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Studies & Degrees in Applied Mathematics

Applied mathematics uses mathematical models, analysis and computation to answer questions that come from outside mathematics. The Department of Applied Mathematics at the University of Washington describes it as interdisciplinary study in the physical, engineering and biological sciences. The Yale University catalogue notes that mathematical models are used in fields as diverse as physics, bioinformatics, robotics, image processing and economics.

Students first build a base in calculus, linear algebra, differential equations and probability. They then learn numerical methods and programming, and apply these tools in modelling courses. At the University of Washington the application areas include mathematical biology, health sciences, mathematical finance, data analysis and climate modelling. At Northwestern University, faculty and students develop mathematical models and the methods to analyse them, validate them and predict new phenomena, often together with engineers and scientists.

Qualifications and levels

Applied mathematics is offered as a degree of its own, as a pathway inside a mathematics degree, and at postgraduate level.

  • Bachelor's degree in the United States. The University of Washington offers a BS in Applied Mathematics, also with a Data Science option; the major itself requires a minimum of 54 to 59 credits, including a computing course. At Northwestern University the Department of Engineering Sciences and Applied Mathematics is part of the McCormick School of Engineering, and the BS requires 48 courses in total, including mathematics, engineering and science. Yale University offers the major as a BA (eleven term courses beyond the prerequisites) or a BS (fourteen).
  • Pathway within a mathematics degree. At the University of Sheffield the BSc in Mathematics takes 3 years and the integrated master's (MMath) takes 4 years. In the third year students choose a pure mathematics, applied mathematics, or probability and statistics pathway, and a placement year is optional. At UNSW Sydney the Bachelor of Science (Advanced Mathematics) (Honours) takes 4 years, and Applied Mathematics is one of its three majors.
  • Master's degree. The University of Washington runs master's programmes on campus and online; its on-campus MSc in Applied Mathematics requires a minimum of 36 credits. Northwestern University awards a Master of Science and a PhD in Applied Mathematics.
  • Doctorate. A PhD is the usual route into university research.

A bachelor's degree in mathematics is not always needed for postgraduate study. Northwestern University states that not all of its incoming graduate students have a bachelor of science in mathematics and that many have degrees in engineering or science.

Where to study it

SpainExchange lists 58 active schools for this subject. The United States has 36 of them, followed by the United Kingdom with 4, and India, Ireland and China with 2 each. There is one school each in Australia, Canada, France, Argentina, Brazil, Azerbaijan and Eswatini.

Most of the listed programmes are taught in English. Examples from the list are the University of Washington in Seattle, Northwestern University in Evanston, Yale University in New Haven, the University of Sheffield and UNSW Sydney. In France, the École normale supérieure in Paris is on the list, and in Asia the University of Calcutta and Vietnam National University, Hanoi.

Entry requirements centre on mathematics. The University of Sheffield asks for A Levels at AAA for its mathematics degrees. Yale University requires multivariable calculus and linear algebra before or during the second year of the major, as well as computer programming skills. International applicants should also check each university's English-language requirement.

Careers

Graduates work in industry, finance, technology companies, government and research. According to Northwestern University, its applied mathematics students graduate with a background suitable for employment in industry or for graduate study in mathematics or an engineering field, including computer science and operations research.

Official figures for the United States come from the Bureau of Labor Statistics (BLS). Mathematicians and statisticians held 33,500 jobs in 2025, and employment is projected to grow 10% from 2025 to 2035. Mathematicians alone held about 2,200 jobs, 53% of them in the federal government. The BLS states that mathematicians and statisticians typically need at least a master's degree, although some positions are open to those with a bachelor's degree. Many graduates work under other job titles, such as data scientist, analyst or engineer, which these figures do not include.

Frequently asked questions

What is the difference between applied and pure mathematics?

Pure mathematics studies mathematical structures for their own sake. Applied mathematics develops and uses mathematical methods to solve problems in science, engineering, business and other fields.

How long does a degree in applied mathematics take?

It depends on the country. At the University of Sheffield a BSc in Mathematics takes 3 years and the MMath 4 years; at UNSW Sydney the honours degree in advanced mathematics takes 4 years.

Do I need programming skills?

Yes. Yale University requires computer programming skills for the major, and the University of Washington includes a computing course in its degree requirements.

Can I take a master's in applied mathematics with an engineering degree?

Often, yes. Northwestern University states that many of its incoming graduate students have degrees in engineering or science. Check the prerequisites of each programme.