And so we’ve lost our math major

The mathematics major is not one that often gets cut, but that is what happened to us. I admit that I saw it coming. Yes, there will be litigation, law suits etc, but most of that is personnel oriented. The fact is that, for now, our math major is gone; not that we won’t try to bring it back when our current top administrators leave, one way or another.

Yes, tenured faculty were cut. That is where litigation will come in. And yes, there is grief over that…a lot of it.

But that is not what this post will focus on.

For some of my colleagues, there is a profound sense of grief of being a math professor at a university that will no longer offer a math major. For them: a big part of their identity was being a mathematician.

Sadly, that isn’t true of me; I lost my identity of being a mathematician decades ago.

Time and time again, I’d go to a conference, be fired up about what I saw, return to campus…and watched the ideas in my head die a slow death under 11-12 hour teaching loads, committee work, etc. Over time, I started switching to MAA type conferences (Mathfest, for example) and finding joy in teaching “out of area” courses, even actuarial science ones. I sort of became “known” for that.

And yeah, I did research, picking off a problem here and there and did enough to make Full Professor at my institution. But more and more, by research became more shallow and more broad. And frankly I lost the appetite for all of the BS that comes with publication (type setting, figures, dealing with pedantic referees, etc) Yes, I have a paper at the referee’s now and I owe a referee’s report as well.

But..well, when I see what the mathematicians are doing at the R1 universities (e. g. Big Ten);, well, what I do simply does not compare..it never did. I came to accept that decades ago.

This is a long winded way of saying that I suffered no ego bruise from this.

Note: I am not saying this is totally over; if/when we get better leardership I might attempt to bring a math major back (yes, I am the incoming chair of the department).

Moving forward: I think that the math major is on the wane, at least at the non-elite universities.

West Virginia Math Department and trends..

First of all, I’ll have to read this 2016 article.

But: it is no secret that higher education in the US is in turmoil, at least at the non-elite universities. Some colleges are closing and others are experiencing cut backs due to high operating losses.

This little not will not attempt to explain the problems of why education has gotten so expensive, though things like: reduction of government subsidies, increased costs for technology (computers, wifi, learning management systems), unfunded mandates (e. g. accommodations for an increasing percentage of students with learning disabilities) and staff to handle helicopter parents are all factors adding to increased costs.

And so, many universities are more tuition dependent than ever before, and while the sticker price is high, many (most in many universities) are given steep discounts.

And so, higher administration is trying to figure out what to offer: they need to bring in tuition dollars.

Now about math: our number of majors has dropped, and much, if not most, of the drop comes from math education: teaching is not a popular occupation right now, for many reasons.

Things like this do not help attract student to teacher education programs:

Virginia argues teacher is not entitled to extra compensation after being shot because the shooting was a "hazard of the job." The school board's attorney says it's an "unfortunate reality" that teaching is "not without its dangers."https://t.co/t3H7Sf70dz

— Celeste Headlee (@CelesteHeadlee) August 11, 2023

One thing that hurts enrollment in upper division math courses is that higher math has prerequisites. Of course, many (most?) pure math courses do not appear to have immediate application to other fields (though they often do). And, let’s face it: math is hard. The ideas are very dense.

So, it is my feeling that the math major..one that requires two semesters of abstract algebra and two semesters of analysis, is probably on the way out, at least at non-elite schools. I think it will survive at Ivy caliber schools, MIT, Stanford, and the flagship R-1 schools.

As far as the rest of us: it absolutely hurts my heart to say this, but I feel that for our major to survive at a place like mine, we’ll have to allow for at least some upper division credit to come from “theory of interest”, “math for data science”, etc. type courses…and perhaps allow for mathy electives from other disciplines. I see us as having to become a “mathematical sciences” type program…or not existing at all.

Now for the West Virginia situation (and they probably won’t be the last):

https://twitter.com/AnonymousF59605/status/1690077384282607616

I went on their faculty page and noted that they had 31 Associate/Full professors; the remainder appeard to be “instructors” or “assistant professors of instruction” and the like. So while I do not have any special information, it appears that they are cutting the non-tenured..the ones who did a lot (most?) of the undergraduate teaching.

