My Journey from Graduate School to Being a University

Professor

byWilliam Yslas Vélez

Department of MathematicsUniversity of Arizona

Tucson, Arizona

The journey that almost did not begin.

When it comes to minority students surviving the mathematical experience in this country, it appears to me that it almost takes a miracle for that to happen.

Mathematics is the new civil rights issue of this century.

And you hold the key.

• At various points in my life it was SUGGESTED to me that my career choice should not include mathematics.

• Undergraduate experiences

• Graduate school

Why am I drawing attention to these experiences

• In your teaching career you are going to encounter students who don’t fit your mold of what a mathematician should be.

• Your actions could determine their future.

• Out of more than 20 students who began graduate school with me, I was the only one to earn a PhD.

The time for miracles is over.

• We, as a mathematics community, should recognize

– The changing and important role that mathematics is playing in society

– http://www.math.uiuc.edu/MSS/2006-Spring/MathWillRockYourWorld.pdf

– The importance of an undergraduate degree in mathematics and the opportunities that are available for undergraduates.

– http://www.ams.org/early-careers/

The changing and important role that mathematics is playing in

society

http://www.ams.org/early-careers/• Early Career Profiles:

Recent bachelors-level graduates in the mathematical sciences•

The Early Career Profile Network• The AMS recruits and supports a network of mathematical sciences departments that systematically provide job profiles of their recent bachelors-level alumni. The Early

Career Profile Network is supported in part by the Alfred P. Sloan Foundation under the auspices of the Sloan Career Cornerstone Series. Read more . . . • View profiles of individuals employed in the following industry sectors:• Agriculture, forestry, fishing, and hunting • Arts, entertainment, and recreation • Construction • Education • Finance and insurance • Government • Health care and social assistance • Information technology • Legal services • Management of companies and enterprises • Manufacturing • Mining • Nonprofit • Other science and technology • Publishing, communications, and libraries • Real estate and rental and leasing • Retail trade • Transportation and warehousing • Travel and food services • Utilities • Wholesale trade • View profiles by undergraduate institution.

• "What Can I Do with a Math Degree?" is a printable poster from the AMS about jobs that math majors might pursue.

•  

– The importance of an undergraduate degree in mathematics and the opportunities that are available for undergraduates.

This last point deserves some attention.

• I cannot tell you how many times I have had a conversation with a mathematician and it goes like this.

• I think that we should increase the number of mathematics majors.

• Reply: But the market for PhDs is not that good.

• I was talking about BS degrees in mathematics.

• Reply: What would you do with a BS degree in mathematics?

I am led to make the following conjecture

• Mathematicians don’t think that mathematics is useful.

• Mathematicians believe that the reason one gets a BS degree is because one is headed for a PhD.

• Mathematicians believe that the BS degree in mathematics will not lead to gainful employment.

How to change this perception?

• Mathematics faculty, graduate and undergraduate students of mathematics should apply for internships

– Faculty: http://www.asee.org/resources/fellowships/nsfro/lablist.cfm

– Graduate Students: http://www7.nationalacademies.org/policyfellows/

– Undergraduate Students: http://www.sandia.gov/SIP/intern-co-op/undergrad.html

As Associate Head for Undergraduate Affairs I have tried to institute the philosophy that before students complete their undergraduate studies in mathematics they will have participated in the three important aspects of being a mathematician.

– learn mathematics– create mathematics– teach mathematics

– Students need to develop a sense of professionalism, and we as faculty need to help them develop this sense.

How do we effect change?

The first item of business is: Do we agree that change is necessary?

If so, what is it that departments and faculty can do to increase the number of mathematics majors?

How do we effect change?

• Outreach is a common answer.

• We need to convince incoming students that they should prepare themselves for the study of mathematics.

Outreach is expensive

• It is difficult to convince faculty to invest energy in leaving the university.

• There is a very important population that we could reach and that would give us an immediate return.

• AP calculus classes.• David Bressoud’s data• AP High School Calculus Class Visitation

project.

• There is an even more important activity than outreach.

• Inreach

• We should have the attitude that every student in our classes is a potential mathematics major.

• The mathematics that we teach, and the classes that we use to communicate that mathematics, should be our most important recruiting tool.

Calculus Minority Advising

• How I got started with Inreach• How I changed over time.• Advising as an aggressive activity.• What happens when students enter my

office, enrolled in calculus and have no major.

• Even more aggressive: What do I suggest when students enter my office with another major.

I now have access to all student records

I look over enrollments for our upper division mathematics classes. If the student is not a mathematics major, I look over that student’s background.

a) If the student has had trouble, I send an email with suggested changes.

b) If I think that the student could add math as another major in the time that they have available, I send a message inviting them to see me in my office.

• I have created a word document that contains examples of messages that I want to send out.

I now have access to all student records

• I look over third semester calculus and sophomore level linear algebra. In particular I look for first year students.

• I look over enrollments in second semester calculus for first year students.

• I ALWAYS pay attention to minority students enrolled in our mathematics classes. Even if I don’t think that I can convince to take more mathematics, I often send them messages,

I go over student records and send out messages to students

• I was going through our math 129 enrollments and I see that you enrolled in this course. It appears that you are majoring in Bioch. and Mol. Biophysics and you have done very well in your courses. Have you given any thought to double majoring in math and BMB? If you are thinking about going on to graduate school in BMB, you will find that having more math would be helpful.

