How do you set yourself apart when studying theory?

The idea of doing extra work in an academic setting is probably nothing new to you. Whether it be to put something extra on your CV, personal skill development and expansion of knowledge etc. etc. there is no doubt that if you put in more work you'll get more out (how much more admittedly can vary).

So whatever the stage you're at in your degree, what 'extra' things can you do? Often it is hard when studying theoretical physics to identify these, they simply aren't as apparent as for experimentalists or other scientists generally (I think). Prospective theorists are, at first glance, in a similar predicament to mathematicians. But over my degree I learned that there is plenty you can do, somethings big and somethings small, to boost your prospects in theory.

Disclaimer: As always, this list is not exhaustive but includes all the major activities I've seen students undertake to enhance their opportunities.


Easier:


Do the optional problems:
Some people need not be told this, plenty of physicists are academic masochists by nature! But plenty of us (myself included) have periods of time where we neglect to push ourselves to do the harder optional problems at the end of a problem sheet or those mentioned in lecture. Try and work through this if you can, sometimes time restraints come into play but if you have the time do your best to attempt optional problems, they often reveal a lot more about the subject than the standard tasks.

Investigate problems that interest you:
This need not be solely related to your courses, of course if your lecturer mentions something and you want to investigate and play around please do! But sometimes interesting topics arise completely outside of university. Time for a personal example.

I play the electric guitar, the part of the guitar where the frets are fitted is called the fingerboard and on electric guitars it is 'radiused' (i.e. it has a curvature). Different electric guitars have different radii, one might follow a circle with a 9.5 inch radius (Fender style) and another a 12 inch (Gibson style). A lot of musicians talk about how different radii feel, but I was interested in an actual numerical comparison. So I used Mathematica to plot various radii aligning a point on the circumference of the radii. Whilst this was a nice comparative diagram, it isn't very numerical so I compared the difference in distance between a flat fretboard and the surface of a given radius fretboard at the edge of the a standard Fender guitar neck. In doing so I was able to express this distance as a function of the radius, illuminating me as to 'how flat' certain radii actually are...

Yes I did actually do this in my spare time, that is something I might do on an afternoon and as you might be able to tell... I really enjoyed it. It was also great practise for Mathematica and some problem solving. So if you ask a question (or someone you know does) and the answer isn't immediately apparent, try and work out an answer!

READ!
You knew it was coming and here it is. But I don't mean trawl through thousands of pages of dry textbook material. First lets identify 'useful things you can read':

• Textbooks
• Journal Articles
• Popular Science Books
• Online articles (e.g. Wikipedia)

These are good for different things. If your lecturer mentions something specific in class that interests you, a textbook might suit. If they mention a piece of research that catches your ear, go read the Journal Article! What if it's too high level? Well maybe a PhysicsWorld article would be a better starting point. If you're in first year the particle physics behind dark matter research is not likely to be accessible for at that point. But a popular science book could provide some valuable conceptual insight that would prepare you for studying the real physics behind the ideas! Huge pdf's are also available, like the entire Feynman lectures which cost over £100 for a physical copy. Ultimately all these sources can benefit you, no matter what stage of studying. The more information you can absorb the better!

Watch/listen to lectures and science communicators:

YouTube is an established learning platform, with an enormous wealth of material that can benefit your studies available for free! This is also something you can do whilst doing other things, useful to keep your mind from rusting up if you need a break from the more intense activities in physics.

Many universities have published recordings of their lecture courses, i.e. Stanford, which are complete lecture courses on subjects like general relativity. There are also historic lectures like recordings of Richard Feynman, which are still very insightful and can often aid your conceptual outlook on problem solving. Public lectures are also useful if you haven't really traversed a subject yet, providing a conceptual grounding for you to work from.

