I recently finished my last term lecturing our second-year Quantum Mechanics course, which I taught for five years. It’s a required class, a mathematical introduction to one of the most important set of ideas in all of physics, and really the basis for much of what we do, whether that’s astrophysics or particle physics or almost anything else. It’s a slightly “old-fashioned” course, although it covers the important basic ideas: the Schrödinger Equation, the postulates of quantum mechanics, angular momentum, and spin, leading almost up to what is needed to understand the crowning achievement of early quantum theory: the structure of the hydrogen atom (and other atoms).

A more modern approach might start with qubits: the simplest systems that show quantum mechanical behaviour, and the study of which has led to the revolution in quantum information and quantum computing.

Moreover, the lectures rely on the so-called Copenhagen interpretation, which is the confusing and sometimes contradictory way that most physicists are taught to think about the basic ontology of quantum mechanics: what it says about what the world is “made of” and what happens when you make a quantum-mechanical measurement of that world. Indeed, it’s so confusing and contradictory that you really need another rule so that you don’t complain when you start to think too deeply about it: “shut up and calculate”. A more modern approach might also discuss the many-worlds approach, and — my current favorite — the (of course) Bayesian ideas of QBism.

The students seemed pleased with the course as it is — at the end of the term, they have the chance to give us some feedback through our “Student On-Line Evaluation” system, and my marks have been pretty consistent. Of the 200 or so students in the class, only about 90 bother to give their evaluations, which is disappointingly few. But it’s enough (I hope) to get a feeling for what they thought.

So, most students Definitely/Mostly Agree with the good things, although it’s clear that our students are most disappointed in the feedback that they receive from us (this is a more general issue for us in Physics at Imperial and more generally, and which may partially explain why most of them are unwilling to feed back to us through this form).

But much more fun and occasionally revealing are the “free-text comments”. Given the numerical scores, it’s not too surprising that there were plenty of positive ones:

• Excellent lecturer - was enthusiastic and made you want to listen and learn well. Explained theory very well and clearly and showed he responded to suggestions on how to improve.

• Possibly the best lecturer of this term.

• Thanks for providing me with the knowledge and top level banter.

• One of my favourite lecturers so far, Jaffe was entertaining and cleary very knowledgeable. He was always open to answering questions, no matter how simple they may be, and gave plenty of opportunity for students to ask them during lectures. I found this highly beneficial. His lecturing style incorporates well the blackboards, projectors and speach and he finds a nice balance between them. He can be a little erratic sometimes, which can cause confusion (e.g. suddenly remembering that he forgot to write something on the board while talking about something else completely and not really explaining what he wrote to correct it), but this is only a minor fix. Overall VERY HAPPY with this lecturer!

But some were more mixed:

• One of the best, and funniest, lecturers I’ve had. However, there are some important conclusions which are non-intuitively derived from the mathematics, which would be made clearer if they were stated explicitly, e.g. by writing them on the board.

• I felt this was the first time I really got a strong qualitative grasp of quantum mechanics, which I certainly owe to Prof Jaffe’s awesome lectures. Sadly I can’t quite say the same about my theoretical grasp; I felt the final third of the course less accessible, particularly when tackling angular momentum. At times, I struggled to contextualise the maths on the board, especially when using new techniques or notation. I mostly managed to follow Prof Jaffe’s derivations and explanations, but struggled to understand the greater meaning. This could be improved on next year. Apart from that, I really enjoyed going to the lectures and thought Prof Jaffe did a great job!

• The course was inevitably very difficult to follow.

And several students explicitly commented on my attempts to get students to ask questions in as public a way as possible, so that everyone can benefit from the answers and — this really is true! — because there really are no embarrassing questions!

• Really good at explaining and very engaging. Can seem a little abrasive at times. People don’t like asking questions in lectures, and not really liking people to ask questions in private afterwards, it ultimately means that no questions really get answered. Also, not answering questions by email makes sense, but no one really uses the blackboard form, so again no one really gets any questions answered. Though the rationale behind not answering email questions makes sense, it does seem a little unnecessarily difficult.

• We are told not to ask questions privately so that everyone can learn from our doubts/misunderstandings, but I, amongst many people, don’t have the confidence to ask a question in front of 250 people during a lecture.

• Forcing people to ask questions in lectures or publically on a message board is inappropriate. I understand it makes less work for you, but many students do not have the confidence to ask so openly, you are discouraging them from clarifying their understanding.

Inevitably, some of the comments were contradictory:

• Would have been helpful to go through examples in lectures rather than going over the long-winded maths to derive equations/relationships that are already in the notes.

• Professor Jaffe is very good at explaining the material. I really enjoyed his lectures. It was good that the important mathematics was covered in the lectures, with the bulk of the algebra that did not contribute to understanding being left to the handouts. This ensured we did not get bogged down in unnecessary mathematics and that there was more emphasis on the physics. I liked how Professor Jaffe would sometimes guide us through the important physics behind the mathematics. That made sure I did not get lost in the maths. A great lecture course!

