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Undergraduate Complexity Research

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Academic Level:
For most summer research programs, this is your upcoming status as of the fall. Always check with the individual program's website for details.

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. See Santa Fe Institute History

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


Housing and a partial meal plan will be provided, at no cost to the student, in single-occupancy rooms with shared bathrooms at St. John's College in Santa Fe. Modest living stipends will also be provided to interns during their stay, along with some support of round-trip travel expenses from the home institution. Because Santa Fe lacks a full public transportation system, we encourage those interns who can bring their private transportation to do so.


For the purposes of this program, an undergraduate student is one who is enrolled in a degree program (part-time or full-time) leading to a bachelor's degree. Students transferring from one institution to another who are enrolled at neither institution during the intervening summer may participate. College seniors graduating in Spring are not eligible; nor are graduating high school students who have not yet enrolled as undergraduates.

Strong mathematical skills and experience with a programming language are favorably considered. Students from all backgrounds in the physical, natural, and social sciences are invited to participate. National Science Foundation funds are limited to supporting U.S. citizens and permanent residents. Women and minority students are encouraged to apply.

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:
Anthropology & Archaeology
Applied Mathematics
Computational Sciences
Computer Sciences
General Math & Computational Sciences
General Social Sciences
Linguistics & Speech Sciences
Psychology & Behavioral Sciences

Biological Anthropology
Chaos Theory
Complex Systems Theory
Computational Linguistics
Computational Social Sciences
Game Theory
Linguistic Theory
Risk Analysis
Social & Organizational Networks
Urban Anthropology

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This program is funded by:
National Science Foundation (NSF)

Page last updated 4/19/2022
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