In an applied Ph.D. program in mathematics, students learn how to use computational methods and mathematical modeling to solve practical problems in government, business, engineering and the physical and social sciences. For a program specialization in pure mathematics, candidates create new mathematics principles, striving to advance mathematical knowledge. Oftentimes, these two classes of mathematics overlap within Ph.D. programs. During their coursework, students complete oral and written examinations, and they'll be expected to write and defend a dissertation.
Students will also engage in internships that may lead to summer employment and eventually to careers in research, finance, engineering or business. Students who graduate from Ph.D. in Mathematics programs are prepared for careers in mathematics, business and education.
Applicants to a mathematics Ph.D. program must possess bachelor's degrees. Although these degrees don't need to be in mathematics, applicants must have completed undergraduate mathematics courses, including algebra and calculus, as well as coursework in fields such as physics, engineering and economics. They must also submit their qualifying GPA and GRE scores and letters of recommendation to gain admission to a Ph.D. program.
Ph.D. in Mathematics
An advance degree in mathematics such as a Ph.D. program allows students to take complex subjects often needed by mathematicians. It also trains them to work with data analysis software which is helpful in conducting mathematical research. Courses typically cover:
- Complex variables
- Probabilities: limit theorems
- Differential geometry
- Computing in finance
- Numerical methods
- Complex analysis
Employment Outlook and Salary Information
Mathematicians find employment in office settings as part of teams of economists, engineers, computer scientists or technicians. In addition to becoming mathematics professors, graduates of Ph.D. programs can gain employment in the government or business sectors. Examples of potential careers include actuarial scientist, economic statistician, computer programmer or systems engineer.
According to the U.S. Bureau of Labor Statistics (BLS), mathematician employment is expected to increase by 26% between 2018 and 2028 (www.bls.gov). This job growth rate is much faster than average compared to other professions, partly because of improved technology and expanding applications of mathematics. As reported by the BLS in May 2019, the median per-hour rate for mathematicians was $50.50, which translates to $105,030 annually.
Students intending to pursue a mathematics Ph.D. degree can choose from applied or pure mathematics program specializations that often includes classes from other related fields, such as computer science, physics, and engineering. Coursework culminates in a dissertation, which prepares graduates to work as professors or mathematicians in a variety of settings.