Popular physics/maths channels are also great, I imagine most of you follow at least some of the following: 3Blue1Brown, Domain of Science (whose map series I love), MinutePhysics, Numberphile, Sixty Symbols, Kurzgesagt - In A Nutshell and I'm sure there are many many more! Some of these offer nice introductory reminders and inspiration with nice graphics (e.g. Kurzgesagt) and others offer higher level content (e.g. 3Blue1Brown).

Talk with your colleagues and lecturers:

If there's one thing I regret about how I handled my degree it's the fact I didn't engage with fellow theory students or try to talk to my lecturers more. The students who did clearly benefited from it and I think it had a very positive effect on their academic performance. This not only exposes you to new ideas but the networking is invaluable, giving you sources of advice to turn especially if you develop a good working relationship with lecturers.

Harder:

An industrial placement scheme:

Many university physics departments have specific placement schemes that offer tailored industry experience. As an aspiring theorist it is understandably tempting to dismiss this as a waste of time, with it being so different to theoretical physics academia. But some placements offer experiences relevant to theoretical physics skills. Although I ended up doing something different I was planning on applying to a data fitting placement (in a solid state physics setting) that would have given me practise with programming and function manipulation etc. These kind of placements usually revolve around programming so make sure you're up to speed on that.

A large scale research placement scheme:

Now this is HARD. The classic placement is the CERN final year 'internship' but plenty of people go to Japan, America, South Korea etc. Usually placements are available on experiments, particular in particle physics, but there can be analysis opportunities at experiments if you're willing to dig. You have to accept with these placements that the chances are you won't really be doing 'theory'. But that doesn't mean they can't do great things for you, plus they are often well funded.

A research placement with a university academic:

Sometimes universities run a formal scheme for this, others don't. This could be at your own university or at another and like large scale placements they are very competitive. For a theorist this is often the best route because university academics are more willing to let students pursue a theoretical topic. I was lucky enough to start my Bachelors thesis early in the form of a summer research placement. A stereotypical example is the UCL particle physics placement scheme that assigns you to a UCL academic to undertake a research project. But beware, these placements are not always funded and if they are they are not usually funded as well as the previous two.

Note: You can do more than one of these! Experimentalists often do an industrial placement in their 2nd year and a research placement in their 3rd year.

I hope that's given you some ideas for some things to do alongside your regular studies!

  

Topics to revise before you start or whilst starting your physics degree

Some people may have already started their courses but plenty haven't and this really applies to your whole first year...

You'll notice plenty of these are maths topics and yes, you will spend a lot of your time doing maths! No matter your specific interests in physics all these topics will be useful to you. As always, this list is not exhaustive. I've given a brief description of why I think its useful to revise a give topic but this is more of a list than an article.

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You'd be lucky to go a lectures in physics without using a sizeable amount of calculus. For differentiation have the chain and product rules easily deploy-able, quotient rule is less common but never hurts to be prepared. Have integration by parts and some common substitutions in your head as well. Physicists often memorise standard results, usually e.g. for trigonometric functions. You should have the basic trig. functions results memorised, hyperbolic trig. functions are something a number of students haven't covered before so don't worry about those (yet).

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These are also very useful and crop up all the time in physics. Its fair to say that different A-level specifications cover different topics in differential equations and to different levels. But revising anything you've covered regarding differential equations would be very helpful for your coming studies.

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In A-level physics they really don't convey to you quite how important SHM/SHO is for so many problems you'll look at in your degree. You'll study this example a lot more and link it to differential equations in your degree. But having a really strong understanding of the material you covered at A-level on SHO will definitely come in useful.

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Yes, although not circuit theory so much. And certainly not in the guise of the above Lagrangian... The most important thing is your understanding of electric and magnetic fields and how the combined field (electromagnetic field) effects systems like free charged particles. You'll probably study the basics of classical electrodynamics in your first year and a strong conceptual basis will make this a lot easier.

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Like can link into electromagnetism. Understanding frequency, wavelength, amplitude and such is very important. Knowing about photons and the consequences of the photo electric effects (some concepts in quantum mechanics basics can help too) will also come in useful. The de Brogile wavelength and associated foundations of quantum mechanics will be useful later as well.

