In the past I’ve often been listed as the nominal professor for various graduate students taking “reading courses,” which basically meant “I’m going to be doing my research, but there’s some university requirement that says I must be registered for a certain number of courses each term, so please sign my sheet.” But this term I have two students doing honest-to-goodness reading courses — trying to learn some specific material that isn’t being offered in any structured course offered at the moment.
And — it’s great! Anyone have their favorite suggestions/anti-suggestions for reading courses? The method I chose was the following: the student and I consult on a course of readings for the term. Every week, the student reads through the relevant material. Then once a week we meet, and I sit in my chair and take notes as the student gives an informal lecture, as if they were the professor and I was the student.
Obviously good for me, since I get to brush up on some things that I knew really well some time ago but haven’t thought about recently. And the students get to dig into something they really care about. But the somewhat-unanticipated bonus is that the students get fantastic practice in teaching and giving talks. Since it’s just one-on-one, we can stop at any moment for me to point something out or for them to ask a question. And I can expound upon my theories of chalkboard etiquette, such as the need to speak out loud every single symbol you write on the board. Over the course of a single hour, I can see the student’s presentation skills improve noticeably (from “good” to “even better”).
The world being what it is, it’s not possible for every course to be taught with just one student and one professor. But despite all the very real advances in technology and pedagogical theory, I still believe that the best teaching happens with two people sitting at opposite ends of a log (or equivalent), passing words and ideas back and forth. Everything else is just trying to recreate that magic.
When I was a graduate student, I didn’t know any GR but my advisor (hint hint) took me as a student anyway, and said I should learn GR. He made me read through his set of notes on GR and when I have a question I would go to his office and bug him, where he would patiently explain the whole thing to me. I didn’t get any reading class credit :(.
By the way, the set of notes became a bestselling graduate textbook, and every physicist should own one.
“And I can expound upon my theories of chalkboard etiquette, such as the need to speak out loud every single symbol you write on the board.”
!!! I don’t know how many times I’ve asked ‘What’s that funny symbol that looks like a crooked L?’ or something similar.
But with a a bit dim student at the other end of the log you would want to die.
Dirac’s constrained Hamiltonian formalism.
It always astonishes me that this isn’t drilled into graduate students as part of an introductory course. It’s simple enough that one can learn the basics of it in a week, and the essential ideas can be illustrated by appealing to simple examples of finite-dimensional classical systems. Moreover, its relationship to gauge theories of all sorts – which comprise essentially all of moden physics – means that one can’t really claim to understand what a gauge theory is without understanding what constraints are, where they come from, and how they’re used to identify the actual physical degrees of freedom in a theory.
For a bit of extra credit, ask them to apply it to some of the canonical examples in field theory: simple Chern-Simons theory with sources, the ADM formulation of classical GR, or even apply it to your favourite string theory.
Nice post.
As and undergrad I did a reading course on the Hawking-Penrose Singularity Theorems using
Roger Penrose’s “Techniques of Differential Topology in Relativity”. I’d highly recommend it.
“the need to speak out loud every single symbol you write on the board.”
Your students must be writing only short, sparse, simple equations.
I suggest tensor and spinor algebra/calculus as a reading course, perhaps with some supersymmetry thrown in, so that the the students get rid of that annoying habit of reading out loud the equations they write on the board. 🙂
Trust me; the equations are anything but short, sparse and simple. If an equation is worth writing on the board, it’s worth saying out loud. Unless the comprehension of your audience is not a primary goal.
Oh! I did one of those this past semester, on f(R) gravity (in fact, my interest in the topic was largely inspired by my meeting with you, Sean). We did it since Yale doesn’t offer anything beyond the standard grad GR course and I was kind of antsy. But I wish you’d posted this a few months ago – the mini-lecture idea is great. The basic format in our “class” was the same, a meeting every week and reading/calculating in between, but ours was a bit more unstructured – sometimes I would explain some key derivations on paper (almost like a problem set), sometimes I’d run through some calculations and we’d talk about them during the meeting and work through, and sometimes I’d just read and report back. Ended up synthesizing a lot of it in a summary paper at the end though, which was plenty useful. But giving the class a firm structure like the one you suggested seems like a really good idea.
Another idea (one we toyed with, and tried to an extent): doing in addition to reading. Did your students try out calculations that they couldn’t find in any of the papers and then run them over with you? Maybe not research-depth, just getting your feet wet. We definitely spent a couple of weeks working on a particularly interesting problem.
Wait, so reading equations out loud *is* good chalkboard etiquette? Oh boy…
My first quarter in physics grad school I took a reading class using Georgi’s book on Lie algebra, with Dennis Silverman, who is still at UCI. It was very useful as I was having trouble reading the book on my own that previous summer.
“Lie Algebras In Particle Physics: from Isospin To Unified Theories”, as cheap as $34 used on Amazon.
Often, people never really learn material until they have to explain it, not from lack of effort but from lack of internalizing it. The weakness is, it is often very difficult to go beyond the material on their own.
In my opinion, the ability to read should be a prerequisite to any graduate program. That your institution has to offer a course in the subject is scandalous.
