Week 1 | Math Camp Begins & Imposter Syndrome Galore

Harrison Shieh
Sep 9, 2018 · 7 min read

Don’t Panic. Don’t Panic. Don’t Panic.
Shit. I’m panicking.

The chalk board screeches. The clock slowly ticks. And a spattering of “uh huh’s” echo in a classroom built during the height of the Cold War. Everyone seems disinterested in the material. Everyone except, that guy. You know the one — always one step ahead of the lecture, shouting out the answers flawlessly. The “Hey Professor, you forgot to assign us homework today!” asshole that always seems to drain the energy from every undergrad class.

Let’s call him Kyle.

Kyle, seemingly focused on a singular mission to flex his intellectual prowess, proceeds to answer the instructor’s questions without missing a single beat — “This is so clearly a Cauchy sequence.” “Can’t we just use the Stone-Weierstrass Theorem for this?”

Cauchy sequences? The Stone who-now theorem? Was I supposed to remember this from real analysis? Does everyone know what the Stone-Weierstrass Theorem is? Am I the only moron who somehow made it through this supposedly rigorous PhD application vetting process? Why does no one else look panicked?

Am I the only moron who somehow made it through this supposedly rigorous PhD application vetting process?

Fig. 1: A simple proof of the cosine formula for dot product that this moron attempted.

This train of thought is all too common amongst grad students. And although this topic has been written about ad nauseam by other grad school bloggers, I figured maybe I’ll talk a bit about my relationship with imposter syndrome.

I know, I know. A bit of a heavy post for a first post (yay), but I think this is important to talk about — especially as it relates to both personal and professional expectations in academia. Grad school is stressful; feeling like an imposter magnifies and focuses that stress in an unhealthy way. So, let’s tackle this:

What Is Imposter Syndrome?

So what is imposter syndrome? It should be pointed out that this isn’t merely wondering whether or not you are able to do something. Most people question their own abilities or their knowledge of a subject. It is healthy to be skeptical of one’s own intellectual prowess or professional qualifications. What imposter syndrome does, however, is take that healthy skepticism and dial it up to 500%. Imagine your internal voice constantly whispering “You’re full of shit and faking it”. A fear of being “discovered” as an intellectual fraud by your peers — a fear that undermines your confidence in your knowledge of the subject, despite having a provable track-record of accomplishment. Imposter Syndrome burrows itself deep into whatever insecurities you have about your professional and academic qualifications, and like a cancer, metastasizes those insecurities throughout your psyche, constantly taunting you with: “Everyone knows you’re an intellectual fraud. Stop kidding yourself.”

Now, for most over-achievers, this fear of constantly being “found out” by your peers as a charlatan is a catalyst to continue achieving. But, imposter syndrome has other plans. In a twist of irony, this additional achievement is viewed internally as 1) inadequate and 2) probably a crock full of shit. So this never ending cycle of constant over-achieving is always counteracted with an incredible burden — an ineffable feeling of uselessness.

So why did imposter syndrome manifest itself during math camp? Going in, I had already felt my math background was somewhat rusty — I haven’t taken a formal math class or done any math in a while. So being thrown into an intensive math review course that covered the amount of topics that it did felt daunting, to say the least. To make matters worse, the impression I got from my cohort was that everyone seemed to know what they were doing. They appeared to be comfortable with the material and understood the rigorous logic behind the theoretical concepts. But here’s the kicker: when class ended and the instructor left, we all turned to each other, each filled with the look of utter exasperation and mild hopelessness. We all had felt overwhelmed and inadequate in our understanding of the material.

I was not alone. In fact, it turns out I wasn’t a moron who had slipped through the cracks. We were all grinding away at rigorous coursework and had all felt the pressure, both internal and external, to succeed.

The lesson here is relatively straight forward: imposter syndrome affects a lot of people from different walks of life — grad students, lawyers, doctors, and over-achievers. What matters, however, is to not take the annoying voice in your head too seriously. It is statistically improbable that you are where you are out of sheer luck. Your achievements were earned because you earned them, not because you are a fraud that has somehow convinced and defrauded everyone into thinking you are something you are not.

Here’s a nice comic from Jorge Chan over at PhDComics.com that crystalizes this feeling:


Source: Piled High And Deeper

Okay, so back to Math Camp. Aside from the constant feeling of academic inadequacy, what exactly is an Econ PhD math camp like? Hell, why is there even a math camp at all? As you can probably infer, graduate level economics has a high barrier to entry — namely, mathematical sophistication. Regardless of how you may feel about the mathematization of economics, the reality is, all global graduate economics programs of any renown require a high degree of comfort with mathematical techniques ranging from univariate calculus to dynamic optimization. Generally, these topics are usually semesters worth of course work. In math camp, we boil it down to three weeks. For example, this week we covered:

  1. Vector spaces, spans, linear independence, matrix invertibility, determinants, systems of equations, and related proofs. (This is generally covered in a semester long intro linear algebra course)

But what the hell is all this math for?

This all seems rather abstract, so let’s apply each of the three topics to economic problems…or at least, let’s see some quick examples:

Linear Algebra. Matrix algebra is commonly used in econometrics (statistical techniques used in economics), since we can represent data as vectors and matrices. For example, in my masters thesis, I utilized a structural vector autoregression (SVAR), which, simply put, is a statistical model that looks at the relationships between variables over time. We can write this like:

Fig. 2: Simple Structural VAR Model. Source: My own MA thesis.

Calculus. Generally, we use multivariate calculus rather than univariate calculus. If you think about it, using a function of a single variable in any capacity to represent the economy is somewhat unrealistic. But more importantly, calculus is the study of how some variables change in response to other variables. Ex. If a representative agent’s income increases, what is the effect on consumption? On utility? Figure 3 shows a more abstract application of calculus to risk aversion problems commonly seen in applied micro.

Fig. 3: Decreasing Absolute Risk Aversion Problem

Log-Linearization. This is a bit more high-level and combines knowledge of logs and Taylor expansions. This is most commonly used in macro models. In fact, most models require some level of log-linearization to reduce the computational complexity required to solve these systems! The added benefit is we can now express our interpretation in terms of percent change deviations!

Fig. 4: Cobb-Douglass Log Linearization. Source: Eric Sims’ Log Linearization Notes (https://www3.nd.edu/~esims1/log_linearization_sp12.pdf)

Graduate level economics has a high barrier to entry — namely, mathematical sophistication.

So what is the point of talking about all this. My reasoning for writing this blog is to treat it as an outlet for me during grad school — to sharpen and hone my non-academic writing and as a way to “vent”, in a sense. And if the by-product of that is some nugget of advice for some prospective or current grad student going through this, then hey, that’s what we call a positive externality in economics.

This inaugural post went through a lot: imposter syndrome and the purpose of math camp. I imagine future posts will vary between grad school posts, economics discussion, and relevant and topical policy analysis as it relates with my journey to becoming an economist. Feel free to leave comments with suggestions!

Happy first blog post and see you next week!

Harrison Shieh

Written by

Econ PhD Student | My Life Is A Corner Solution | www.harrisonshieh.com

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