And also inevitably, some students wanted to know more about the exam:

• It is a difficult module, however well covered. The large amount of content (between lecture notes and handouts) is useful. Could you please identify what is examinable though as it is currently unclear and I would like to focus my time appropriately?

And one comment was particularly worrying (along with my seeming “a little abrasive at times”, above):

• The lecturer was really good in lectures. however, during office hours he was a bit arrogant and did not approach the student nicely, in contrast to the behaviour of all the other professors I have spoken to

If any of the students are reading this, and are willing to comment further on this, I’d love to know more — I definitely don’t want to seem (or be!) arrogant or abrasive.

But I’m happy to see that most students don’t seem to think so, and even happier to have learned that I’ve been nominated “multiple times” for Imperial’s Student Academic Choice Awards!

Finally, best of luck to my colleague Jonathan Pritchard, who will be taking over teaching the course next year.

[Update: The bug seems fixed in the latest version, 10.0.2.]

I am in my third year teaching a course in Quantum Mechanics, and we spend a lot of time working with a very simple system known as the harmonic oscillator — the physics of a pendulum, or a spring. In fact, the simple harmonic oscillator (SHO) is ubiquitous in almost all of physics, because we can often represent the behaviour of some system as approximately the motion of an SHO, with some corrections that we can calculate using a technique called perturbation theory.

It turns out that in order to describe the state of a quantum SHO, we need to work with the Gaussian function, essentially the combination exp(-y²/2), multiplied by another set of functions called Hermite polynomials. These latter functions are just, as the name says, polynomials, which means that they are just sums of terms like ayⁿ where a is some constant and n is 0, 1, 2, 3, … Now, one of the properties of the Gaussian function is that it dives to zero really fast as y gets far from zero, so fast that multiplying by any polynomial still goes to zero quickly. This, in turn, means that we can integrate polynomials, or the product of polynomials (which are just other, more complicated polynomials) multiplied by our Gaussian, and get nice (not infinite) answers.

Unfortunately, Wolfram Inc.’s Mathematica (the most recent version 10.0.1) disagrees:

The details depend on exactly which Hermite polynomials I pick — 7 and 16 fail, as shown, but some combinations give the correct answer, which is in fact zero unless the two numbers differ by just one. In fact, if you force Mathematica to split the calculation into separate integrals for each term, and add them up at the end, you get the right answer.

I’ve tried to report this to Wolfram, but haven’t heard back yet. Has anyone else experienced this?

Some time last year, Physics World magazine asked some of us to record videos discussing scientific topics in 100 seconds. Among others, I made one on cosmic inflation and another on what scientists can gain from blogging, which for some reason has just been posted to YouTube, and then tweeted about by FQXi (without which I would have forgotten the whole thing). There are a few other videos of me, although it turns out that there are lots of people called “Andrew Jaffe” on YouTube.

I’m posting this not (only) for the usual purposes of self-aggrandizement, but to force — or at least encourage — myself to actually do some more of that blogging which I claim is a good thing for us scientists. With any luck, you’ll be able to read about my experiences teaching last term, and the trip I’m about to take to observe at a telescope (a proper one, at the top of a high mountain, with a really big mirror).

[On a much more entertaining note, here’s a song from a former Imperial undergraduate recounting “A Brief History of the Universe”. Give it a listen!]

The academic year has begun, and I’m teaching our second-year Quantum Mechanics course again. I was pretty happy with last year’s version, and the students didn’t completely disagree.

This year, there have been a few changes to the structure of the course — although not as much to the content as I might have liked (“if it ain’t broke, don’t fix it”, although I’d still love to use more of the elegant Dirac notation and perhaps discuss quantum information a bit more). We’ve moved some of the material to the first year, so the students should already come into the course with at least some exposure to the famous Schrödinger Equation which describes the evolution of the quantum wave function. But of course all lecturers treat this material slightly differently, so I’ve tried to revisit some of that material in my own language, although perhaps a bit too quickly.

Perhaps more importantly, we’ve also changed the tutorial system. We used to attempt an imperfect rendition of the Oxbridge small-group tutorial system, but we’ve moved to something with larger groups and (we hope) a more consistent presentation of the material. We’re only on the second term with this new system, so the jury is still out, both in terms of the students’ reactions, and our own. Perhaps surprisingly, they do like the fact that there is more assessed (i.e., explicitly graded, counting towards the final mark in the course) material — coming from the US system, I would like to see yet more of this, while those brought up on the UK system prefer the final exam to carry most (ideally all!) the weight.

So far I’ve given three lectures, including a last-minute swap yesterday. The first lecture — mostly content-free — went pretty well, but I’m not too happy with my performance on the last two: I’ve made a mistake in each of the last two lectures. I’ve heard people say that the students don’t mind a few (corrected) mistakes; it humanises the teachers. But I suspect that the students would, on the whole, prefer less-human, more perfect, lecturing…

Yesterday, we were talking about a particle trapped in a finite potential well — that is, a particle confined to be in a box, but (because of the weirdness of quantum mechanics) with some probability of being found outside. That probability depends upon the energy of the particle, and because of the details of the way I defined that energy (starting at a negative number, instead of the more natural value of zero), I got confused about the signs of some of the quantities I was dealing with. I explained the concepts (I think) completely correctly, but with mistakes in the math behind them, the students (and me) got confused about the details. But many, many thanks to the students who kept pressing me on the issue and helped us puzzle out the problems.

