Advice for a young academic: imposter syndrome

Peter G Knight

A great deal has been written in the last few years about so-called “imposter syndrome” – the feeling experienced by many young academics that somehow they don’t really belong in their new role as a lecturer and that somehow they should never have been allowed to make the step up from being a student. The fear is that you are not good enough, that you don’t deserve this, that you won’t cope and that you will in due course be found out and exposed. There are books about it. There’s a TED Talk about it. Seeing what has already been written makes me feel like an imposter even thinking about writing this post.

If you are in that situation I have two pieces of advice to get you started:

1. Get used to it. We all feel that way. Welcome to academia.
2. Don’t worry. You are not an imposter. You are as good…

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One-Word Math Classes

Math with Bad Drawings

You know what’s often missing from math class? Yes, candy bars, but even more important than that: coherence.

Math class shouldn’t be a mishmash pile of facts, thrown together haphazardly, like an academic version of The White Album. It should be a perfectly interlocking tower of truths, climbing upwards with singular purpose—an academic Sgt. Pepper or Abbey Road.

A good class isn’t a greatest hits record. It’s a concept album.

In that spirit, I’ve been taking each topic in the secondary math curriculum—algebra, geometry, calculus, etc.—and trying to boil it down to its one-word essence. Here are the rules of the game:

1. You must choose a single word to complete the sentence, “[Branch of math] is the mathematics of _____.”

For example, you might say, “Topology is the mathematics of dinosaurs,” or “Category theory is the mathematics of abstraction,” or “Combinatorics is the mathematics of sadness.” (To be…

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Mathematics, poetry and beauty

Peter Cameron's Blog

Comparing mathematics with poetry is an infinitely rich game. For every opinion you express, there is an equally valid counter-opinion. Contrasted to Hilbert’s dismissal of a student who had left mathematics for poetry, “I always thought he didn’t have enough imagination for mathematics”, someone said to me recently that the early death of Schubert was a greater tragedy than that of Galois, since what Galois could have achieved would sooner or later be done by someone else, whereas Schubert’s potential was lost forever.

So it isn’t so surprising that a book by Ron Aharoni, newly translated into English, doesn’t come to a definite conclusion one way or the other. The best we can do in a book entitled Mathematics, Poetry and Beauty is to give many examples of beautiful mathematics and beautiful poetry and discuss what the similarities and differences are.

Ron Aharoni is a mathematician whose field is combinatorics…

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An open letter to Gov. Scott Walker: stop perpetuating the myth of the lazy professor

I found this very nice blog post on the myth of the lazy professor. (no, I’m not avoiding studying for prelims by reading all of WordPress. Why do you think that?) I’ve spent four years at two different universities, and during those four years I’ve never met a professor who didn’t work 50-60 hours a week. The myth of the lazy professor ties in to so many of my favourite misconceptions about teaching. My mother is a high school teacher, and she gets it from politicians all the time: “teachers only spend 15-20 hours a week in the classrooms, they have such a nice cushy job”. That’s the opposite of true. A bare minimum of preparation before each class is about 20 minutes, then on top of that there is preparing homeworks, labs and exams. And then there is at least 5-6 hours of grading each week for each class, and on top of that talking to students and their parents, and doing various administrative tasks that keep popping up. 15-20 hours of contact time is a full-time job. More than that actually, if you want to do a good job and not just a passable one. Those 20 minutes of preparation will be more like an hour if you want to give a good, engaging class.

A college professor is only supposed to teach 50% of the time, and spend the rest on research, so the normal 6 or so hours of face time with students is spot on. Especially if you consider that advising graduate students and undergraduate students comes on top of the regular teaching. So to everyone who thinks that college professors have it easy: think again.

Oh, and as a side note: I find it funny that people love to tell teachers how easy they have it, but public speaking is consistently the thing most people fear. And yet people call out teachers and professors for having an easy job. I find it extremely frustrating, especially coming from people I know who work in industry. They can take weeks to prepare for a 20 minute presentation, yet are shocked that it takes 20-60 minutes to prepare a 50 minute class. There is a lot more to teaching than what you see in a classroom. Anyway, I’ll stop ranting now and let you read this excellent blog post.

The Contemplative Mammoth

Dear Gov. Walker,

Last week, you told professors at the University of Wisconsin that they needed to “work harder.” You were making a case that the Wisconsin state budget crisis could be ameliorated by increasing employee efficiency, and you suggested having faculty teach at least one more class. I’m not going to talk about whether or not the budget crisis is manufactured (some have argued it could be solved by accepting federal funds for the state’s Badger Care health program), or whether your real goal is really partisan politics, and not fiscal responsibility.

Ouch. Photo by fellow UW Madison geographer Sigrid Peterson.

Instead, I want to talk about the myth of the lazy professor, a stereotype that you’ve reinforced with your comment. I spent 2005 to 2012 at the University of Wisconsin, where I obtained a PhD in the Department of Geography; I am now an assistant professor at the University of Maine.

When you…

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What if mathematicians wrote travel articles?

I’m posting an update of my own tomorrow probably, after my analysis final with some of the material I talked about during the conference I attended a few weeks ago. In the mean time, I found this post very enjoyable (in fact, Izabella Laba’s entire blog is very enjoyable).

