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Undergraduate Student Research
Cindy Wyels
CSU Channel Islands
Panel presentation to Section NExTSo Cal-NV MAA, Fall ‘05
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Types of research projects
• Voluntary mid-year projects
• Required (senior) projects
• Summer (REU-like) projects
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Recruiting students for research projects?
• 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.
1. Create a climate in which involvement in extra- curricular activities is the norm.
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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
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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.
Karl: “I wonder if there’s a pattern to how many ways you can sum squares to get that first number…”
0 = 02 + 02, 1 = 02 + 12, 2 = 12 + 12
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Types of Projects
• research
• application
• modeling
• Computer simulation
• Computer implementation
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How do you keep students involved and make sure (mid-year) projects are completed?
1. Weekly or biweekly meetings, with time to work.
2. Student-generated progress reports
3. Schedule a presentation at the time you begin the project.
4. Redefine “completion” as necessary.
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Active reading
Focused pondering
Critical idea testing
Conjecturing
Talking/ arguing
Programming
Writing/ scribbling
Proving
“What should I do when I’m working on my project?”
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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
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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
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Ronald Phillip Victor
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Student Outcomes
• Better understanding of mathematical enterprise
• Enhanced self-confidence in mathematical abilities
• Class credit
• Major scholarships
• Intrinsic rewards
• Publication
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• 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
Venues for Presentations
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Faculty Outcomes?Fun
Intellectual stretching
Revamp priorities
Recognition?
Tenure/ promotion boost?
Danger: time costs.
Assess value!
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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