Today’s mistake was less conceptual, but no less annoying — I wrote (and said) “cotangent” when I meant “tangent” (and vice versa). In my notes, this was all completely correct, but when you’re standing up in front of 200 or so students, sometimes you miss the detail on the page in front of you. Again, this was in some sense just a mathematical detail, but (as we always stress) without the right math, you can’t really understand the concepts. So, thanks to the students who saw that I was making a mistake, and my apologies to the whole class.

A couple of weeks I received the Student On-Line Evaluation (SOLE) results for my Quantum Mechanics course.

There were only two specific questions, rating each of the following from “Very Good” through “Poor” (there’s a “no response” off to the right, as well):

1. The structure and delivery of the teaching sessions
2. The content of this module

The numerical results (at right) were pretty good. Note that 114 students — about half — responded.

The rest of the results are free-form comments. With such a big class it’s very difficult to find a style of teaching that suits everyone. Hence, the comments showed a split between the students who enjoyed the very mathematical approach of the course and those who wanted more physical examples from the beginning (not that easy in the context of an axiomatic approach to quantum mechanics — but there are a few simple system like quantum dots that exhibit some of the properties of the simplest systems we study in class; it’s clear that these should be highlighted more than I have). Similarly, some students wanted a more step-by-step approach to the mathematics, whereas others would prefer just a sketch of the proofs on the board (“put the algebra in the notes and let students work through it”).

But one set of comments especially hit home. Here’s a good example:

Frankly, I think that Prof. Jaffe has the potential to be an outstanding lecturer, one which he wastes by not being properly prepared. Just showing up to lectures and writing down on the board what was in (the previous lecturer’s) notes without thinking much about it in advance results in time spent staring at notes and board which could otherwise have been used to face the audience and explain what it is we’re doing. Maybe that sounded harsh, but he really is very good and could be outstanding if he put a little more into preparing for lectures and didn’t stick to his notes quite so much… If you actually perform the calculations, and think about the various steps yourself, then it all happens in a way, and at a pace, which suits us as students and allows us to follow.

(OK, I picked one that made an effort to heap on some praise along with the criticism.) I have to admit that this point, repeated by several students, seemed right on, for at least some of the lectures. I did always make an effort to go over the notes in detail beforehand. But these were notes indeed written by the previous lecturer, and this gives a few problems. Yes, I probably wasn’t always careful enough to go over the details of the mathematics beforehand. So sometimes I did spend too much effort trying to puzzle out exactly what I wanted to say (some students also complained about the occasional mistakes I made on the board, perhaps related to this). But sometimes the problem is more subtle: I might not always want to explain the concepts in the same way as the previous lecturer — and sometimes I might only realise this when actually doing the explaining! Either of these can happen in any lecture, but the combination of teaching this course for the first time, and doing so from someone else’s notes, certainly made it worse.

Next year, things will at least be different: I’ll be teaching for the second time, and so have some idea of the pitfalls from this past year. Moreover, our department is making some significant changes to the overall structure of the curriculum, phasing out our system of tutorials and so-called classworks for a series of three medium-sized (20 student) group sessions each week. This is happening alongside some specific changes to the quantum mechanics curriculum, with more material in the first year (happening already). My course will be shortened by a full five lectures, but I suspect that this combination of changes will give me a bit more breathing room, as well as a few different ways to make sure the material gets said in different ways, appropriate for different students.

Further criticism, comments, ideas, etc., are always welcome.

A week ago, I finished my first time teaching our second-year course in quantum mechanics. After a bit of a taster in the first year, the class concentrates on the famous Schrödinger equation, which describes the properties of a particle under the influence of an external force. The simplest version of the equation is just This relates the so-called wave function, ψ, to what we know about the external forces governing its motion, encoded in the Hamiltonian operator, Ĥ. The wave function gives the probability (technically, the probability amplitude) for getting a particular result for any measurement: its position, its velocity, its energy, etc. (See also this excellent public work by our department’s artist-in-residence.)

Over the course of the term, the class builds up the machinery to predict the properties of the hydrogen atom, which is the canonical real-world system for which we need quantum mechanics to make predictions. This is certainly a sensible endpoint for the 30 lectures.

But it did somehow seem like a very old-fashioned way to teach the course. Even back in the 1980s when I first took a university quantum mechanics class, we learned things in a way more closely related to the way quantum mechanics is used by practicing physicists: the mathematical details of Hilbert spaces, path integrals, and Dirac Notation.

Today, an up-to-date quantum course would likely start from the perspective of quantum information, distilling quantum mechanics down to its simplest constituents: qbits, systems with just two possible states (instead of the infinite possibilities usually described by the wave function). The interactions become less important, superseded by the information carried by those states.

