians are positioned not only to have the best profession, but also to be the most in-demand.

For further reading, you should check out SIAM's Why Do Math? website (www.whydomath.org), which describes in-depth descriptions of several applications of mathematics that have made a significant impact on society.