Now for the uninitiated: keeping current with research at the R-1 level is, in and of itself, is a full time job. Now I am NOT one of those who says that “researchers are bad teachers” (that is often untrue) but I can say that teaching full loads (10-12 hours of undergraduate classes) is a very different job than running a graduate seminar, advising graduate students, researching, and getting NSF grants (often a prerequisite for getting tenure to begin with.

So, a lot of professor’s lives are going to change, not only for those being let go, but also for those still left. I’d imagine that some of the research professors might leave and have their place taken by the teaching faculty who are due to be cut, but that is pure speculation on my part.

Commentary

It is not a surprise that my posts here have fallen off by quite a bit. Part of it is that I’ve been assigned a lot of teaching of courses that I have to do extra preparation for.

And yes, the nature of the job has changed. Student body is more or less the same size, but we’ve been reduced from 15 tenure track lines to 9. This means: larger size sections, more students to advise (per professor) and less selection among upper division classes.

Ok, jobs change and I am not treated that poorly. Yes, I wish our classrooms had better IT structure and we didn’t have so many per section.

But the real issue is the loss of tenure track lines and the reliance on visitors.

The number of applicants, at least for the temporary jobs, has dropped by an order of 10.

What is going on, I think: university administrations have embraced, IN PART, a “run it like a business” attitude.

So, they see small class sizes as wasted resources. They see work week “down time” to think about scholarship OR to think about how to approach/teach a class as wasted time. I can’t remember the time I last thought about mathematics during an academic year.

And frankly, I am often not tempted: IF one gets a bit of time to do math, subsequent open slots are often filled by duties, student needs (more students = more exceptional cases; e. g. accidents, illnesses, etc.) and by the time I can get back to it, I’ve often forgotten my train of thought.

And so, what is offered to those who apply for our jobs?
Mostly, it is packed schedules, packed classrooms and not much job security (yes, tenure track faculty can be let go for reasons other than performance).

And back to the “run it like a business model”: we want business demands on potential workers, but we don’t want to compete with respect to compensation.

In my day: I took less money than I could have made outside, in return for being able to do a bit of scholarship and have a bit of fun with classes and enjoy a “family like” atmosphere with extra job security.

That has been taken away; only the “lower pay” remains, and new job seekers are savvy enough to see that.

If we want to “run it like a business”, we need to compete with businesses for young talent, and we aren’t doing that.

My guess: things will be very grim over the next half-decade to a decade, at least at the non-R1 universities.

So, you want our tenure-track academic math job…

Background: we are a “primarily undergraduate” non-R1 institution. We do not offer math master’s degrees but the engineering college does.

Me: old full professor who has either served on or chaired several search committees.

I’ll break this post down into the two types of jobs we are likely to offer:
Tenure Track lecturer

Tenure Track Assistant Professor.

Lecturer

No research requirement; this job consists of teaching 12 hour loads of lower division mathematics classes, mostly “business calculus and below”; college algebra and precalculus will be your staples. There will be some service work too.

What we are looking for:

Evidence that you have taught lower division courses (college algebra, precalculus, maybe “baby stats”) successfully. Yes, it is great that you were the only postdoc asked to teach a course on differentiable manifolds or commutative ring theory but that is not relevant to this job.

So hopefully you have had taught these courses in the past (several times) and your teaching references talk about how well you did in said courses; e. g. students did well in said courses, went on to the next course prepared, course was as well received as such a course can be, etc. If you won a teaching award of some kind (or nominated for one), that is good to note. And, in this day and age..how did the online stuff go?

Teaching statement: ok, I am speaking for myself, but what I look for is: did you evaluate your own teaching? What did you try? What problems did you notice? Where could you have done better, or what could you try next time? Did you discuss your teaching with someone else? All of those things stand out to me. And yes, that means recognizing that what you tried didn’t work this time…and that you have a plan to revise it..or DID revise it. This applies to the online stuff too.

