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Research Experiences for Undergraduates in Mathematical Modeling

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Academic Level:
Undergraduate Students

The ability to mathematically model complex systems has become a prerequisite to successful science in any field. Many undergraduate programs in computer science, mathematics, and physics, however, still fail to fully address the theory and practice of mathematical modeling. Writing a simulation is not enough; career scientists today should be able to analyze results, recognize statistical regularities, formulate conjectures, and pursue possible proofs about why these conjectures are true.

Focusing on the computational and mathematical modeling of complex systems, the Santa Fe Institute's Edward A. Knapp Undergraduate Fellowship (previously known as the Research Experiences for Undergraduates program) uses an integrated approach to train aspiring scientists to gain quantitative insights into complex systems. Techniques range from rigorous theorem-proof, to physics-style calculations, to computational experiments and simulations. Fellows will move back and forth freely along this spectrum identifying opportunities to solve a system exactly or approximately, running simulations to see if solutions are accurate, making new conjectures based on the simulations, proving or disproving these conjectures, and so on. The aim is to understand the assumptions behind a given mathematical tool, judge whether it is applicable, consider if simplification is possible, and analyze the data produced by simulations.

This program is transdisciplinary, with problems, methods, and data sets drawn from across the scientific spectrum. The Fellowship will train a cohort of young scientists to move confidently from coding a large-scale simulation to analyzing it theoretically. While of interest to students from computer science, pure and applied mathematics and physics, and engineering, it is also open to applicants from quantitative biology and the social sciences.

This program is highly individualized. Each student works with one or more faculty mentors on a specific, mutually selected project. Projects can be based on suggestions from SFI mentors, ideas from student interns, or a combination of the two. (See The initial weeks of the program are devoted to meeting potential mentors and selecting projects.

Participants are expected to be in residence in Santa Fe for approximately 10 weeks.

Application Deadline: 1/4/2017
Note: Most programs maintain a similar program cycle (including similar application deadlines) year after year. Click here to understand dates and deadlines on

Participating Institution(s):
(Click an institution to see all programs it hosts)
Santa Fe Institute (Lead)

Program Materials:
 • Program Website 

This Program can be Described by:
Academic Disciplines:
Computational Sciences
General Earth & Agriculture Sciences
General Engineering & Physical Sciences
General Math & Computational Sciences
General Medical & Life Sciences
General Social Sciences
General Technology
STEM Fields

Complex Fluids
Complex Network Systems
Complex Systems Theory
Computational Biology
Computational Ecology
Computational Modeling
Computational Social Sciences
Computational Statistics
Computer Modeling
Computer Programming

Questions about this program?
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This program is funded by:
National Science Foundation (NSF)

Page last updated 10/27/2016
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