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You knew you'd need it. A classical mechanics module will inevitably come up in your first term, it will work up from where you left of at A-level. Some courses revise the infamous 'SUVAT' equations others won't. My advice is to treat this like calculus, its really bread and butter stuff you need to have it at your command. Rotational mechanics will be expanded on significantly so make sure you are good with the basics you did at A-level. Newtonian gravity will also come up.

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Your understanding of vectors may be from a trigonometric point of view or a column vector point of view. Both will be useful, vectors are another key piece of mathematics that physicists use all the time and you will only use them more as you progress through your course.

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Ah you thought you'd be leaving this behind and getting straight to string theory... not yet. You'll study classical matter theory at some point in your first two years (likely your first), ideal gases will be featuring on a regular basis. Any other material you covered relating to solids, liquids and gases will probably be useful too.

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Yep, I hate them but labs are a part of physics degrees (most of them anyway). The experiments you do are often very different to A-level but your ability to work with data is very transferable. Understanding errors, fitting data, interpreting equations in a graphical context and all that stuff is all going to come in useful. More formal statistics is also going to be important, mapping standard deviations (a basic example) are something you'll use all the time (I know to some other sciences the idea of SDs being more advanced is laughable but trust me... many physics students arrive thinking they won't need stats). I'd also encourage you to learn some coding, Python is a common language in physics, I wish I had...

Things that you won't actually need...

You might be saddened to here that you won't need material from the following areas (at least not immediately):

• Particle physics (typically 3rd year)
• Nuclear physics (typically 2nd year)
• Astrophysics (across 2nd/3rd year, sometimes a bit in 1st year)

You'll be glad to here that most courses cover some basic quantum mechanics and special relativity in the first year. These are the modern topics most students look forward to, but for my money the more classical topics can be just as much fun!

If you haven't covered some of the above topics in great detail don't worry, everyone goes into university knowing some stuff others don't and not knowing stuff others do. The first year is designed to get everyone on a level playing field, then the meat mincer of second year starts! I reckon the top three most important are: Calculus, Classical Mechanics and Statistics. The others you could pickup along the way but a basic understanding of these is key!

Can you have a social life whilst studying physics?

This might seem like a more light hearted topic in comparison to my other articles but its a serious subject worth consideration no matter what stage of studies you're at. Whether you're just starting or in a final year, so called 'work-life balance' is important. I'll confess that I hate the term 'work-life' because it implies that work is bad and I hope that most university students enjoy their studies. But academic study is hard/stressful and engaging in social activities and past-times is not only fun and enjoyable but also stress relieving!

How do you find a right balance for you? How do you deal with the pressures from either side? Hopefully I can provide some answers.

Disclaimer: Inevitably my own approach to this has an effect on how I answer these questions, nevertheless I'll try to answer as objectively as I can. But you should probably know I'm not a very social person (surprise surprise) and whilst I tend to be reasonably flexible with my work schedule in my last academic year I almost always handed in problem sets a good few days before deadlines. Not everyone does it that way and with good reason, different things work for different people.

Can I really afford to spend time on things outside of physics?

Yes of course you can! There is often a perception that most successful physicists spent all their time doing nothing but study, to my knowledge that is certainly not the case (though they probably spent a lot of time on physics).