I was fortunate to do my undergraduate degree in England. Weekly sessions with my tutor were the best education experience of my life. I learned to think and to write under the pressure of presenting weekly essays to someone who had devoted his life to the topic I was trying to understand. Lack of clarity and intellectual sloppiness was persecuted mercilessly.
I have tried to persuade several Honors Colleges in US to adopt a tutorial system, but “busy” faculty always resisted mightily. I don’t think that“busy”faculty get it: tutorial education is a very much a two-way street. Sit yourself across from a bright undergraduate who has been studying something like his life depended on it for several weeks, and any weakness & fuzziness in your own thinking is going to be on display.
Sean, set your students problems that interest you. I’m a logician, so when we’d come to a meta-theorem that interested me, but I didn’t like the textbooks proofs, I’d say “I don’t like how Godel proves this part. See if you do it by…” Several published papers came from these challenges. Make it interesting & fun for yourself, and don’t just ask them to regurgitate.
Marvelous post Sean! One thing I think you imply but do not directly address is the interest of the people involved. The people are having a conversation and they are both interested and animated.
Of course you are talking about post-secondary education and so this is less of a problem. However one of my pet theories of the problem with primary and secondary education is that it’s based upon a broadcast model. Student and teacher. Sadly, all too often the students aren’t very interested, and whether the teacher has anything to do with that or not, the results broadly speaking are clear for all to see.
I’d love to see a system where students of all ages can follow their interests and get personalized educations. I don’t know how to do this; maybe technology holds the key, maybe it’s something else entirely. And it does not address those students who are simply not interested in school of any sort–how to we address them? Also how do we shore up kids who really need to know a certain amount about the world that’s outside of their interests and strongest skill sets?
Didn’t Plato have ideas about learning that were similar to this?
As an undergrad, i did a reading course in the history of thermodynamics, which sounds dry, but … it covers the development of the formal concepts of both entropy *and* energy. That’s right, energy as a physical concept didn’t emerge until thermodynamics — potential energy was not a formal part of Newtonian mechanics. And i think (although i didn’t get a chance to really check this) that the concept of entropy actually *predates* energy. Wild. Not to rant, but it’s so worth reading some Clausius if you can afford the time.
And now, i’m kind of mentoring an exceptionally brilliant sixth grader. We’re coding up a little n-body simulation of the solar system. But then, after reading ‘Critical Mass’ by Phillip Ball, the thing i think i want to do next is look into simple social physics ‘games’ designed to reproduce flocking behaviors and traffic flows.
What about the shotgun seminar? 4 or 5 students doing the same reading course all prepare a lecture, but only one gives it. This is determined at the last moment by some RNG (like casting die). We all know that preparation is more than half the work, so all benefit. There is also the advantage that the audience is bigger (not just you) and should know the material quite well, so questions are interesting.
@ Brian Too … “Didn’t Plato have ideas about learning that were similar to this? …”
Maybe you were thinking of Socrates. The Socratic Method insofar as the dialog aspect is concerned i guess.
Isn’t Plato mostly about … The Platonic Realm and his Solids or something ?
Anyway Sean, the ‘presentation training’ is a really good idea. I just heard somewhere that many people fear public speaking more than they fear death itself. Whatever the truth of that, i would imagine that having one’s presentation style and content well practiced can only help matters … And of course imagining the audience is in their underwear while giving one’s talk, lol.
@ Brian Too … “Didn’t Plato have ideas about learning that were similar to this? …”
Maybe you were thinking of Socrates. The Socratic Method insofar as the dialog aspect is concerned i guess.
Isn’t Plato mostly about … The Platonic Realm and his Solids or something ?
Anyway Sean, the ‘presentation training’ is a really good idea. I just heard somewhere that many people fear public speaking and stage fright more than they fear death itself. Whatever the truth of that, i would imagine that having one’s presentation style and content well practiced can only help matters … And of course imagining the audience is in their underwear while giving one’s talk, lol.
As an aside, i’d be curious to know someday how an oral thesis defense happens. Particularly with respect to how the adverserial aspects are handled and whether it is a presentation of the thesis and its defense or just a defense of an already presented paper, whether it is one on one or one on many, etc. Also i guess, what weighting is given if any, to style or presentation issues like stage fright.
Chalkboard? What is this chalkboard of which you speak?
Oh how I wish the projector had never been invented….
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Gah. The thought of getting through an equation heavy lecture with every equation being read out loud, instead of explained as it is derived, is mind numbing to contemplate.
g subscript u subscript v equals eight pi g divided by c to the fourth power times t subscript u subscript v…
Now let’s read through the derivation of the field equations via the Einstein-Hilbert or Hilbert-Patilini action. Uggghhhhhh. The incidence of “…” between lines mysteriously shoots up ten thousand percent.
Well, Eric, the EFEs are much easier to read out loud if you don’t say “subscript”, “power”, or
times”, use “over” instead of “divided by”, and set c=1 🙂
“If an equation is worth writing on the board, it’s worth saying out loud. ”
It’s remarkable how these dogmas are completely arbitrary. In the group where I did my PhD, our advisors had the exactly opposite dogma,
“Something not worth writing on the board is not worth saying out loud either.”
We had to write on the board everything we said, so we ended up writing idiocies like “Good morning all”. I guess reading a proof of Stoke’s theorem aloud makes as much sense.