The Accidental Mathematician

Some time ago I suggested that scientists might not always make the best writers. I guess I wasn’t the only person ever to make this profound observation. Slate has since published this piece on how political scientists would cover the news; see also here. As hilarious as these are, I would say that there’s more to the picture. The story below is inspired by this one (hat tip to Terry Tao). Believe it or not, there are actual reasons why we have to write like this sometimes. I’m as guilty as anyone. In fact, I’m in the middle of revising one of my papers right now…

In this article we describe the plane flight that Roger and I took to San Francisco. The purpose of our trip was to meet Sergey, our collaborator on the paper “The structure of fuzzy foils” (J. Fuzzy Alg. Geom. 2003) who also co-organized…

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Almost Everywhere

Part of mathematics is learning the language and terminology. Early on, we learn symbols like and , and later we come across acronyms like w.l.o.g. (without loss of generality) and t.f.a.e (the following are equivalent). I’ve been revising analysis lately, for my prelim in analysis on Friday, and I came across a new one: almost everywhere, a.e.

It is a phrase from measure theory, so first I’ll explain some basics of that. Measure theory is about sets. Simply put, it describes ways to assign to each set a positive real number that can be interpreted as the size of the set. It must satisfy three basic properties: the measure of every set must be positive, the measure of the empty set must be zero, and the measure must be additive (with respect to disjoint sets).

A property is then said to hold for a set almost everywhere if the subset of elements for which it doesn’t hold has measure 0. We say that a set with full measure is one for which the complement has measure zero. An example would be a filled in rectangle. The (area of the) border of the rectangle has measure zero, and the interior is thus a set of full measure. This means that the rectangle consists only of the interior, a.e.

This was a short post, since I’m very busy preparing for my prelims. Next time, I’ll discuss a generalisation of the Riemann integral: the Lebesgue integral, and I’ll hopefully have more time to write about it in more detail.

MOOCs

I have been trying to distract myself from the impending future, revising for my final exams and revising my senior thesis. At the moment I channel all my energy to ‘productive procrastination’, I am taking several MOOCs on coursera in some of my interests other than mathematics. My current favourite one is on public speaking, something I imagine will come in handy as a teaching assistant. It will be good to have had some training in forming arguments and projecting to an audience before I need to teach calculus to undergraduates. If I become even half as good as Professor McGarrity, I will be an amazing TA. Some of that charisma could be useful to convince students that maths is great.

Other courses I am taking are in information security, psychology, game theory and a computing class on compilers. The game theory one is really fascinating, since we study general game play, so machines that can play and win any game. It ties into artificial intelligence a lot more than I realised when I signed up for it which is really cool.

I know that a lot of people like to hate on MOOCs and claim that one can’t learn a subject very well from them. It’s true that it takes a lot of discipline to learn as much as you would in a classroom setting, and I have failed to complete quite a few of them. But even if not every participant learns as much as they potentially could, they still reach so many more students than any classroom. Everyone who is there is there voluntarily, so no one is sitting off time because the class is required for their major. Even in the classes that I failed to complete, I still learned a lot.

For someone who wants to try out a MOOC, I would recommend Dan Ariely’s class on behavioural economics. It was one of my first classes and Professor Ariely is amazing. Other than coursera I know that edX offers MOOCs as well, and they are supposed to be really good. I have no experience with them yet, but I will be taking a class on Linux there in the fall.

I would strongly recommend taking a MOOC or two in any area you are interested in. They are free, available from anywhere and taught by experts in their field, by top universities. I have learned about philosophy, psychology, economics, management, computer science and gastronomy, to name a few. They might not give formal qualifications but they do add skills to your CV, and they are perfect to procrastinate with on a day like this.

Day 1

Today I accepted a place as a graduate student in mathematics at a small, private research university in the US. Right now I live and study in England, so this will be quite a large change for me. I’m really excited, and really terrified about all these news.

I decided to start blogging today to chronicle this new part of my life. I will write about large events in my life as well as mathematics that I find interesting. At the moment, my interests are in algebra, topology and graph theory, but I imagine that I will refine those interest considerably during the next few years. My senior thesis is on knot theory and topological graph theory and I will, in a few weeks, post it on the blog so you can read it.

The next few posts will probably be about preparing to move to a different continent and adjusting to life as a graduate student. I have to go through the visa process, find an apartment, figure out all the little details that are different in the US compared to Europe and so on. Expect many posts about culture shock.

I’m really hoping that I made the right decision with my choice of university. I had offers both from a large public university and a small public university, but I think, or maybe hope, that a private university would be a better fit for me. One of the main reasons I decided on my university, we’ll call it U, is that I was interviewed and the interviewer really managed to present U as a friendly, yet competitive place. I thrive off competition, but I also don’t like working in very tense environments. I also don’t want to get lost in a large department, and one of my other options is HUGE. So, I think that I made the right choice with U.

I have received very good advice from my current professors, and they tell me not to stress about which university to choose. Most of the universities that are ranked in the top 100 in most lists are amazing places that offer a lot of chances to grow as a mathematician. As long as it is a friendly place, I will be able to make it something amazing.