I'm not going to reel off all the research that thousands of articles have talked about regarding how down-time and certain types of activities can really boost your productivity. Instead I'll give some examples of some of the things successful students in my cohort did on a regular basis outside of physics:

• A number of them regularly went swimming multiple times a week with the college club. This was particularly beneficial for them as they had a structured way to socialise outside of lectures, I noticed it strengthened their friendships and it made them happy! Most people participated in some kind of sport, some of them played a role in running sports clubs.
• They took part in physics society social events, including many of the top of the class students. Events included pub crawls and bowling nights. This gave people a chance to let off some steam and converse about non-physics stuff, this usually had a good impact on people provided they didn't get absolutely plastered.
• I myself and I think a few others managed to spend a significant amount of time a week practising an instrument, I actually managed to be an instrumental teacher (part-time) for about 2 years over the course of my degree. I found this to be a very good relaxation tool whilst still feeling like I was progressing at something, I imagine the results would be similar for any more technical activity like (sorry to be stereotypical) playing chess or something more craft based if you can do that in your uni accommodation.
• Plenty of people were members of societies, I know at least one person wrote a number of physics articles for the university magazine for example. So its certainly not impossible to have pretty serious commitments outside of your studies.

Not only can you spend time away from physics but my experience (and research) points towards it being very important. I think the benefits of exercise cannot be ignored but if you don't want to go to the gym I really do sympathise with you, I hate gyms. But if you can find a sports class with a comfortable environment or even if you just do a bit of exercise in the privacy of your own accommodation I think you'll reap the benefits.

Humans are also fundamentally social beings, this is something that stereotypically students of sciences grapple with more than others I think, particularly physicists. The fact is that social interaction is crucial to your health, both physical and mental, that is under no doubt whatsoever. Keeping yourself healthy maximises your productivity and effectiveness when working. You'll find that if you work whilst in a bad mental state you are likely to perpetuate it, as you're unlikely to make much progress for the amount of effort you'll feel like you're putting in. 

There has been a lot in the news recently about student mental health and the statistics regarding suicide rates in the student population. It is more apparent than ever that we need to look after our minds whilst we undertake this tough but (hopefully) rewarding journey. Social interaction is the cornerstone of this and taking part in more organised events as well as spending time casually with friends is very important for any student.

On a less serious note, I think its important not to let study suppress your other hobbies/interests. Keep doing the sports you've been pursuing, same goes for any hobbies like instruments, crafts etc. I did reasonably well in my degree and I still managed to practise guitar and listen to music, play Skyrim, watch films/TV and spend a good amount of time cooking!

So now I've convinced you spending time away from physics is good, I now have to reign it in and convince you that you must be careful how much time you spend away from it...

I want to be a physicist but I still want to 'live'

My first answer to that question is: if you want to be a physicist you should live physics. But that's kind of a cheap answer so for those unsatisfied let me elaborate. Having spent three years doing my degree I've seen people change from having dreams of working in physics to not really caring so much. And there's nothing wrong with that, but sometimes the reason for that change was valid, other times it wasn't. If after studying the subject for such a long time you become dis-interested fair enough, but for some it was a case of their grades dropped because they didn't dedicate enough time to their studies and they saw that as them not 'being right for physics'.

Now I'm not judging people with drops in grades, some people get them for legitimate reasons (I've been there). But I'd be lying if I didn't say that some people get in that situation because ultimately they didn't put the time in. There's no 'I'm just not that smart' card you can pull here in my opinion, if you want the grade you have to put the time in. That amount of time is different for different people, I know for me that's usually longer than others! 

The fact is you get one shot at your degree, sure there's opportunities to retake a year etc. but that can cause serious problems with regards to academic record and whilst again this can happen for very legitimate reasons it is best avoided. Here's a couple of examples of ways I've seen people distracted from their studies to their detriment:

• Going out too much: You knew it was coming, it applies a lot of students. The fact is spending multiple hours in the late-evening/early-morning drinking several times a week isn't going to do your studies any good. Going out once our twice a week seemed not to cause people too much trouble but I tended to notice that when people did three or more heavy nights in the week the would have serious problems getting multiple problem sets in on time. What I can't escape is that the top of the class students went out once a week at most. I'd attribute a lot of my successes in my degree to the fact that I never go out drinking! But all in moderation, its about taking a serious look at whether your studies are being impacted by the amount you are going out (sometimes people find this difficult to assess though...)
• Devoting too much time to sports: I saw this happen to at least a couple of people. This was due to either being part of running a club or being involved in competitive matches. The key thing in both situations is to ensure that when you get into it there needs to be an escape route you can take if its impacting your studies. You MUST put your degree first. If you can't do that, that might suggest something about how much interest you actually have in the subject. It's fine if your passion for the subject is dead and gone but at least be ready to put some damage control in place so you can still come out with a degree.
• Procrastination: Whilst I've never experienced the first two I think this one can affect all of us. This often goes in line with your mental health, many of us when feeling down will occupy ourselves with unproductive and non-beneficial tasks. Now a bit of procrastination (a bit) has shown to be good, but it's important to keep it in check. Some use schedules to tackle this, that doesn't work for me so I simply monitor what I'm doing and whether I'm on track for meeting deadlines and getting the best marks I can.

So how do you achieve a balance? We here's my take on it.

Finding a 'balance'

Whilst I'll discuss my approach I think in the interests of objectivity its only fair that I'll give a counterexample. One of the top students in my year almost always did their problem sheets the night before they were due, they also did a ridiculous number of activities outside their studies. Whilst I'm pretty convinced they were a polymath it does show that everyone has their methods. Some people work incredibly well under pressure and enjoy having to manage multiple aspects of their life on an hourly basis. At the other end are more straight arrow types, they often still have hobbies but do work significantly in advance and have rigorous structure to their time. I'm somewhere in the middle...

I've already spoken about problem sets and not leaving them till a day or so before the deadline. But I also understand sometimes this is unavoidable, sometimes you have to do a set the night before its due in. My thought is that if you're facing this situation on a weekly basis you either aren't structuring your time correctly or you aren't spending enough time studying/working. Grades are a different matter, for some people where they are at now means that they need five hours on a sheet to get a 2:2, for others they only need an hour to get a 1st. If you're in the former position this can be very disheartening if you hear how the latter is doing. But if that's where you're at you have to make a choice, is that grade worth your five hours? This is perhaps worth an entirely new article, I'll probably write one about it soon.

I think your own happiness is ultimately the best measure. Because the fact is not everyone wants to put in the work they need to in order to graduate with a 1st, that's fine! But you don't want to be in the position where you graduate with something less than you expected/wanted. The best way to keep track of this is to pay attention to your problem set grades, they are highly indicative of how you are progressing and you should feel an emotional impact from them. I'm not saying if you get a 2:2 when you're after a 2:1 you should feel bad but that you should care that its not what you wanted and do something about it.

That could mean implementing a tighter schedule, going out less etc. Likewise if you consistently get what you want and you feel like you could still get it with some more free time injected into your life, give it a try! There are no set rules but the key is to be willing to change your lifestyle to fit what you want in the hope that it might make you a bit happier.

External pressures that push you to work

Lecturers in physics can often be very demanding (very very very demanding). They can expect you to put in a lot of extra work, completing exercises for the reader etc. There is also little sympathy for your commitments outside of your studies, you can't ask for a coursework extension because you had a sports match on during the weekend. To some this seems harsh but I'm afraid I'm with the lecturers on this, just be aware of it and plan accordingly.

Problem sets are perhaps where things get a bit more hazy. They can vary in difficulty drastically and in my experience lecturers can be very poor at structuring their coursework. We all have our limits, if for you four hours on a sheet is max then work to that. But don't expect lecturers to sympathise with you as students regarding the length of problem sets. Sometimes changes are made but in my experience its often a 50:50 chance at best. Having a personal limit on your work time is a good resolve to have when facing such pressures.

You also might find that your fellow students unintentionally push you to get things done. If you chat with a straight arrow type you might find yourself pressured to complete coursework ahead of your own personal schedule. For some people this might be the push they need, but if your system works for you and is getting you the marks you want its important to remember that everyone does things differently.

