Random Basic Skills I recommend for Students looking for research jobs in the US (in no particular order of importance)

  • Learn how to touch type on an American keyboard This is a basic skill that most US students are taught in secondary school. However if you don't know it (and many foreign students do not) you should take a course in touch typing. It is not hard to learn, especially if you have ever played a keyboard instrument. Your ability to communicate electronically, write manuscripts, and edit things online will be much faster if you learn how to touch type. By touch type I mean typing on a keyboard without looking at the keys while you type. This involves correct body position and posture and the ability to watch the screen for typos as you move your fingers around the keyboard. The correct body position will also save you potential problems with carpal tunnel and other repetitive stress injuries. There is a standard way to touchtype on a QWERTY keyboard which involves basing the four fingers of each hand on the asdf (left) and jkl; (right) keys and moving from there with the thumbs working the space bar. In reality I think we all look the the keys occasionally especially for the far away symbols and such but to be able to type text without looking is really very valuable on a day to day level. For example, it allowed me to type this webpage in a very short time, off the top of my head.

  • Learn how to drive a car and get a drivers license. Even if you live in a big city with good public transportation, you will likely get invited to a conference that is in a small college town, two hours drive from the nearest major airport with only inconvenient shuttle service. Most conferences like this assume people will just rent a car and drive there. Moreover, if you can drive, your access to things in the US will be an order of magnitude better. It is also important to practice safe driving so that you do not get in an accident during your driving.

  • Given the above, learn how to change a tire with a manual jack. And make sure you car has a good spare, a jack that fits the car, and jumper cables. When I bought my first car, a four year old Plymouth Reliant, back in 1987, I had to borrow money from my father until I got my first graduate student paycheck. My father lent me the money on the contingent that I rotated all the tires myself (no help) with the jack and the spare. It took some time, especially since I did it in his driveway which has a slope, but it was the best lesson for a new car owner. Four years later when I went for a job interview at a leading research university, my host got a flat tire on the way back from picking me up at the airport. I showed him how to change the tire (in my suit and stockings, on the side of the road in the winter) and I later got the job. Not sure if it had anything to do with the tire, but it could not have hurt. Seriously though, I've also been stranded myself on the side of a highway with no cell phone and no AAA and changed the tire. You have to be careful with oncoming traffic and not to do anything stupid, but this is a skill everyone should know if they own a car. Even if you have AAA and a cell phone. Even if you don't like to get your hands dirty (and they will get dirty if you change a tire, so it's good to keep a spare role of paper towels or some old rags in the car).

    The jumper cables are not for changing the tire but for charging the battery if it goes dead. You need another car or a special battery to use jumper cables (i.e. you need a charge from somewhere). AAA, if you can afford it, is also quite useful as they will come and do these things for you free of charge provided you can get a hold of them (hence cell phone).

  • Learn how to write scientific papers This means, first of all, knowing correct English grammar and appropriate style. But also how much detail to include depending on the audience. Courses offered to foreign students in technical writing often fall far short of training them on how to write their first article. Practice writing up your work early and often and get it critiqued by your advisor or someone you know. Even if you are not a foreign student, you still may need work on writing, especially if your undergraduate training was purely in technical areas (e.g. as in an engineering school or degree). If you have not been taught how to write well, assume that you will have to learn it from experience and practice. The quicker you master this the sooner you will be able to publish your work independently. It is my experience as editor on several applied math journals that a significant number of scientific manuscripts are returned to the authors without review because they are written so poorly as not to convey clearly the value of the paper.

  • Learn to read both current and historical scientific literature Many students make the mistake of following through on a project assigned to them without learning the scientific literature. Then when it comes time to publish their work, they discover a portion of it has already been done. Worst of all, this discovery could come in the form of a referee report (rejecting the manuscript) which has wasted a lot of time of the student and also serves to degrade the scientific reputation of the student and all other authors. It also serves to annoy the authors of the published paper in question and can make enemies.

    If your advisor gives you a project to work on that is supposed to be new research, ask what are the most relevant papers in the literature an do a literature search yourself to determine the state of the art for your problem. Go and discuss the other papers with your advisor so you get their perspective on the literature. Since there is a vast literature out there, this means that you need to learn to read papers for overall content without going through all the details. Then pick and choose which ones require a more detailed reading.

    Make sure you do not overlook the literature that is not in print online, some excellent and relevant papers published just 10-15 years ago are not online and require you to physically walk to the library and read the papers in the journal (or make a photocopy and bring it back). I have seen manuscripts written by younger authors rejected because they duplicated material that was published in the older printed literature.

    When I wrote my PhD thesis, latex had just been invented an essentially none of the journals were publishing online (the internet was in its infancy and had not yet gone commercial). So I know how it is to go to the library and photocopy. It's not all that time consuming if you do it efficiently and copy several articles at once. I have one paper that needed a sharp estimate from a paper of Nagy written in the first half of the 20th century. We had to go to the library and look it up in print. But this prior paper allowed us to prove a sharp estimate in our work that matched results from asymptotics and simulation. I can not stress how important it is to take into consideration the full scientific literature when writing your own research papers.