Diversity Statement Yes, that is a relatively new requirement for us. What I look for: how do you adjust to having some cultural variation in your classroom? Here are examples of what I am talking about:

We usually get students from the suburbs who are used to a “car culture.” So, I often use the car speedometer as something that gives you the derivative of the car’s position. But I ended up with a student from an urban culture and she explained to me that she and her friends took public transportation everywhere…I had to explain what a speedometer was. It was NOT walking around knowledge.

Or: there was a time when I uploaded *.doc files to our learning management system. It turns out that not all students have Microsoft word; taking a few seconds to make them *.pdf files made it a LOT easier for them.

Other things: not everyone gets every sports analogy, gambling analogy (cards, dice, etc.) so be patient when explaining the background for such examples.

Also: a discussion on how one adjusts for the “gaps” in preparation that students have is a plus; a student can place into a course but have missing topics here and there. And the rigor of the high school courses may well vary from student to student; some might expect to be given a “make up” exam if they do poorly on an exam; another might have been used to be given credit for totally incorrect work (I’ve seen both).

Also: if you’ve tutored or volunteered to help a diverse group of students, be sure to mention that (e. g. maternity homes, sports teams, urban league, or just the tutoring center, etc.)

Transcript: yes, we require it, but what we are looking for is breath for the lecturer’s job: the typical is to have three of the following covered: “algebra, analysis, topology, probability, statistics, applied math”

Cover letter: Something that shows that you know the type of job we are offering is very helpful; if you state that you “want to direct undergraduate research”, well, our lecturer job will be a huge letdown.

Assistant Professor

This job will involve 9-12 hours teaching; 10-11 is typical and we do have a modest research requirement. 2-3 papers in solid journals will be sufficient for tenure; you might not want to have your heart set on an Annals of Math publication. If you do get one, you won’t be with us for long anyway. There is also advising and service work.

What we are looking for: teaching: we want some evidence that you can teach the courses typically taught by our department. This means some experience in calculus/business calculus for our math track, and statistics for our statistics track. For this job, some evidence for upper division is a plus, but not required nor even expected; is is an extra “nice to have.”

But it is all but essential that your teaching references talks about your performance in teaching lower division classes (calculus or below); if all you have is “the functional analysis students loved him/her”, that is not helpful. Being observed while teaching a lower division course is all but essential.

Teaching and Diversity statement : same as for the lecturer job. An extra: did you have any involvement with the math club?

Research: the thing we are looking for is: will you “die on the vine” or not? Having a plan: “I intend to move from my dissertation in this direction” is a plus, as is having others to collaborate with (though collaboration isn’t necessary). Also, a statement from your advisor that you can work INDEPENDENTLY ..that is, you can find realistic problems to work on and do NOT need hand holding, is a major plus. You are likely to be somewhat isolated here. And of course, loving mathematics is essential with us. Not all candidates do..if you see your dissertation as a task you had to do to get the credential then our job isn’t for you.

Another plus: having side projects that an undergraduate can work on is a plus. We do have some undergraduate research but that won’t be the bulk of the job.

Transcript: same as the lecturer job.

My teaching during the COVID-19 Pandemic

My university has moved to “online only” for the rest of the semester. I realize that most of us are in the same boat.
Fortunately, for now, I’ve got some academic freedom to make changes and I am taking a different approach than some.

Some appear to be wanting to keep things “as normal as possible.”

For me: the pandemic changes everything.

Yes, there are those on the beach in Florida. That isn’t most of my students; it could be some of them.

So, here is what will be different for me:
1) I am making exams “open book, open note” and take home: they get it and are given several days to do it and turn it back in, like a project.
Why? Fluid situations, living with a family, etc. might make it difficult to say “you HAVE to take it now…during period X.” This is NOT an online class that they signed up for.
Yes, it is possible that some cheat; that can’t be helped.

Also, studying will be difficult to do. So, getting a relatively long “designed as a programmed text” is, well, getting them to study WHILE DOING THE EXAM. No, it is not the same as “study to put it in your brain and then show you know it” at exam time. But I feel that this gets them to learn while under this stressful situation; they take time aside to look up and think about the material. The exam, in a way, is going through a test bank.

