Research in Scientific Computing in Undergraduate Education

07. Research topics for Freshmen

We engage selected students from their beginning years as freshman, through graduation as seniors, in deep, broad and extensive research experiences in computational science. We mentor beginning students through a two-year process of initiation into the research process in computational science.

Freshman and Sophomore students learn important research skills of observation, experimentation, classification, organization and conjecturing. Other, generic research skills which are important for carrying out successful research include the following:
• Literature surveys: even popular science magazine articles work well for undergraduates.
• Seminar attendance at mathematics department colloquium series and assigned computational science seminars.
• Summarizing seminar talks effectively.
• Getting an idea from seminar talks.
• Writing up a summary of a project
• Writing up a paper after a semester.
• Presentations in class or at a student conference.
• Observing, experimenting, classifying, organizing and conjecturing.

Students obtain an introduction to open research problems in areas of computational science, such as discrete dynamics, initially using spreadsheets as computational tools. Progressively, they are introduced to more powerful tools such as MATLAB, Maple and Mathematica. Our Freshman level research experience are geared toward developing the skills of exploration and experimentation, and training students to keep accurate and organized records of their research and present their work to peers.

Freshman students

We expect that Freshman students will join a cohort of other students, and faculty, to investigate serious research problems in mathematics and science from a computational perspective. Generally , Freshman students have limited mathematical knowledge and background, and limited experience in working and thinking like a mathematician. Our aim is to immerse Freshman students in a research environment where they learn the purpose of the research project, learn to read and summarize, learn to use computational tools, and learn to tackle problems themselves while working with a cohort of other students.

To get started Freshman students need a combination of exercises, investigations, and exposure to open research problems. Some specific examples of these, many of which run quite deep and involve serious mathematics, but all of which are easily stated, and approachable by Freshman students, are listed below:

1. Friends of 10

2. Catalan pseudoprimes

3. Integer values of recurrences

4. Convergence of a sequence

5. Collatz conjecture

6. Strategies for Sprouts

7. Network analysis

8. Existence of solutions of recurrence relations

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