External pressures that push you away from work

First lets note that some of these pressures are justified, health (and that of those close to you), family matters etc. If you are experiencing such difficulties please talk to your department and get your deadlines moved and such.

The more... unjustifiable pressures mostly come from your fellow students. Being convinced to go out for drinks again and similar situations are often continuous social pressures that students are under. A willingness to say no is often not common amongst the general student population, I would encourage you to develop such a willingness. 

I think this is especially important if you have friends studying degrees with a different workload or deadline structure. Some other courses require fewer hours of work per week or they have an essay based coursework system, this can offer a different level of flexibility unlike physics where you have to manage a number of weekly deadlines. It's important that your friends recognise the pressures you are under. 

If I'm being completely honest and bias, science students tend not to have the same amount of free time as some other degrees, sorry BAs if that offends you its just what I've seen. Physics in particular is seen as a pretty 'hardcore' subject, if you're studying it you probably know that. Don't forget it and understand what that means for your social life in comparison to students of other subjects.

Ways not to deal with the pressure

Using drugs (including legal ones like alcohol and 'legal' study drugs) to prop yourself up is a really, really bad idea. Whether it be aiming for stress relief, to keep you awake so you can study/party all night, or anything else really, I've never seen someone who used drugs at uni end up in a good position. Not to mention that if you get found to be storing/using on university property you are at serious risk of being expelled from your university. If you feel that you are reliant on any substance please seek help with the relevant services at your university.

Running away from issues like falling grades is a really bad idea as well. Get in touch with your tutor or relevant members of staff and get help. Also, talk with your friends! I know I'm always willing to help out a friend with managing work, you should do the same. That said, never give someone a copy of your coursework, its ok to talk about problems but don't simply hand over a copy. It doesn't help people in the long run. Likewise don't ask someone for a copy of their work, it puts that person in a very difficult position.

A lot of opinions/information for you there, with any luck that gives you a clearer idea of how to achieve the fabled 'work-life balance'. Everyone does it differently but it's crucial that you find it as soon as possible!

How to approach your first problem sheets/sets... 5 points of advice

As far as I am aware most physics courses in the UK have coursework in the form of problem sheets (a.k.a problem sets). These are a series of (often connected) problems designed to challenge you to implement the techniques you have learnt in lectures to textbook problems or examples from more front line research topics. 

If you've just received your offer for a physics course you might well be receiving your first problem sheets in freshers week (that should give you a good idea of what you've let yourself in for). For many people it can take a while to get into the swing of doing these sheets, my uni certainly didn't give me general advice on how to tackle problem sheets. This can be a bit disheartening, especially seeing as looking back there are simple steps you can take to make things easier.

Not like A level problems/homework:

This is something I'm sure that you're all aware of, but my main point is that by recognising this you'll be better prepared. With higher study comes more independent work (inevitably) and tougher material. Typically undergraduate problems require you to make more leaps on your own, fill in gaps in your knowledge of your own accord and to be more thorough in your explanations. I'll expand on these below.

Lectures may not give you everything:

You have to understand what lectures are designed for, they are to provide you with a base line of knowledge and skill. You may need to search elsewhere for information or methods that will enable you to solve a problem. 

Sometimes this involves looking through the course textbooks or reading more widely through your university's library. Many often turn to the internet, a technique which is a source of much debate. In my personal experience looking online is usually useful for finding good textbooks or a bit of background information, but I don't find it often leading me to solving problems asides from the occasional online textbook or university PowerPoint.

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Often students who do well on problem sheets are familiar with a wide range of textbooks they can turn to on various subjects. I would suggest familiarising yourself with the books at your disposal in the library, they are crucial tools for problem sheets and might save your skin more than once!

Draw on other areas:

The solution to a problem might be found outside the immediate vicinity of the course that set the sheet. Skills that another course is teaching you might be the key to your solution, if you're doing a quantum mechanics problem you might find a linear algebra technique you learnt in maths gives you a quick solution!