2) Previously, I thought of testing as serving two purposes: a) it encourages students to review and learn and b) distinguishing those with more knowledge from those with lesser knowledge. Now: tests are to get the students to learn..of course diligence will be rewarded. But who does well and who does not..those groups might change a little.

3) Quiz credit: I was able to sign up for webassign, and their quizzes will be “extra credit” to build on their existing grade. This is a “carrot only” approach.

4) Most of the lesson delivery will be a polished set of typeset notes with videos. My classes will be a combination of “live chat” with video where I will discuss said notes and give tips on how to do problems. I’ll have office hours ..some combination of zoom meetings which people can join and I’ll use e-mail to set up “off hours” meetings, either via chat or zoom, or even an exchange of e-mails.

We shall see how it works; I have a plan and think I can execute it, but I make no guarantee of the results.
Yes, there are polished online classes, but those are designed to be done deliberately. What we have here is something made up at the last minute for students who did NOT sign up for it and are living in an emergency situation.

Applying for an academic job: what I look for in an application

Disclaimer: let me be clear: these are MY thoughts. Not everyone is like me.

I have served on several search committees and have chaired several of them as well. My university: an undergraduate university where we have a very modest, but mandatory research requirement (much less than what an R1 has). Teaching loads: mostly service classes; maybe an upper division class; typically 10-12 hours per semester. Service loads are heavy, especially for senior faculty.

These thoughts are for the applicant who wants to be competitive for OUR specific job; they do not apply to someone who just wants to make a blanket application.

General suggestion: Proofread what you submit. You’d be surprised at how many applications contain grammatical mistakes, spelling errors and typos.

Specific suggestions:
Take note of the job you are applying for. We have two types of tenure track positions: assistant professor positions and tenure track lecturer positions.
One can obtain promotion from the assistant professor position; one cannot be promoted from our lecturer position.

Assistant professor position: has a research and service requirement and involves teaching across the curriculum (lower and upper division classes)
Lecturer position: has a service requirement and involves teaching freshman courses..occasionally calculus but mostly pre-calculus mathematics (college algebra, precalculus, perhaps business math, non-calculus based statistics).

Teaching: What I look for is:
1. Relevant experience: how will you do when you walk into the classes YOU are teaching? Can we reasonably predict success from your application?

2. References: if you are applying for the lecturer position, you should have a teaching reference from someone who has observed your teaching in a pre calculus class (algebra, trig, pre calculus, etc.). Letters that say “X is a great teacher” and is followed by the current buzzwords really don’t stand out. Letters that say “I observed X teaching a precalculus class and saw that…” get my attention.

If you are applying for the assistant professor position, I’d like to see the observation from, say, a calculus class.

Observations of how well you lead a graduate student review for the Ph. D. exam on the topology of manifolds really isn’t helpful to us.

3. Teaching statement: I don’t care about all of the hot buzzwords or how you want to make the world a better place. I’d like to see that you thought about how to teach and, even better, how your initial experiences lead to adjustments. Things like “I saw students could not do this type of problem because they did not know X..” catch my eye as do “I tried this..it didn’t work as well as I had hoped so I tried that and it worked better ..” also catch my eye. Also, “students have trouble with these concepts and I have found that they really haven’t mastered…” are also great.

4. Please be realistic: if you ware applying for the lecturer position, it doesn’t help to state your heart is set on directing student research our teaching our complex variables class. If your heart IS really set on these things, this job is not for you.

Research (assistant professor position only) What I am looking for here is someone who won’t die on the vine. So I’d like to see evidence of:

1. Independence: can you work independently? Can you find your own problems to work on? Do you have collaborators already set (if appropriate)? What I mean: you cannot be too advisor dependent at our job, given its limited resources and heavy teaching load. An advisor’s letter that says “student X suggested this problem to work on” stand out in a positive way.