Really, it should be thought of as a full year-long course, and indeed much of the good stuff comes in the second term when the students take “Applications of Quantum Mechanics” in which they study those atoms in greater depth, learn about fermions and bosons and ultimately understand the structure of the periodic table of elements. Later on, they can take courses in the mathematical foundations of quantum mechanics, and, yes, on quantum information, quantum field theory and on the application of quantum physics to much bigger objects in “solid-state physics”.

Despite these structural questions, I was pretty pleased with the course overall: the entire two-hundred-plus students take it at the beginning of their second year, thirty lectures, ten ungraded problem sheets and seven in-class problems called “classworks”. Still to come: a short test right after New Year’s and the final exam in June. Because it was my first time giving these lectures, and because it’s such an integral part of our teaching, I stuck to to the same notes and problems as my recent predecessors (so many, many thanks to my colleagues Paul Dauncey and Danny Segal).

Once the students got over my funny foreign accent, bad board handwriting, and worse jokes, I think I was able to get across both the mathematics, the physical principles and, eventually, the underlying weirdness, of quantum physics. I kept to the standard Copenhagen Interpretation of quantum physics, in which we think of the aforementioned wavefunction as a real, physical thing, which evolves under that Schrödinger equation — except when we decide to make a measurement, at which point it undergoes what we call collapse, randomly and seemingly against causality: this was Einstein’s “spooky action at a distance” which seemed to indicate nature playing dice with our Universe, in contrast to the purely deterministic physics of Newton and Einstein’s own relativity. No one is satisfied with Copenhagen, although a more coherent replacement has yet to be found (I won’t enumerate the possibilities here, except to say that I find the proliferating multiverse of Everett’s Many-Worlds interpretation ontologically extravagant, and Chris Fuchs’ Quantum Bayesianism compelling but incomplete).

I am looking forward to getting this year’s SOLE results to find out for sure, but I think the students learned something, or at least enjoyed trying to, although the applause at the end of each lecture seemed somewhat tinged with British irony.

This week I received the results of the “Student On-Line Evaluations” for my cosmology course. As I wrote a few weeks ago, I thought that this, my fourth and final year teaching the course, had gone pretty well, and I was happy to see that the evaluations bore this out: 80% of the responses were “good” or “very good”, the remainder “satisfactory” (and no “poor” or “very poor”, I’m happy to say). I was disappointed that only 23 student (fewer than half of the total) registered their opinion on subjects like “The structure and delivery of the lectures” and “the interest and enthusiasm generated by the lecturer”.

The weakest spot was “The explanation of concepts given by the lecturer” with 5 for satisfactory, 11 for good and 7 for very good — I suppose this reflects the actual difficulty of some of the material. In the second half of the course I need to draw more heavily on concepts from particle physics and thermodynamics that undergraduate students may not have encountered before, concepts that are necessary in order to understand how the Universe evolved from its hot, dense and simple early state to today’s wonderfully complex mix of radiation, gas, galaxies, dark matter and dark energy. Without several days to devote to the nuclear physics of big-bang nucleosynthesis, or the even longer necessary to really explain the quantum field theory in curved space-time that would be necessary to get a quantitative understanding of the density perturbations produced by an early epoch of cosmic inflation, the best I can do is give a taste of these ideas.

And I really appreciated comments such as “Work with other lecturers to show them how it’s done”. So thanks to all of my students — and good luck on the exam in early June.

Somehow I’ve managed to forget my usual end-of-term post-mortem of the year’s lecturing. I think perhaps I’m only now recovering from 11 weeks of lectures, lab supervision, tutoring alongside a very busy time analysing Planck satellite data.

But a few weeks ago term ended, and I finished teaching my undergraduate cosmology course at Imperial, 27 lectures covering 14 billion years of physics. It was my fourth time teaching the class (I’ve talked about my experiences in previous years here, here, and here), but this will be the last time during this run. Our department doesn’t let us teach a course more than three or four years in a row, and I think that’s a wise policy. I think I’ve arrived at some very good ways of explaining concepts such as the curvature of space-time itself, and difficulties with our models like the 122-or-so-order-of-magnitude cosmological constant problem, but I also noticed that I wasn’t quite as excited as in previous years, working up from the experimentation of my first time through in 2009, putting it all on a firmer foundation — and writing up the lecture notes — in 2010, and refined over the last two years. This year’s teaching evaluations should come through soon, so I’ll have some feedback, and there are still about six weeks until the students’ understanding — and my explanations — are tested in the exam.

Next year, I’ve got the frankly daunting responsibility of teaching second-year quantum mechanics: 30 lectures, lots of problem sheets, in-class problems to work through, and of course the mindbending weirdness of the subject itself. I’d love to teach them Dirac’s very useful notation which unifies the physical concept of quantum states with the mathematical ideas of vectors, matrices and operators — and which is used by all actual practitioners from advanced undergraduates through working physicists. But I’m told that students find this an extra challenge rather than a simplification. Comments from teachers and students of quantum mechanics are welcome.

I’ve just finished another term, in fact the heaviest teaching load I’ve ever had at once: a twenty-six hour lecture course, three hours a week as one of several computer lab “demonstrators”, and another four hours or so per week in first-year student tutorials.

