# Programs in mathematics

Mathematics is a powerful tool with many applications. Advanced mathematical training can lead to many career opportunities, including business, finance, medicine, engineering, and basic sciences.

At the same time, mathematics is a self-contained subject that is worth studying simply for its elegance. While challenging at times, the study of mathematics can bring a tremendous sense of accomplishment. Mathematics is an ideal subject for people who enjoy abstract thinking.

## More about mathematics

### The nature of mathematics

Mathematics is much more than the arithmetic and algebra we study in public school. It is the science of patterns—a way of thinking about the world. The symbols and terminology used by mathematicians to represent and understand patterns are analogous to the letters or pictograms that we use to represent the words and sounds that form the basis for language. They are akin to the notations and terminology used by musicians to represent melodies, harmonies, tempos, and rhythms. Mathematicians looking at the world strip away much of the complexity to reveal underlying abstract structures and patterns.

Analysis of these structures provides broadly applicable information in much the way that X-rays of people's skeletons reveal information unrelated to the details of their external appearance. Researchers develop mathematical models of phenomena like seismic activity, turbulent airflow, and biological species interactions, and they apply advanced mathematics to find faster and more accurate methods of approximating the dynamics of these complicated behaviors.

### Why study mathematics?

The study of mathematics develops critical thinking skills that are useful in most occupations and in many other aspects of our lives.** **Quantitative and analytical critical thinking skills are the driving forces in almost all industries. Career opportunities abound for math majors—in data science, statistics, actuarial work (risk management), cryptography, operations research (decision-making), market analysis, financial management, public school teaching, and many other areas. Statistician, mathematician, financial manager, actuary, and operations research analyst are ranked as five of the seven Best Business Jobs by the US News & World Report in 2019.

### The universality of mathematics

Mathematics permeates modern-day life in ways that are not obvious to most people. Check digits based on number theory ensure the accuracy of driver's license numbers, vehicle identification numbers, ISBN numbers for books, scanned bar codes, credit card numbers, airline tickets, and bank transactions. Mathematics is the basis for all of physics and engineering, as well as data science, perspective in art, computer graphics in movies and video games, global positioning systems, the biomechanics of ice-skating jumps and tennis serves, the analysis of risk by insurance companies and gamblers, navigation on the sea and in the air, analysis of automobile traffic flow, medical magnetic resonance imaging, and much more.

The following story illustrates the particular perspective that mathematics offers:

Two anthropologists and a mathematician were arguing about why humans had domesticated fire. One anthropologist argued that humans needed fire primarily to stay warm at night. The other anthropologist insisted that humans needed fire primarily to cook food. The mathematician proposed that some ancient human had been intrigued by fire and decided to figure out how it worked. Only later, suggested the mathematician, did others come along and find uses for fire.