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Undergraduate Student Research

This presentation discusses different types of undergraduate research projects, strategies for recruiting students, sources for project ideas, and techniques for keeping students involved and ensuring project completion.

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Undergraduate Student Research

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  1. Undergraduate Student Research Cindy Wyels CSU Channel Islands Panel presentation to Section NExT So Cal-NV MAA, Fall ‘05

  2. Types of research projects • Voluntary mid-year projects • Required (senior) projects • Summer (REU-like) projects

  3. Recruiting students for research projects? 1. Create a climate in which involvement in extra- curricular activities is the norm. • frosh (and ongoing) advising • department culture (required activities?) • promote REUs, NASA internships, SURF, etc. • become a publicity hound (off and on-campus) • encourage students to present 2. Ask them.

  4. Where do you get ideas for suitable projects? Beg, borrow, steal, and … hoard. (Keep a file.) Develop a mindset of noticing problems. Some sources Math Horizons talks/ posters at meetings Monthly problem section MAA columns local situations your own research students’ interests open problems web pages

  5. 2000 Putnam: Prove that there exist infinitely many integers n such that n, n + 1, and n + 2 are each the sum of the squares of two integers. 0 = 02 + 02, 1 = 02 + 12, 2 = 12 + 12 Karl: “I wonder if there’s a pattern to how many ways you can sum squares to get that first number…”

  6. Types of Projects • research • application • modeling • Computer simulation • Computer implementation

  7. How do you keep students involved and make sure (mid-year) projects are completed? • Weekly or biweekly meetings, with time to work. • Student-generated progress reports • Schedule a presentation at the time you begin the project. • Redefine “completion” as necessary.

  8. “What should I do when I’m working on my project?” Active reading Focused pondering Critical idea testing Conjecturing Talking/ arguing Programming Writing/ scribbling Proving

  9. My responsibilities • Provide structure • Know the literature; have ideas for good student problems • Teach students how to read mathematical literature, how to “do research” • Teach students software, presentation, and writing skills • Encourage, encourage, encourage! • Discuss ideas • Help determine avenues for further investigation • Help pull ideas together, write proofs • Provide resources and advice about grad school and career options

  10. Student Outcomes • local acclaim • Good résume/ application fodder • Oral or poster conference presentation • Final write-up (in form of journal article) • Improved computer, writing, and presentation skills • Good source for letters of recommendation

  11. Ronald Phillip Victor

  12. Student Outcomes • Better understanding of mathematical enterprise • Enhanced self-confidence in mathematical abilities • Class credit • Major scholarships • Intrinsic rewards • Publication

  13. Venues for Presentations • So Cal-NV MAA Fall Meeting • So Cal Conference on Undergraduate Research (SCCUR) • Joint Meetings • Pacific Coast Undergraduate Math Conference • So Cal-NV MAA Spring Meeting • (CSU Research Symposium) • local colloquia

  14. Faculty Outcomes? Fun Intellectual stretching Revamp priorities Recognition? Tenure/ promotion boost? Danger: time costs. Assess value!

  15. Resources for Student Readings • A Mathematician’s Survival Guide, Steven G. Krantz – particularly the chapter titled “How do I work on my thesis problem?” • How to Read Mathematics, Shai Simonson and Fernando Gouveau, http://academics.stonehill.edu/compsci/History_Math/math-read.htm • How to Give a Good Talk, Joseph A. Gallian, Math Horizons, April 1998 • How to Prepare a Poster, Sven Hammarling and Nicholas J. Higham, http://www.nmsu.edu/GRAS/PreparePoster.htm • YMN site, MAA site, many others: grad school advice

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