University of Arizona

What you'll study

The programme combines core graduate mathematics with specialised coursework in computational and applied mathematics. Typical topics include numerical analysis, numerical linear algebra, scientific computing, numerical solution of partial differential equations, optimisation and computational methods for data analysis. Students also study advanced topics from the broader mathematics curriculum such as real and complex analysis, differential equations and probability/statistics to provide theoretical grounding for computational work.

• Numerical Analysis and Error Analysis
• Numerical Linear Algebra and Matrix Computations
• Scientific Computing and High‑Performance Computing Techniques
• Numerical Methods for Ordinary and Partial Differential Equations
• Optimisation and Computational Inverse Problems
• Computational Statistics, Machine Learning or Data Analysis (elective)
• Advanced Analysis and Mathematical Modelling seminars

The degree can usually be taken with a research (thesis) option or a coursework (non‑thesis) option. Thesis students undertake an original research project under faculty supervision, while non‑thesis students complete additional coursework and often a capstone project. Students commonly augment mathematics courses with electives from computer science, engineering or applied sciences to gain practical programming and parallel computing skills.

Entry requirements

Applicants are expected to hold a bachelor’s degree in mathematics or a closely related quantitative discipline (such as applied mathematics, physics, engineering or computer science) with a solid foundation in calculus, linear algebra, and differential equations. Typical supporting materials include official transcripts, a statement of purpose describing research or career goals, and letters of recommendation from academic or professional referees.

Evidence of programming experience (for example in MATLAB, Python, C/C++ or Fortran) and coursework in advanced calculus, real analysis or numerical methods strengthens an application. International applicants must meet the university’s English proficiency requirements. The department may consider applicants with non‑traditional backgrounds who demonstrate strong quantitative preparation through coursework or professional experience.

Career prospects

Graduates with a master’s in computational mathematics are equipped for a wide range of technical careers. Common roles include computational scientist, numerical analyst, data scientist, quantitative analyst, software engineer specialising in scientific computing, and research analyst in industry or government labs. The skill set is also valued in finance, aerospace, energy, healthcare analytics, and technology companies that require large‑scale simulation, modelling or algorithm development.

Many students use the MS as preparation for doctoral study in applied mathematics, computational science or related fields. Those completing the thesis option often continue to PhD programmes, while non‑thesis graduates frequently move directly into industry or research positions that emphasise applied programming and modelling skills.

Why study at University of Arizona

The University of Arizona Department of Mathematics offers a strong applied and computational curriculum with active research groups in numerical analysis, scientific computing and applied mathematics. Graduate students benefit from access to campus high‑performance computing resources and interdisciplinary collaborations across engineering, physical sciences, biosciences and data science institutes.

Faculty members supervise research projects that connect theory with practical applications, and the department runs seminars and reading groups that expose students to current problems in computational mathematics. The university’s research environment and partnerships with industry and national laboratories provide opportunities for internships and collaborative projects that enhance employability and research experience.