For those from outside of the Imperial system: our tutorials are small group meetings during which we go over a selection of the problem sheets handed out during the week in the lecture courses; here, like most of the UK, these are not explicitly marked, but instead the students get the solutions a week or so after they are handed out. The tutorial session is one of the few chances for any sort of discussion or feedback.

The tutorials can be fun and even challenging (but I’m glad I get to see the answers before the students). It is heartening to see the students trying — sometimes struggling — to really understand the problems. However, the fourth hour in a week going over the same problems can get repetitive; there aren’t that many different questions the students ask.

On the other hand, lab demonstrating doesn’t offer much intellectual at all. I have mostly supervised computer labs, which involves standing around while the students work their way through a “script”, writing programs and (we hope) learning about programming. I admit that I don’t think this is a particularly efficient use of my time: although considerable overall high-level organization is needed, the labs themselves could be (and indeed are, partially) monitored by graduate students. Unfortunately, they don’t get more than beer money for their trouble — and postdocs don’t get paid at all.

The best part of undergraduate teaching for me, though, is lecturing. When it goes well, it can be a remarkably effective way of communicating. Of course, it doesn’t always go well. Sometimes I’m not as well-prepared as I would like, or sometimes I don’t even understand the material as well as I need to. Sometimes the students don’t have the background that I thought they did. And sometimes the material is just hard, too hard to really get the first time through. Even problem sheets and studying for exams isn’t always enough: I certainly admit that I didn’t really understand much of the material that I now use every day until I was in graduate school, applying it in the course of my research. And some stuff I didn’t understand until I had to teach it (which implies that there is plenty of physics that I still don’t understand, so still much more to learn).

This term’s Cosmology course felt pretty good: after three years not only do I understand the material, but also I understand something about how to explain it to not-yet-expert upper-level physics students. The downside of this is that my explanations get a bit longer every year, so it gets harder and harder to squeeze in the most exciting material which inevitably has to come at the end, building on the foundation of the rest of the course.

This year, the Physics Department has an artist-in-residence, Geraldine Cox. Among her many other cool projects, she has been lurking in the back of our lecture theatres, sketching furiously. Many thanks to her for these pictures of me at the blackboard, in one of my favorite striped shirts:

(The graph on the upper left is labeled “Do we live in a special time?” — We seem to live at a time labeled by the vertical line, just as the Universe is transitioning from being mostly made of “matter” — the middle of the three plateaus in the graph — to mostly something very like Einstein’s cosmological constant, or the so-called “Dark Energy” — the rightmost plateau, which may go on infinitely far to the right. So we might have expected to find ourselves near a plateau rather than a one of the few times in between. This is an anthropic argument, and must be treated with care.)

As always, I welcome feedback, anonymous or otherwise, from any of my students on this course or any other. (When I asked for some comments a few weeks into the term, the most amusing came from the student who praised my voice and asked if I was a singer — which doesn’t jibe with the other, less positive, comments on my American accent….)

Finally, today was one of the high points of post-graduate teaching: one of my students, Jude Bowyer, passed his PhD viva with his thesis, Local Methods for the Cosmic Microwave Background. Well done to the soon-to-be Dr. Bowyer!

We get most of the official feedback on our teaching through a mechanism called SOLE — Student On-Line Evaluations — which asks a bunch of questions on the typical “Very Poor” … “Very Good” scale. I’ve written about my results before — they are useful, and there is even some space for ad-hoc comments, but the questionnaire format is a bit antiseptic.

On some occasions, however, students make an extra effort to let you know how they feel. Last year, I received an anonymous paper letter in the old-fashioned snail-mail post from a student in my cosmology course which said, among other statements, that I should “show appropriate humility and shame by not teaching any undergraduate courses at all this coming year.” Well, that year has come and gone, and I was not absolved of teaching responsibilities, so I soldiered on.

Today, I received another anonymous letter, from a most assuredly different student, who said that this year’s cosmology course “is without a doubt the most interesting undergraduate course I have taken at Imperial.” This would have left me ecstatic, except that this otherwise well-intentioned and obviously smart student managed to put the envelope in the mailbox with insufficient postage, which meant that I had to trudge across to the local mail facility and pay the missing 10p, along with a full £1 fee/fine! (If the author of the letter happens to read this, please consider a donation of £1.10 plus appropriate interest to the charity of your choice!).

It would be self-serving of me to make too much of this, beyond noting that, although I did make some significant changes in this year’s course, these letters more likely indicate the very different reactions that a given course can engender, rather than a vast improvement in my teaching.

My apologies to both students if they would have preferred I not quote them on-line, but such is the price of anonymity.

My colleagues and I spend what is probably an inordinate amount of time complaining about the occasional lapses of the basic skills of our students, their inability to take notes, their obsession with marks and what’s going to be on the exams. Because, like everyone else, we like to complain.

But pretty often I get the chance to see them at their best. In the Physics department at Imperial, we interview students who are on the boundaries between final “degree classifications”, the British system of awarding degrees as First Class, 2.1, 2.2, etc. Last week, I was on the panel for this year’s cohort. And it was a pleasure to sit in front of a few of our students and watch them, in real time, thinking like physicists. Of course this means making the occasional mistake, but it also means that delicious “aha!” moment when they figure something out and (this is the best part) they know that they have, whether it’s finding a sign error in their derivation of the motion of a pendulum, or a thought experiment explaining why Einstein’s relativity makes sense.

