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Applied Mathematics and Statistics (PhD)

Doctor of Philosophy

Delivery Options

Campus

Fall 2026 Deadline

Priority: December 15th
Domestic: July 1st
International: March 1st

Apply Now Contact Admissions Team

Department

Applied Mathematics and Statistics

Why study this degree at Mines?

Applied mathematics and statistics sit at the center of modern engineering, science and decision-making. From modeling physical systems to making sense of massive datasets, the ability to frame problems mathematically and extract insight from data is essential across industries. As systems become more complex and data-rich, employers increasingly need experts who can move beyond standard methods, develop new approaches and prove that their results hold up under scrutiny.

A Doctor of Philosophy in Applied Mathematics and Statistics from Colorado School of Mines prepares you to do exactly that. This program focuses on building deep mathematical and statistical expertise while keeping your work focused on real problems drawn from engineering and the sciences. You will develop the theoretical foundation needed for original research and the applied perspective needed to ensure your work matters beyond the page. At Mines, applied mathematics and statistics are not abstract side disciplines. They are tools used daily to solve consequential problems, making this program a strong fit if you want your research to connect directly to how systems behave, perform and fail in the real world.

Program Overview

The Doctor of Philosophy in Applied Mathematics and Statistics is an on-campus doctoral program designed for you to conduct original research in mathematics and statistics with clear applications to engineering, physical sciences and data-driven fields.

This program strengthens your bachelor’s or master’s degree by moving you from applying existing techniques to developing new methods and theory. You will gain advanced training in areas such as mathematical modeling, probability, statistical inference and numerical analysis. The curriculum is flexible by design, allowing you to tailor coursework to your research focus while ensuring you build strong core foundations.

You and Mines PhD: A right fit?

You may be a strong fit for this program if you:

Enjoy abstract thinking but want your work tied to real applications
Are comfortable working independently on open-ended problems
Have a strong background in mathematics or a closely related field and are motivated to deepen it through research

Key Program Research Groups

Research engagement:

The department provides a collaborative home for PhD research, with faculty-led groups focused on modeling, computation and data analysis. Regular seminars and research meetings help you sharpen ideas and communicate results clearly.

Mathematical modeling of physical and engineering systems:

This area focuses on developing mathematical descriptions of complex systems in engineering and science. Research often involves differential equations, dynamical systems and continuum modeling. Coursework supports deep understanding of modeling techniques and analysis. Methods may include analytical derivations and computational simulations, with applications that translate directly to engineering research and technical roles.

Probability, statistics and data-driven modeling:

Research in this field addresses how uncertainty is modeled, measured and interpreted. Topics include statistical inference, stochastic processes and data analysis. You will use mathematical theory alongside computational tools to extract insight from data. Graduates often move into roles that require rigorous statistical reasoning in research, analytics and quantitative decision-making.

Numerical analysis and scientific computing:

This research area develops algorithms for solving mathematical problems that cannot be addressed analytically. Work includes numerical methods for differential equations, optimization and large-scale computation. Coursework emphasizes both theory and implementation. These skills are highly valued in research and development settings where simulation and computation drive design decisions.

Optimization and inverse problems:

Here, research focuses on finding optimal solutions and inferring system properties from limited data. You may work on deterministic or stochastic optimization methods, often motivated by engineering applications. Tools include mathematical analysis and computation, with outcomes relevant to system design, control and parameter estimation.

Interdisciplinary applied mathematics:

Many projects cut across traditional boundaries, embedding applied mathematics and statistics into broader research teams. This area emphasizes collaboration, problem formulation and translating mathematical insight into usable results. It is well suited if you want your dissertation to connect directly with applied research in engineering or science.

Other Options

World-Class Labs, Centers and Facilities

As an applied mathematics and statistics student, you can build your coursework and independent study around Mines specialized labs and centers. Because applied mathematics and statistics is inherently collaborative, many of your most powerful research resources are campus-wide and domain-linked:

A woman writing on a blackboard in a classroom.

Diniz Behn Research Group

Professor Cecilia Diniz Behn applies multiscale mathematical modeling to investigate key research questions in metabolism, sleep and circadian rhythms. Her research group models key dynamics in whole-body metabolism including changes in glucose, glycerol, and insulin; sleep and circadian neurophysiology; and the diverse interactions among these systems.

Desk with math notes featuring graphs, a laptop keyboard, car keys, and a black patterned water bottle.

Mines Optimization and Deep Learning (MODL) Group

The MODL Group co-led by Assistant Professors Samy Wu Fung and Daniel McKenzie conducts research in the intersection of deep learning and optimization. Current areas of interest include inverse problems, learning-to-optimize, applied probability, zeroth order optimization, and implicit deep learning.

A brick building with a tree in front of it.

Hammerling Research Group

Associate Professor Dorit Hammerling leverages the power of computation and mathematical modeling to solve vexing problems relating to energy, climate, engineering, and society. Her research group builds innovative modeling architectures and openly develops original software.

Faculty Expertise

Steve Pankavich

Professor-DH

Cecilia Diniz Behn

Professor

Soutir Bandyopadhyay

Professor

Application Requirements

Bachelor's degree
GRE: Not Required
Letters of Recommendations (3 letters).
Resume or Curriculum Vitae (CV)
Statement of Purpose
Transcripts
International students please review the English proficiency requirements

Program Curriculum

View Academic Catalog

Career Outlook

Nationally, demand is especially strong for data-intensive and optimization-centric roles. Median starting salary for recent graduates of this program is $93,000.

Learn more about Mines' comprehensive career development resources and this degree's salary potential.

Explore Mines Career Center

Employers who seek Mines graduates include

Technology and Data-driven Companies

Companies such as Google, Microsoft, Amazon, IBM, Meta, NVIDIA

Engineering and Scientific Organizations

Companies such as Boeing, Lockheed Martin, Northrop Grumman, Raytheon, General Electric, Siemens

National Laboratories and Research institutions

Such as National Laboratory of the Rockies, Sandia National Laboratories, Los Alamos National Laboratory, Lawrence Livermore National Laboratory, Pacific Northwest National Laboratory

Consulting and analytics

Companies such as McKinsey & Company, Boston Consulting Group, Bain & Company, Accenture - Deloitte

Frequently Asked Questions

Why pursue a PhD in Applied Mathematics and Statistics?

A PhD is valuable if you want to create new methods, not just apply existing ones. In applied mathematics and statistics, doctoral training teaches you how to formulate problems, develop theory, validate results and communicate insight clearly. This level of expertise is essential for research, advanced analytics and technical leadership roles.

How applied is this PhD program?

Very. While the program builds strong theoretical foundations, research is often motivated by real problems in engineering and science. You will be encouraged to connect mathematical ideas to measurable outcomes and practical use cases.

What careers are available with this degree?

Graduates pursue careers in research and development, data science, quantitative analytics, national laboratories, consulting and academia. The common thread is the ability to solve complex problems with mathematical and statistical rigor.

Do you need a master’s degree to apply?

A master’s degree is helpful but not required. Strong preparation in mathematics or a closely related field is essential, and your background will be evaluated alongside your research interests.

How does this program differ from a pure mathematics PhD?

This program emphasizes application and collaboration. While theory matters, research is typically connected to applied problems, making it a strong fit if you want your work to influence engineering, science or data-driven decision-making.

Featured Alumni

Meet Philip Emmette '21, MS '22

The AMS department is a great community to be a part of. The faculty is really helpful and caring, the courses available are flexible and the department is smaller so you really get hands-on, one-on-one support. I really feel like Mines is setting me up for success in the future.