Undergraduate Student Research

Cindy Wyels

CSU Channel Islands

Panel presentation to Section NExTSo Cal-NV MAA, Fall ‘05

Types of research projects

• Voluntary mid-year projects

• Required (senior) projects

• Summer (REU-like) projects

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.

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

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

Types of Projects

• research

• application

• modeling

• Computer simulation

• Computer implementation

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.

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?”

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

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

Ronald Phillip Victor

Student Outcomes

• Better understanding of mathematical enterprise

• Enhanced self-confidence in mathematical abilities

• Class credit

• Major scholarships

• Intrinsic rewards

• Publication

• 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

Faculty Outcomes?Fun

Intellectual stretching

Revamp priorities

Recognition?

Tenure/ promotion boost?

Danger: time costs.

Assess value!

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