Another common occurrence is using programming or software to overcome a problem. Can't solve an integral because it's freaking huge? Well unless the question is literally 'solve this integral', use Mathematica, its what any sensible physicist would do. Can't visualise a function, graph it on a computer! You can also use these methods to check your answers if using them as part of your solutions is not valid.

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Be thorough:

Undergraduate problems are often more open-ended than in A-level, with less direction to the realms of the correct answer provided. In order to arrive with confidence at an end point each step you take must be very water tight. The problems are often designed so that if you take steps lacking in security you will often arrive at the wrong answer. Question the appropriateness of your mathematical methods at each point in your calculations and whether your assumptions are appropriate also.

I have also found that thoroughly explaining my steps and choices in my solutions often helped the marker understand my intentions and direction. This enabled my markers to give me more feedback and sometimes to give me a few more marks where I had made mistakes.

Communication and Persistence:

Obvious but talk with your colleagues (don't copy, but talk) and also academic staff if you are struggling to make progress. You might also find you learn more than you expected to if you talk to an academic!

Some problems you will solve like *that*. Others might occupy you for hours. The key is to not give up unless it is occupying an 'unreasonable' amount of your time. My limit personally is about 10 hours for a sheet (I had about 2-3 sheets a week) but I'm unnecessarily stubborn and I work slowly. I know people who regularly got firsts that never spent more than 4 hours on a sheet. Find your limit and work to it!

In your first weeks its important to make lots of time for problem sheets in order to get to grips with them before the increase in difficulty (which can happen suddenly). DO NOT leave them to the last minute and do not trust yours or your colleagues estimates of how long the sheet will take, it will take as long as it does and you just have to deal with it! Hopefully some of the above advice will come in useful and the best of luck with your first problem sheets!

How is studying theory different? What do YOU need to do differently?

Different physicists need different tools in their lines of work, the two main groups in physics are theorists and experimentalists. It's fair to say that there are a lot more experimentalists than theorists (rightly so), so often the path for experimentalists is quite well laid in the structure of physics courses. Sometimes it's not so clear for theorists what they need to be doing to get to where they want to be. Asides from choosing theory options in your degree there are some general points of advice I'd like to give, hopefully they'll be useful! So here's some things I think you'll need to do differently to your experimental colleagues, regardless of your specific direction.

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More Maths!

This is not a stab at experimentalists, not some 'theorists are smarter than experimentalists' rubbish. Physicists need tools to solve problems and experimentalists need to use tools outside maths to solve the problems they look into. They use engineering, electronics and other skills which although related to maths don't necessarily require them to be actively solving maths problems constantly. For theorists, maths is their domain and their only real tool.

Theorists often need very specific mathematical tools relevant to their research, for example fluid mechanics researchers often need techniques from non-linear dynamics. But there are areas of maths that are practically ubiquitous throughout all physics, and crucial for both the experimentalist and theorist. Theorists must be particularly well versed in these, fluent in common mathematical language and having a good understanding of it. So here are three areas I think are key.

Calculus is an essential tool for almost all scientific fields, but theorists need serious calculus abilities. In particular geometric integrals involving volumes and surfaces of spheres and cylinders crop up a lot. Vector calculus is also an important arrow in your quiver, useful for topics like electromagnetism.

Differential equations crop up in physics all the time, solving them is a common necessity in problem solving. As a theorist you will almost certainly work with differential equations at some point in your career. You should be well versed in how to solve many types of differential equation problems analytically and potentially numerically (more on numerical methods later).

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Linear algebra is arguably the least fundamental of these three, but undoubtedly a key piece of your tool kit. Studying this leads to group theory which is essential for a number of fields. Understanding vectors and matrices along with the relevant techniques and manipulations is an important part of a theorists skill set.

Most importantly, if you want to do theory you better love maths! I've known plenty of experimentalists who view maths as a necessary evil but never a theorist who shared that view.

