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# What is Mathematics and Statistics?

## Mathematics & Statistics Department

### What is Mathematics & Statistics?

Mathematics is the abstract science of numbers, quantity and space. Mathematics may be studied in its own right (*pure mathematics*), or as it is applied to other disciplines such as physics and engineering (*applied mathematics*).

Statistics is the science of collecting and analyzing numerical data in large quantities, especially for the purpose of inferring proportions as a whole from those in a representative sample.

### What does a Mathematician do?

Mathematicians solve problems. Problems they work on range from pure mathematical problems to applied problems. Mathematicians try to find common features in seemingly distinct problems. That is, they look for patterns. They classify what behaviors can result from certain systems. For example, differential equations can be used to show that an electrical RLC circuit “behaves” in exactly the same way as a spring-mass system, oscillating back and forth until the motion damps out. Graph theory can be used to schedule tournaments with scheduling constraints, or to show that certain scheduling constraints are impossible to meet. Often studies which are considered at one time pure mathematics, with no application in mind, turn out to be the most useful. For example, pure research studying efficient factoring algorithms for large integers led to extremely useful algorithms for computer encryption.

Applied mathematicians use mathematical theory, computational techniques, algorithms and the latest computer technology to solve economic, scientific, engineering and business problems. This process often involves building a mathematical “model” of the application, using mathematical theory to understand the behavior of the model, and then interpreting this behavior in the context of the original application. Some applications include designing the most fuel efficient rocket path to the moon, advising the DNR how many deer licenses to sell, and predicting the effect of vaccinations on epidemics.

### What does a Statistician do?

Statisticians develop techniques to overcome problems in data collection and analysis. They use statistical methods to collect and analyze data and to help solve real-world problems in business, engineering, healthcare and other fields. For example, they design medical experiments to make sure that valid conclusions can be drawn about the use of medications, they suggest marketing strategies based on relatively small samples of consumers, and they decide what premiums to charge on insurance policies.

### How do I know if Math or Stats is right for me?

Do you like to solve problems? Do you want to know “why” things work as they do, not just “how” they work? Do you feel uncomfortable plugging into an equation when you don't know where the equation came from? Do you want to know how many voters to sample to be able to accurately predict the outcome of an election? If you ask yourselves these kinds of questions, mathematics or statistics might be right for you.

### Career Opportunities

Career opportunities for mathematics and statistics are extensive. Obvious careers involve working as an actuary for an insurance or consulting company, or as a teacher. Most mathematics and statistics majors, however, use their problem solving skills in the business world – analyzing processes, data, and algorithms, or in government research. Employers hire mathematics and statistics majors because employers know those students are able to work on hard problems, and to make logical decisions. Check out descriptions for a wide variety of jobs in mathematics and statistics.