For the interviews, I was paired with one of our external examiners, UCL particle physicist and fellow-blogger Jon Butterworth. On the same day as our interview, the Guardian published Simon Jenkins’ latest in a series of risible anti-science screeds, and Jon decided to take him to task neither with reasoned argumentation nor with a counter-polemic, but with parody. As with many great ideas on the internet, this one got picked up and built upon, so that the Guardian, to its credit, eventually gave Jon his own space to reply. Jenkins likely thinks we’re producing too many scientists (Imperial only trains scientists, doctors, and engineers, after all!) but I hope that Jon was pleased with the ones he saw.

So my congratulations to this year’s graduating students, and the best of luck to them whatever they go on to do. Pace Jenkins, the world needs more well-trained scientists like them, not fewer.

I just received the SOLE (Student On-Line Evaluation) results for my cosmology course. Overall, I was pleased: averaging between “good” and “very good” for “the structure and organisation of the lectures”, “the approachability of” and “the interest and enthusiasm generated by” the lecturer, as well as for “the support materials” (my lecture notes), although only “good” for “the explanation of concepts given by the lecture”, with an evenly-dispersed smattering of “poor” and “very good” —- you can’t please all of the people all of the time. That last, of course, is the crux of any course, and especially one with as many seemingly weird concepts as cosmology (the big bang itself, inflation, baryogenesis, …). So perhaps a bit of confusion is to be expected. Still, must try harder.

The specific written comments were mostly positive (it’s clear the students really liked those typed-up lecture notes), but I remain puzzled by comments like this: “Sometimes 2-3 mins of explanation (which is generally good) is reduced to one or two words on the board which are difficult to understand when going over notes later.” Indeed — I expect the student to take his or her own notes on those “2-3 mins of explanation”, if they were useful and interesting. But many of the comments were quite helpful, about the pace of the lectures, the prerequisites for the course, and, especially, the order in which I use the six sliding blackboards in the classroom.

So, thanks to the students for the feedback (and good luck on the exam…).

I’ve just finished teaching my eleven-week winter-term Cosmology course at Imperial. Like all lecturing, it was exhilerating, and exhausting. And like usual, I am somewhat embarrassed to say that I think I understand the subject better than when I started out. (I hope that the students can say some of the same things. Comments from them welcome, either way.)

It’s my second year, and I think I am slowly getting the hang of it. It’s hard to fit all of the interesting and up-to-date research in cosmology into 26 lectures, starting from scratch. This time I spent a little more time in the early lectures trying to give a heuristic explanation of some of the more advanced background topics, like the interpretation of the metric in Einstein’s General Relativity, and the physics behind the transition of the Universe from and ionized plasma to a neutral gas.

In a way, much of this was prelude to some of the most most exciting research in modern cosmology, the growth of large-scale structure from its first seeds into the pattern of galaxies we observe in the Universe today. Explaining this requires a lot of background: early-Universe thermodynamics and why the Universe started out hot, dense, and dominated by radiation; enough relativity to motivate how structure grows differently on large and small scales; and the generation of the initial conditions for structure, or at least our best current idea, inflation, which takes initial quantum randomness and blows it up to the size of the observable Universe (and solves quite a few other problems besides). All of this, and the background required even to get to these topics, barely fit into those 26 lectures (and I admit I was a little rushed toward the end…). And it was even harder to compress them down into four hours of postgraduate lectures.

Alongside this, I decided that none of the available textbooks had quite the right point of view for my discussion, at least not at the undergraduate level I was aiming for (and there are some very good textbooks out there, including Andrew Liddle, An Introduction to Modern Cosmology; Michael Rowan-Robinson, Cosmology; and Peter Schneider, Extragalactic Astronomy and Cosmology: An Introduction). So I also wrote a hundred or so pages of notes (which are available from my Imperial website, if you’re interested in a crash course).

I’m often puzzled by exactly what students want from the 26 hours of lectures themselves. Many, it seems to me, would prefer to merely transcribe my board notes without having to pay close attention to what I am actually saying; perhaps note-taking is not a skill that students perfect at school nowadays. I hope at least that those written notes make it a bit easier to both listen and think during the lectures. (Again, constructive criticism is more than welcome.)

This week I’ll be giving a review (just half an hour!) of cosmology at the IOP’s High-Energy and Astroparticle Physics 2010 meeting. And then I get to indulge in some of my hobbies, like doing scientific research.

The students in my cosmology course had their exam last week.

There’s no doubt that they found the course tough this year — it was my first time teaching it, and I departed pretty significantly from the previous syllabus. Classically, cosmology was the study of the overall “world model” — the few parameters that describe the overall contents and geometry of the Universe, and courses have usually just concentrated upon the enumeration of these different models. But over the last decade or two we’ve narrowed down to what is becoming a standard model, and we cosmologists have begun to concentrate upon the growth of structure: the galaxies and clusters of galaxies that make the Universe interesting, not least because we need them for our own existence. Moreover, that structure directly teaches us about those contents which make them up and the geometry in which they are embedded. I wanted to give the students a chance to learn about the physics behind this large-scale structure, not traditionally at the heart of undergraduate cosmology courses.