    Another reason to follow the scientific literature is that it gives you a broader perspective about what has been done and what are the active areas of research. You will have to pick your own problems at some point in time and you will need to know this by that time.

  • Learn to compute This is a bit vague, but it means that you should become comfortable with using the computer, not just for latex (see below) but also for scientific computing. What this means depends on your career choice in mathematics. In my area it means numerical analysis and scientific computing, including mastery of some basic computational languages and packages like C++ and Matlab. Learn the abilities and shortcomings of the computer, the latter includes things like floating point arithmetic, binary arithmetic, and round off error. Not only will this be useful to you but it will also help you in critiquing work of others that makes heavy use of computing.

  • Learn latex Most mathematical papers are typeset in latex so you should learn it early and master such things as bibtex for bibliographic references. A PhD thesis often involves over 100 pages of written material, typeset, and you will not want to be doing cross referencing by hand. Moreover, if you learn bibtex you do not even have to alphabetize your bib references yourself, it will be done for you. Some people prefer to use packages when using latex, however since it is source code driven, and packages typically only run on specific platforms, I suggest everyone learn how to use latex starting from source code. It is similar to using a programming language and it is easy if you can start with a template from someone else's paper. The hardest part of latex is learning how to "debug" your sourcecode based on the cryptic error messages that latex spits back at you (and it will do so, quickly and often). Getting advice from peers is a good way to start with such problems.

  • Learn powerpoint, etc At some point you will have to give presentations in front of an audience. It is helpful if you know how to use powerpoint and can give presentations in this format. It will allow you to incorporate movies and pictures seamlessly into your talk. Moreover it is easier on the arm than writing on the chalk board.

  • Learn how to lecture at the blackboard If you are a TA you will get practice, however even the TAs may not actually have lecturing experience. Everyone should learn how to lecture at the blackboard if they are in an academic profession. This turns out to be easier than you might think, if instead of thinking about it from the point of you looking out at the audience, you think in terms of what the people at the back of the room are seeing at the front. Evernthing that I will now say is complete common sense based on the above premise, nevertheless most people do not take these details into consideration when they start lecturing. I had the advantage of taking courses in college from some outstanding lecturers (one professor could have photographed his lectures and published the pictures of the board) and I think this helped to put blackboard lecturing in perspective.

    Everyone should practice their first lecture by writing it out on a board and then going to the back of the room and seeing what it looks like. Correct your presentation until it looks really good from the back of the room. Next, make sure that if you expect the audience (e.g. students) to take notes, that you write at a pace they can keep up with. There is a sure-fire way to gauge pace. After you write a paragraph on the board, look at the audience and stop talking/writing until most of them have finished taking notes. Then continue. The silence is a lot shorter than you might think. Make sure you write everything you want in their notes, on the board. A Typical student will copy what you write and not embellish, even if you say more than what you actually write. This can be tiring for your arm but it is necessary if you want to deliver a good blackboard lecture. In addition bring a friend to listen to your delivery and see if they can hear you from the back of the room. If you aim for the back of the room when you lecture, everyone in between should be able to hear and see you. If you aim for the front, you will almost surely miss the people in the back. If you have trouble speaking loudly, consider getting a voice coach (just temporarily) or practice breathing deeply to your diaphram and pushing with your stomach and back muscles when you talk. It may feel like yelling but remember that you are a performer when you give a lecture. You are not having an intimate conversation with the person in the front. Therefore, act like a peformer and speak to the back of the room as if you were acting in a play. If you have ever sung in a choir it is similar only speaking instead of singing. Asking questions is also good and keep the whole group in mind when you do so. There is an aspect to giving public lectures that has elements of improvisational acting. If you have done that you should be great at giving lectures. If not (and most of us have not, myself included), after giving a number of lectures you will get more comfortable talking off the top of your head in front of a crowd and having them enjoy the experience. For the most part, they are there to learn and are expecting to enjoy the experience so if you don't do anything to shatter that expectation, you will do just fine (i.e. it is the `innocent until proven guilty' rule that applies to university teaching, unlike some other types of teaching). This last idea is important to keep in mind if you tend towards stage fright.

    If you do not teach and tend towards stage fright and have to give a presentation, then consider powerpoint, see above, as it gives you some physical material to hide behind and saves the problem of writing well on the chalk board.

    When delivering a research lecture at the board, you can take some liberties with the above (in particular the note taking) but it should be only so that you can deliver additional information to the group. Moreover, the `back of the room' rule still applies.

    Perhaps most importantly, always try to guage the knowledge level of your audience when giving a lecture. You want them to walk away with new information that connects well to what they already know. This rule applies whether giving a calculus lecture or a research colloquium.