My Journey from Graduate
School to Being a University
Professor
by
William Yslas Vélez
Department of Mathematics
University 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.
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We, as a mathematics community,
should recognize
– The changing and important role that
mathematics is playing in society
– http://www.math.uiuc.edu/MSS/2006Spring/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/
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Early Career Profiles:
Recent bachelors-level graduates in the mathematical sciences
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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.
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"What Can I Do with a Math Degree?" is a printable poster from the AMS about jobs that math majors might pursue.
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– The importance of an undergraduate degree
in mathematics and the opportunities that are
available for undergraduates.
This last point deserves some
attention.
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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
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Mathematicians don’t think that mathematics is
useful.
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Mathematicians believe that the reason one
gets a BS degree is because one is headed for
a PhD.
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Mathematicians believe that the BS degree in
mathematics will not lead to gainful
employment.
How to change this perception?
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Mathematics faculty, graduate and
undergraduate students of mathematics should
apply for internships
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Faculty:
http://www.asee.org/resources/fellowships/nsfro/labl
ist.cfm
Graduate Students:
http://www7.nationalacademies.org/policyfellows/
Undergraduate Students:
http://www.sandia.gov/SIP/intern-coop/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
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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
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Benjamin is a physics major
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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
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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/
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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
500
450
400
350
300
250
200
150
100
50
0
1995- 1996- 1997- 1998- 1999- 2000- 2001- 2002- 2003- 200496
97
98
99
00
01
02
03
04
05
Mathematics Degrees Awarded
1995-2005
70
60
50
40
30
20
10
0
1995- 1996- 1997- 1998- 1999- 2000- 2001- 2002- 2003- 20041996 1997 1998 1999 2000 2001 2002 2003 2004 2005
Fa
Sp ll 2
rin 00
g 0
20
Fa 01
Sp ll 2
rin 00
g 1
20
Fa 02
Sp ll 2
rin 00
g 2
20
Fa 03
Sp ll 2
rin 00
g 3
2
Fa 004
Sp ll 2
rin 00
g 4
20
Fa 05
ll
20
05
Mathematics Minors
2000-2005
600
500
400
300
200
100
0
Real Analysis of Several Variables
MATH 425B
40
# of students enrolled
35
30
25
20
15
10
5
0
YR 00-01
YR 01-02
YR 02-03
YR 03-04
Academ ic Year
YR 04-05
YR 05-06
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
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Departmental
University-wide
Local
National
International
– http://math.arizona.edu/~ura/
– http://ubrp.arizona.edu/
– http://www.rayjobs.com/index.cfm?Option=T
ucson
– http://www.nsf.gov/crssprgm/reu/reu_search.
cfm
– http://www.mines.edu/reu-mcs/ &
– http://www.stolaf.edu/depts/math/budapest/
Professionalism
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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
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We as mathematicians need to be more proactive 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.