• If you would like to explore this possibility, send me a message and we can arrange to meet. My office is part of the Math Center.

• Best. WYV

I now have access to all student records.

• Some examples:

• Mark-Physics, Astronomy & Math

• Most messages do not result in an immediate reply, but when they do, I think about what to say to that student.

• Ben was transferring from a community college.

An example of the messages that I send out to students

• Benjamin is a physics major

• Dear Benjamin:

I was going over enrollments for math 223 and I came across your name. It appears that you are interested in physics. Have you ever thought of adding mathematics as another major? If you have any thought of pursuing an advanced degree in physics you will find that the undergraduate mathematics will be of tremendous assistance in that endeavor.

If you would like to talk about these possibilities, send me a message and we can arrange to meet in my office. My office, Math East 142, is part of the Math Center.

Best. WYV

The message ends with my titles, and contact information so that

students know this is from a member of the department

• -- William Yslas Velez Director, Math Center Math East 142 Associate Head for Undergraduate Affairs

Address Department of Mathematics 617 N. Santa Rita P.O. Box 210089 The University of Arizona Tucson, Arizona 85721-0089

Office Phone: 520-621-2259 Fax: 520-621-8322 Office: Math East 142 website: http://math.arizona.edu/~velez/

•

Student’s Response

• Hi Mr. Velez, I'm already planning on adding Geology and Astronomy as second and third majors.

• If this changes, I'll certainly consider the possibility. Thanks, -Ben

My Reply

• That sounds great. You might consider adding the math minor. After 223 and 254, you only need to have two more math courses to have the minor in math. After 254, I suggest that you take 422 and 410. If you are interested in declaring the math minor, let me know and I can make that change in your student records.

I wish you continued success. It is so great to know that there are such dedicated students as you.

Best. WYV

I have his interest

• Hi Mr. Velez, I'm considering switching to the Math major in place of Geology.  The course load required for the Geology major in conjunction with Physics and Astronomy is absolutely overwhelming, and I had neglected to consider the honors requirements when I put my schedule together.  I need to head down to Tucson to get my student ID and talk to the Astronomy advisor at some point in the near future.  Perhaps I can come by your office as well?

Thanks, -Ben

Now a math major

• What day do you want to stop by?

Best. WYV

• Ben has now declared math as a major, adding that to his physics major. He is overly enthusiastic about pursuing his studies.

The quality of our students is staggering

• In preparation for a site visit for our VIGRE grant I went over student records.

• Of the ~450 mathematics majors, 127 had GPAs over 3.5.

• Of those, 64 had perfect 4.0 GPAs.

Data

Number of math majors

050

100150200250300350400450500

1995-96

1996-97

1997-98

1998-99

1999-00

2000-01

2001-02

2002-03

2003-04

2004-05

Mathematics Degrees Awarded1995-2005

010203040506070

1995-1996

1996-1997

1997-1998

1998-1999

1999-2000

2000-2001

2001-2002

2002-2003

2003-2004

2004-2005

Mathematics Minors2000-2005

0100

200300400

500600

Fall 2

000

Spring

200

1

Fall 2

001

Spring

200

2

Fall 2

002

Spring

200

3

Fall 2

003

Spring

200

4

Fall 2

004

Spring

200

5

Fall 2

005

Real Analysis of Several VariablesMATH 425B

0

5

10

15

20

25

30

35

40

YR 00-01 YR 01-02 YR 02-03 YR 03-04 YR 04-05 YR 05-06

Academic Year

# o

f st

ud

ents

en

rolle

d

I am trying to get our faculty involved

• Email message to all of our teaching staff at the end of the semester.

Suppose that I now have a student interested in a math major?

1. What are the opportunities for mathematics majors?

2. How can I increase their sense of professionalism?

3. In order to provide advice, I have to understand their career goals and how mathematics can fit into those career goals.

• I want to state very emphatically (lest we forget) that my goal is to increase the mathematical content of their undergraduate curriculum. It is not to get them to go into graduate school in mathematics, or even to go to graduate school. We need an army of mathematics majors in all areas of life in this country.

Opportunities

• Departmental

• University-wide

• Local

• National

• International

– http://math.arizona.edu/~ura/– http://ubrp.arizona.edu/– http://www.rayjobs.com/index.cfm?

Option=Tucson– http://www.nsf.gov/crssprgm/reu/

reu_search.cfm– http://www.mines.edu/reu-mcs/ &– http://www.stolaf.edu/depts/math/budapest/

Professionalism

• Resume

• http://amuc.org

Advising

– Most students don’t know that REU projects pay them to spend the summer thinking about mathematics and graduate school will pay them to go to graduate school in the STEM fields.

– Faculty assume incorrectly that bright students don’t need mentoring. Students can be bright and still be ignorant of the appropriate career path to take.

Final Thoughts

• We as mathematicians need to be more pro-active in helping our students select more mathematics in their undergraduate coursework. Hopefully those courses will entice students into the continued study of mathematics. If these courses don’t accomplish this, then we need to re-evaluate the goals of our courses.

• None of this happens by accident. It is up the mathematics community to educate ourselves as to how best to entice our students into the study of mathematics.