2. Plan: do you have plan moving forward?

3. Realism: you aren’t going to in a Fields Medal or an Abel Prize at our job. You aren’t going to publish in the Annals of Math. If you have your heart set on working on the toughest cutting edge problems, you will likely fail at our place and end up frustrated. And yes..staying current at the cutting edges of mathematics is all but impossible; they best you’ll be able to do is to tackle some of the stuff that isn’t dependent on heavy, difficult to learn machinery. You simply will not have large blocks of uninterrupted time to think.

Over-scheduling of senior faculty and lower division courses: how important is course prep?

It seems as if the time faculty is expected to spend on administrative tasks is growing exponentially. In our case: we’ve had some administrative upheaval with the new people coming in to “clean things up”, thereby launching new task forces, creating more committees, etc. And this is a time suck; often more senior faculty more or less go through the motions when it comes to course preparation for the elementary courses (say: the calculus sequence, or elementary differential equations).

And so:

1. Does this harm the course quality and if so..
2. Is there any effect on the students?

I should first explain why I am thinking about this; I’ll give some specific examples from my department.

1. Some time ago, a faculty member gave a seminar in which he gave an “elementary” proof of why is non-elementary. Ok, this proof took 40-50 minutes to get through. But at the end, the professor giving the seminar exclaimed: “isn’t this lovely?” at which, another senior member (one who didn’t have a Ph. D. had had been around since the 1960’s) asked “why are you happy that yet again, we haven’t had success?” The fact that a proof that could not be expressed in terms of the usual functions by the standard field operations had been given; the whole point had eluded him. And remember, this person was in our calculus teaching line up.

2. Another time, in a less formal setting, I had mentioned that I had given a brief mention to my class that one could compute and improper integral (over the real line) of an unbounded function that that a function could have a Laplace transform. A junior faculty member who had just taught differential equations tried to inform me that only functions of exponential order could have a Laplace transform; I replied that, while many texts restricted Laplace transforms to such functions, that was not mathematically necessary (though it is a reasonable restriction for an applied first course). (briefly: imagine a function whose graph consisted of a spike of height at integer points over an interval of width and was zero elsewhere.

3. In still another case, I was talking about errors in answer keys and how, when I taught courses that I wasn’t qualified to teach (e. g. actuarial science course), it was tough for me to confidently determine when the answer key was wrong. A senior, still active research faculty member said that he found errors in an answer key..that in some cases..the interval of absolute convergence for some power series was given as a closed interval.

I was a bit taken aback; I gently reminded him that was such a series.

I know what he was confused by; there is a theorem that says that if converges (either conditionally or absolutely) for some then the series converges absolutely for all where The proof isn’t hard; note that convergence of means eventually, for some positive then compare the “tail end” of the series: use and then and compare to a convergent geometric series. Mind you, he was teaching series at the time..and yes, is a senior, research active faculty member with years and years of experience; he mentored me so many years ago.

4. Also…one time, a sharp young faculty member asked around “are there any real functions that are differentiable exactly at one point? (yes: try if is rational, if is irrational.

5. And yes, one time I had forgotten that a function could be differentiable but not be (try: at

What is the point of all of this? Even smart, active mathematicians forget stuff if they haven’t reviewed it in a while…even elementary stuff. We need time to review our courses! But…does this actually affect the students? I am almost sure that at non-elite universities such as ours, the answer is “probably not in any way that can be measured.”

Think about it. Imagine the following statements in a differential equations course:

1. “Laplace transforms exist only for functions of exponential order (false)”.
2. “We will restrict our study of Laplace transforms to functions of exponential order.”
3. “We will restrict our study of Laplace transforms to functions of exponential order but this is not mathematically necessary.”

Would students really recognize the difference between these three statements?

Yes, making these statements, with confidence, requires quite a bit of difference in preparation time. And our deans and administrators might not see any value to allowing for such preparation time as it doesn’t show up in measures of performance.

A rant about academic publishing

Ok, it is nearing the end of the summer and I feel as if I am nearing the end of a paper that I have been working on for some time. Yes, I am confident that it will get accepted somewhere, though I will submit it to my “first choice” journal when it is ready to go. I have 6 diagrams to draw up, put in, and then to do yet another grammar/spelling/consistent usage check.