Programming:
Whilst there are areas of theory that don't use computers as a primary tool I'd be lying if I said they aren't crucial to most areas of theory. They can perform calculations that simply aren't worth your time, or calculations that are impractical for humans to carry out. Computers are key for a number of theoretical activities such as:

• Constructing simulations of many-particle systems
• Modelling fluid dynamics
• Finding numerical solutions to systems of differential equations
• Computing large matrix operations symbolically or numerically
• Kinematics calculations from track measurements in particle detectors

You can imagine how the above can be relevant to multiple fields. The main programming language used is C++, but Fortran is also used by some theorists. Symbolic manipulation languages like Mathematica are also used, with C++ extensions like Eigen often used by particle physicists.

Python is often the starting point for most physicists, it leads nicely into C++. All of this said don't feel pressure to take programming courses, I only have a compulsory 2nd year programming course under my belt and it hasn't caused any problems yet. I spoke to a UCL Particle Theory PhD about half a year ago (he'd done an MSci at Oxford), he said that plenty of PhD students teach themselves programming as and when they need such capabilities.

Quantum Mechanics:

Alongside your maths courses, quantum mechanics is a subject any prospective theorist should absorb thoroughly. It is the basis for almost all modern physics outside of relativity, so being quick with quantum is pretty much a pre-requisite for being a theorist except in a few areas (fluid mechanics comes to mind). Topics like quantum field theory (a graduate level topic) build on this foundation and are the primary tool of both particle physics and condensed matter physics (along with others).

Whilst knowledge of quantum mechanics is key for both experimentalists and theorists, theorists should be well versed in the mathematics of the theory, experimentalists often focus more on the physical phenomena that arises from quantum mechanics.

Statistical Mechanics:

This is an increasingly required area of expertise for theorists of all walks. Last academic year I spoke with a condensed matter theorist, Dr Andrew Ho, who told me that whilst previously areas like particle theory weren't expected to be well versed in statistical mechanics that has been changing. Within statistical mechanics is the most modern interpretation of thermodynamics, which is often used in calculations for various experiments.

Monte Carlo methods are increasingly prevalent in particle physics, as well as various data analysis techniques are also used for the large data sets that come out experiments like the LHC. Whilst data analysis can be a discipline of itself in physics, theorists can be heavily involved in statistics and data analysis. These are often contextualised in the setting of statistical mechanics.

So whilst this discipline may be seen as more relevant to experimental studies, it seems that statistical mechanics is increasingly relevant to many theorists.

Classical Mechanics:

And to a high level, we're not talking SUVAT style here! Specifically the topic of Lagrangian and Hamiltonian formalism is an essential requirement for most fields in theory. In depth knowledge of rotational mechanics is also likely to be useful. Experimentalists are often very familiar with calculations for specific mechanical systems they work with (though plenty of them are great with Lagrangian and Hamiltonian mechanics). As a theorist you need to be familiar with a high level of generalised classical mechanics. The primary reason for this is that Hamiltonian and Lagrangian formalism is the basis of field theory, a cornerstone tool for most theorists. If you have the option to take an undergraduate course in advanced mechanics you must absolutely take it!

Numerical Methods:

This is a slightly unspecific comment but it should suffice. There are plenty of problems in physics that can't be solved exactly, even with algebraic approximations. Systems of differential equations come to mind, some of them are only solvable numerically. There are algebraic alternatives to numerical methods like perturbation methods and asymptotics, but numerical methods are incredibly relevant to current research. You might find that none of these come up in your undergraduate course and that's absolutely fine. But if you have the opportunity to study them, consider if they are relevant to your current interests, I'd strongly suggest studying them if there is even a bit of relevance.

(Image Credit: The Great Courses Plus)

So there's some points about what you might need to do differently in your studies to your experimental colleagues and some general advice about what you might find useful if you want to pursue theory. This list is not at all exhaustive, but I hope it highlights some important areas to focus on.