Unfortunately, this also meant that the traditional undergraduate textbooks didn’t cover this material at the depth I needed, and so the students were forced to rely on my lectures and the notes they took there (and eventually a scanned and difficult-to-read copy of my written notes).

I sensed a bit of worry in the increasing numbers of questions from students in the weeks before the exam, and heard rumors of worries. But the day of the exam rolled around, and indeed when I re-read the questions it didn’t seem too bad, although there were some grumbles evident in the examination room.

Later I learned that there was a “record-breaking” number of complaints about the exam. I gather it was perceived to be difficult and unfamiliar.

So marking the exams in the past week, I was happy to find that the students performed just fine: the right “bell-shaped curve”, the correct mean, etc. (Of course I should point out that all results are subject to final approval by the Physics Department Examiners Committee.) I admit some puzzlement, therefore, about the reaction to the exam. Were they worried because the questions were different from those they had seen before? That, I admit, was the point of the exam — to test if they have actually learned something. Which, I am happy to point out, it seems that they had!

There was one question that almost all students got wrong, however. I asked about the “Cosmological Constant Problem” and whether it could be solved by the theory of cosmic inflation. The Cosmological Constant is a number that appears in General Relativity, and, although we can’t predict it for certain, we are pretty sure that if it’s not strictly zero, in most theories we would estimate that it ought to have a value something like 10¹²⁰ (that is 1 followed by 120 zeros!) times greater than that observed in the Universe today. I suppose I didn’t write on the board the words “Cosmological Constant Problem” next to that extraordinarily large number. (In the end, I reapportioned the small number of marks associated with that problem.) Inflation involves something very much like the cosmological constant, but occurring in the very early Universe — so inflation can’t help us with the 120 zeroes, alas.

Next year, I’ll be sure to spell all of this out, but I’ll also show this movie of my old grad-school friend, collaborator, and colleague Lloyd Knox, now a professor at the University of California, Davis, singing this song about Dark Energy (of which the cosmological constant is a particular manifestation):

The scientifically-accurate lyrics are sung to the tune of Neutral Milk Hotel’s “In the Aeroplane over the Sea”.

Finally, I’d welcome comments on the course or the exam, anonymous or otherwise, from any students who may come across this post.

Just a quick apology for the lack of words appearing on the page here lately. In addition to planning for the upcoming launch of the Planck Satellite, I’ve been swamped with teaching my first-ever full-length undergraduate cosmology course. It’s lots of fun, but the biggest challenge is just systematizing this whole body of knowledge that I am supposed to already know so well. Like most scientists, I don’t quite want to take the information directly from someone else’s textbook (although there are quite a few good ones at the right level, notably Rowan-Robinson’s Cosmology and Liddle’s An Introduction to Modern Cosmology) so I am trying to put it all together in a way that fits my way of thinking about it (and, I hope, my students’). But probably, this is just my version of Blake’s “I must create a system or be enslaved by another man’s” (of course I am purposefully ignoring his next line from Jerusalem, the very wrongheaded miscomprehension of science, “I will not reason and compare: my business is to create”).

P.S. If you’re a student, feel free to comment here (anonymously, if you’d prefer) or on our favorite e-learning system at Imperial).

I gave the last lecture in my Fourier class today. I think the course started alright, but I seemed to be losing the students for the last few lectures (not helped by the fact that three of the ten hours of the course were 5-6pm on Fridays, but a good workman doesn’t blame his tools…). Trying to get some immediate feedback (although still too late to do this year’s cohort any good) I handed out sheets of paper and asked them to write down, anonymously, something they understood, something they didn’t understand (a request greeted with an uncomfortably loud giggle) and any other comments. Although I only got about a dozen responses, there were some commonalities: indeed the first half of the course (Fourier Series) seemed well-understood, and the second half (Fourier Transforms) much less so; I should try to include more examples of the use of the methods (which will require changing the syllabus a bit), and more explanation of what the mathematics mean.

But one remark stood out: “Your handwriting is really bad. And you smell. Sorry.” Further comments — perhaps from readers who might have some knowledge of the subject — welcome.

Too busy for much blogging for the next few weeks. In the meantime:

First, my grad students: Goodbye to one just finishing, hello to my new one, congratulations to the one who just transferred to official PhD-student status, and, finally, to the one staying on as a postdoc! I’m excited that I’m able to still work with all of them on various projects, all concentrating on understanding the state of the Universe at its very earliest moments.

Second, to the undergrads: I hope that my teaching is going better than last year.

Third, the new record from my homestate boy, Bruce Springsteen, is better than you might expect from a still-left-wing pro-Union old-fashioned rock’n’roller. And “Girls in Their Summer Clothes” sounds like it could have been written and performed by Stephen Merritt and his Magnetic Fields (this is intended as a huge compliment!).