Part of this “comes with the territory” of trying to stay active when teaching at a non-research intensive school; one tends to tackle such projects in “modules” and then try to put them together in a seamless fashion.

But that isn’t my rant.

My rant (which might seem strange to younger faculty):

A long time ago, one would work on a paper and write it longhand and ..if you were a professor, have the technical secretary type it up. Or one would just use a word processor of some sort and make up your Greek characters by hand. You’d submit it, and if it were accepted, the publisher would have it typeset.

Now: YOU are expected to do the typesetting and that can be very time consuming. YOU are expected to make camera ready diagrams.

And guess what: you aren’t paid for your article. The editor isn’t paid. The referee(s) isn’t (aren’t) paid. But the journal still charges subscription fees, sometimes outrageously high fees. And these are the standard journals, not the “fly by night” predatory journals.

This is another case where the professor’s workload went up, someone else’s expense went down, and the professor received no extra benefit.

Yes, I know, “cry me a river”, blah, blah, blah. But in this respect, academia HAS changed and not for the better.

Numerical solutions to differential equations: I wish that I had heard this talk first

The MAA Mathfest in Chicago was a success for me. I talked about some other talks I went to; my favorite was probably the one given by Douglas Arnold. I wish I had had this talk prior to teaching numerical analysis for the fist time.

Confession: my research specialty is knot theory (a subset of 3-manifold topology); all of my graduate program classes have been in pure mathematics. I last took numerical analysis as an undergraduate in 1980 and as a “part time, not taking things seriously” masters student in 1981 (at UTSA of all places).

In each course…I. Made. A. “C”.

Needless to say, I didn’t learn a damned thing, even though both professors gave decent courses. The fault was mine.

But…I was what my department had, and away I went to teach the course. The first couple of times, I studied hard and stayed maybe 2 weeks ahead of the class.
Nevertheless, I found the material fascinating.

When it came to understanding how to find a numerical approximation to an ordinary differential equation (say, first order), you have: with some initial value for both . All of the techniques use some sort of “linearization of the function” technique to: given a step size, approximate the value of the function at the end of the next step. One chooses a step size, and some sort of schemes to approximate an “average slope” (e. g. Runga-Kutta is one of the best known).

This is a lot like numerical integration, but in integration, one knows for all values; here you have to infer from previous approximations of %latex y(t) $. And there are things like error (often calculated by using some sort of approximation to such as, say, the Taylor polynomial, and error terms which are based on things like the second derivative.

And yes, I faithfully taught all that. But what was unknown to me is WHY one might choose one method over another..and much of this is based on the type of problem that one is attempting to solve.

And this is the idea: take something like the Euler method, where one estimates . You repeat this process a bunch of times thereby obtaining a sequence of approximations for . Hopefully, you get something close to the “true solution” (unknown to you) (and yes, the Euler method is fine for existence theorems and for teaching, but it is too crude for most applications).

But the Euler method DOES yield a piecewise linear approximation to SOME which might be close to (a good approximation) or possibly far away from it (a bad approximation). And this that you actually get from the Euler (or other method) is important.

It turns out that some implicit methods (using an approximation to obtain and then using THAT to refine your approximation can lead to a more stable system of (the solution that you actually obtain…not the one that you are seeking to obtain) in that this system of “actual functions” might not have a source or a sink…and therefore never spiral out of control. But this comes from the mathematics of the type of equations that you are seeking to obtain an approximation for. This type of example was presented in the talk that I went to.

In other words, we need a large toolbox of approximations to use because some methods work better with certain types of problems.

I wish that I had known that before…but I know it now. 🙂

At long last…

I’ve been silent on this blog for too long. Part of what is happening: our department is slowly morphing into a “mostly service courses” department due to new regulations on “minimum class size” (set to 10 students for upper division courses). THAT, plus a dearth of “mathematics teaching majors” is hurting our “majors” enrollment.

So it has been “all calculus/all the time” for me lately. Yes, calculus can be fun to teach but after close to 30 years…..zzzzzz….

And it would be unethical for me to try something new just because I am bored.

But I finally have something I want to talk about: next post!