PhD, University of Pittsburgh

Jake Mirra: I discovered while a PhD student that my real passion is teaching

Jake Mirra

Jake Mirra

Ph.D. Student

Department of Mathematics, University of Pittsburgh

Jake Mirra is a Ph.D. student in Mathematics at the University of Pittsburgh.

When I’m done here, people will be calling me Dr. Mirra.  Now that’s cool.

My advice for students who want to enter this field

Talk.  To people.  Real people.  Let me say it again.  Talk to real people.  And not just one.  Talk to lots of people.  Send emails.  Set up meetings.

Learn what you’d be getting into.  You will learn that, with math as anything else in life, the real story is complicated.  What it’s like to be a graduate student depends on your personal situation, who your advisor is, what your department is.

And, believe it or not, it is not necessarily the case that employers will be lining up to hire you for a six-figure job when you finish your PhD.  They might or might not, depending on the department, your advisor, your specialty, and the quality of your research.

Advice for new students new to this department

Your first two years at this department could be fairly miserable, or they could be wonderful, depending on how you prepare.

Here at Pitt, there are two preliminary exams that you’re required to have passed by the end of your second year, on analysis and linear algebra.  If you spend a year taking practice tests from the department website and preparing for them, you could pass the prelims your first day in the department.  Advisors will be lining up to talk to you, and you’ll already be ahead of schedule!

My short-term and long-term career plans

So, my plan is pretty unorthodox as far as geometric analysts go.  I discovered while a PhD student that my real passion is teaching, and in fact I don’t care so much for the research. 

So, while I will write my dissertation and complete my PhD, I don’t think I will be going on to do a post-doc and hunting for a tenure-track professorship.  I might want to get directly into teaching, maybe even at the high school level. 

Again, this is unusual (how many of your high school math teachers were referred to as “Dr.” ?) but I think my PhD will be valuable to finding work in that field – if that’s what I end up doing. 

What I do in my free-time

I’m training for a marathon, so lots of running.  I travel, too, occasionally.  And I play the piano – that’s something that’s stuck since childhood.  Also, Pittsburgh is pretty lively at night – on the weekends I have a good time going out with friends.

My idea of a “hard” life is working a menial minimum wage job for 8 to 12 hours a day and hardly getting by.  I basically did that as an undergrad. 

My quality of life drastically increased when I entered graduate school.

Why I chose University of Pittsburgh

I loved mathematics as an undergraduate at the University of Pittsburgh, and I was very good at it. So when the department invited me to pursue a PhD – with a nice benefits package for me and my family, decent pay, and a full year of fellowship funding with no strings attached, it was hard to find a reason to say no. 

At the time I already had two children with a third on the way, and this meant I had a stable job for the next four to six years with a PhD in Mathematics to look forward to at the end. 

My research area and its importance

The story of my research begins with what you call Euclidean space.  That’s the space we all know and love: the shortest path between two points is a straight line and there’s no curvature. 

To make things more interesting (and useful) we consider a type of “space” that’s more general, called a Riemannian manifold.  The surface of the Earth, for example, is a Riemannian manifold.  In a Riemannian manifold such as this, the shortest path between two points is what we call a geodesic – in the case of the Earth, these paths are the great circles that airplanes fly, since one cannot fly in a straight line (through the Earth) from Pittsburgh to Beijing.  

I study spaces called sub-Riemannian manifolds.  One needs a bit of imagination to understand these.  A sub-Riemannian manifold could be used to describe the “space” of configurations of a car on the street.  It might have three coordinates: an equation.pdf-coordinate, a equation_1.pdf-coordinate, and a equation_2.pdf-coordinate to describe the direction it is pointing.  Since there are three coordinates, this is a three-dimensional space.  However, we are not at liberty to travel though this space in any direction we want.  After all, the car cannot “slide” to the left or right – it is constrained to travel only in the direction it is currently pointing (its equation_3.pdf-coordinate). 

Roughly speaking, I have just described a sub-Riemannian manifold: a manifold in which the directions are constrained in a certain way, so that only certain paths are “legal.” 

The reader should note, my research is not concerned with optimizing one’s ability to parallel park (although it could be used for that).  Rather, the mathematicians like me who are in this field of research are studying these sub-Riemannian manifolds from an exploratory perspective.  Our goal is not necessarily to use them, but to extend our understanding of them. 

If this work allows others to use sub-Riemannian geometry more effectively, then we will of course be happy, but applications are not an immediate goal of my research. 

Applications of mathematical research can be surprising, far-reaching, and unintended.  Although my research is classified as geometric analysis, I use algebraic and topological tools in addition to analytic ones.  In turn, the tools we develop to study sub-Riemannian manifolds could be used in other areas of mathematics for which the tools weren’t intended. 

This sort of thing happens all the time and makes mathematics an exciting, elegant, interconnected field. 

Funding and/or scholarships as a Graduate Student

I have lived in Pittsburgh for most of my life, went here for undergrad, and now I’m here for grad school.  The math department funds my research and provides me with a stipend and health insurance, and in return I work for the department as a teaching assistant.

This means I work about 20 hours per week on preparing for and teaching recitations for professors, holding office hours, and grading quizzes and exams for undergraduate students taking math classes – usually calculus.

This, in my opinion, is a great job.

What I like most about being here

I really enjoy teaching, which is a huge plus, because I get to do lots of it.

The work is reasonably low-stress.  I’m expected to be doing research, and I do it, and there’s no one breathing down my neck.  In fact, attention from my advisor is a good thing, and I meet with him several times a week.  

Is it hard being a graduate student?

Here’s where I disagree with some of my colleagues.  No, I don’t think it’s particularly hard to be a graduate student, at least, not in my department!

Let me qualify that by saying, my idea of a “hard” life is working a menial minimum wage job for 8 to 12 hours a day and hardly getting by.  I basically did that as an undergrad.

My quality of life drastically increased when I entered graduate school.  I quit my retail job immediately and was taking home more money each month, doing things I actually enjoyed. 

Is it easy?  No, but really, what in life is easy?  I refuse to complain.  When I’m done here, people will be calling me Dr. Mirra.  Now that’s cool.

Favourite books

There is a book that strongly influenced me toward studying mathematics.  As an undergraduate, I read through Real Analysis (Third Ed.) by H. L. Royden and I fell in love with the type of thinking that is used by mathematical analysts to prove universal truths.  Also more recently, The Art of Learning by Josh Waitzkin has shaped my perspective on learning and teaching.