Next time, an update on the odd combination of Philip Glass’s versions of Leonard Cohen’s poems. And maybe that 16-solar-mass Black Hole (technical paper here). Conversely, I am unlikely to usefully comment on race relations as seen through the eyes James Watson or Sasha Frere-Jones. But the rest of the blogosphere has those well in hand.

Well, Summer break is over, the days are surprisingly short already, the sky is rarely clear, and the students are back.

Warm-weather highlights ranged from the intellectual pleasures of my visits to Portugal and Chicago, to the rather more visceral ones of Sonic Youth’s Daydream Nation at the Roundhouse, The Hold Steady at Shepherds Bush, and the diminutive Prince somehow filling up the massive O2 arena formerly known as The Dome. I also let my PhD Alma Mater pimp me to promote themselves, but I got lunch with the writer of Freakonomics out of it, and a surprisingly wonderful cocktail party at the residence of the used-car-salesman-cum-American Ambassador in London.

But now, back to real work. I’ve spent the day in front of my computer, more even than usual, dealing with the repercussions of our having decided to give the returning second-year students a test to get them to flex their mathematical muscles in preparation for the year — during which they’re liable to see lots of new mathematical and physical concepts for the very first time. We’ve decided to run the test through our online learning system, and, unfortunately, new technology almost always has its quirks: we had some fires to quench in the early hours of the day, but things seem to be running smoothly now. My proverbial and actual fingers are all crossed.

I’ll be covering quite a few of those new concepts in my second attempt at teaching our course on Fourier Methods; it didn’t go very well, last time, I must admit, and I’m hoping that the changes I’ve made in both the form and the content of the course — and the test they’re taking now — will make it better for the students. Feedback, positive, negative, or even ranting, is appreciated, from any present or past students.

I’ve just finished my lectures for the course in Fourier Series and Fourier Transforms that I’ve been teaching.

It was an intense, exhilarating and ultimately frustrating three-and-a-half week adventure —and I fear that it didn’t go very well. It’s tough material, probably the first stuff that these second-year students have seen in their undergraduate career that’s really brand new to them. And, of course, this was my first time teaching it so our combined inexperience didn’t exactly presage a “positive learning outcome”.

What did I learn, then?

• Precision counts: I made my fair share of mistakes, mostly just typos, but those are easy for me to correct or even ignore, much harder for the 180 other people in the room who don’t already understand the material.
• Organization counts: actually, my lectures were highly structured, but I don’t think that always came through as I spoke. Explicit (numbered sections, bullet points, real sentences) is better than implicit.
• Preparation counts: In principle all of us lecturers know what the student have already learned, but just because something has been on on a syllabus doesn’t mean they really understand. Particularly with math, I think we often expect a level of facility that comes with years and years of practice doing integrals, solving equations, getting used to unfamiliar notation, that the students don’t yet have. (Needless to say, we’re usually convinced that things were better when we were in their place, but I’m not always so sure, as we look back with our rose-tinted shades.)

Still, I did some things right. The students may disagree, but I think I actually did a reasonable job at explaining the material in a way that isn’t just copying from the books. Perhaps that’s why my lecture notes seem to be more popular than the lectures themselves. And at least my loud Yankee voice carries to the back of the room.

Feedback is, of course, welcome.

p.s. On a more amusing note (purposely buried down here, free of links), it looks like Imperial Astrophysics is going to be getting a very special new (-ish) graduate student soon.

Today I started teaching my first real lecture course (as pointed out in the comments, the link is only accessible within the Imperal network).

I am teaching the second-year physics students mathematical techniques of Fourier Series and Fourier Transforms — this is the theorem that you can represent any function as a sum of so-called sinusoidal waves. That bit I think I explained all right. But then we had to start getting down into the mathematical details. Unfortunately, I think I lost them somewhere trying to make the analogy between vectors (i.e., arrows in space) and functions; you can describe a vector by giving its value in three perpendicular directions (x, y, z, for example), just like you can describe a function f(t) by giving its value at each value of t. A full set of these directions (x, y, z in the case of spatial vectors, or the individual values of t for the function) is called a basis. But we can rotate our vector to describe it any basis that is convenient.

The idea behind Fourier Series is that there is a specific basis made of sine and cosine waves — and expanding our function in this basis lets us understand things like sound and light in terms of frequency: light as a mixture of colors or sound as a mixture of pitches. For many problems in physics, these mixtures (with the somewhat more technical name of “linear superpositions”) are described by very simple formulae. Indeed, in addition to his laws of motion, Isaac Newton is famous for the first description of light this way (although he didn’t have the mathematical technology that Joseph Fourier would only develop in the 19th Century).

Indeed, there are some mathematical formulae behind all of this — not too complicated technically, but I’m not sure I was able to get the concepts behind them through to the students. It’s hard to calibrate to exactly what the students already know (which may not be the same as what they’ve already seen in their coursework!). Also, I worry that I may have drowned them in a sea of notation without actually explaining what I meant in quite enough words.

(In the unlikely event that any of Imperial’s second-year students are reading this, feel free to leave an anonymous comment and let me know what you thought!)