99

Yes! In fact, I think you're well on your way to doing better than your peers! Taking longer to understand something isn't something to be proud of! There's no need to reinvent the wheel. If someone can help you understand something, you would be well-advised to make use of them. In the same way, you would be well-advised to attend the lectures, thereby ...


56

First of all, I believe this is extremely common these days. More and more I notice students neglecting to develop important problem solving skills and instead developing great “google-fu” and “stack-exchange-fu” skills to achieve the same goals. Now, don’t get me wrong, SE-fu is a terrific skill to have. Just like you are worried about using the internet ...


25

I think the main advantage is that an ambiguity of a/bc is avoided. For example, g/m^2s may be read as g m^{-2} s^{-1} or g m^{-2} s depending on whether multiplication takes priority over division. As far as I know, there is no consistency in opinions about it, so to avoid confusion a slightly uglier notation with negative powers may be worth accepting.


18

I wouldn't worry too much. It sounds like you are making excellent progress. You are still an undergraduate, you have tons of time ahead of you! There are lots of good ways to learn mathematics. Talking with others (including over the Internet) is one. Allowing yourself to get stuck, and trying hard to come up with your own proofs is another. If you feel ...


15

This is going to sound stupid, but I've seen it work. Try dividing the blackboard with vertical lines to create narrower "pages." This will make it easier to write in a straight line and will discourage you from writing too large. Of course, the "pages" need to be large enough that you don't write too small.


15

"... unless you went through a textbook and attempted to prove every theorem yourself first you won't truly understand the subject" Nonsense! This is anxious, perfectionistic thinking, and internalizing thoughts like this ultimately caused me to leave academia. I felt that I couldn't pursue my research unless I fully understood everything from first ...


14

Instead of me looking through your questions on Math SE like Ethan Bolker suggests, let me tell you what I would look for and evaluate instead, and then let yourself do the self-evaluation (which is also an important skill to develop as a researcher!). Basically, I would look at if your questions are well received. If you hit the hallmarks of a "good ...


13

No-one really knows the educational effects of reliance on SE yet, mostly because you, and your generation, are the canaries down the coal-mine. Most of the experts who answer questions on the technical SE sites are people who completed their graduate education before SE existed, and some before the Internet was even in regular use. Those of us who answer ...


10

As you mention this is about the physical act of writing, then yes, there are things you can do. Put a projector with text on various sizes (like the vision testing charts optometrists use) and walk to the end of the room to see which size is more fitting given the room size, then go back to the board and mark the size. You then can measure it with a normal ...


10

There are a lot of aspects of training to be a mathemtician. For example, you want to learn: Mathematical theory (definitions, key theorems, key constructions) Literature search (figuring out what's in which papers, finding results in books, using google to find relevant ideas) Mathematical tricks and proof techniques How to struggle with a difficult ...


9

Knowledge of the English language is often a hit-or-miss requirement, i.e., either you have a recognized English qualification (TOEFL, IELTS...) and you can study there, or you do not have it and you cannot study there. In many institutions, this is checked by administrative personnel, independently of the selection committee. Having better English ...


8

1) Unless you have something close to an Annals level paper, I would say you should be applying for close to 100. This probably isn't actually possible; to hit this number reasonably, you have to apply for temporary positions and for non-research oriented positions. Think of it this way. Positions taking applications on Mathjobs are getting something like ...


7

Maybe it's silly, but there is a section on Blackboard Technique in Gian-Carlo Rota's Ten Lessons I wish I had been Taught that I have always found very useful: Blackboard Technique Two points. a. Make sure the blackboard is spotless. It is particularly important to erase those distracting whirls that are left when we run the eraser over the blackboard in ...


7

My opinion, which I think is far from universal, is that the tenure track and postdoc markets are quite different in this way. Postdocs are hired to work with one or two particular faculty members, and so if there's no one close to your work at a school they're very unlikely to hire you as a postdoc. If I'd made a list of the 10 most likely places to ...


6

Yes, after a year you should definitely write to the editor and ask for an update. Production completed likely means that the paper is actually ready for immediate publication either in print or online. But check, nevertheless. Print, especially, takes a while to get out the door. But even online publication takes a while to move from staging to final ...


6

I'm currently chairing the search committee for a tenure track position in applied mathematics at a smaller (not R1) research-oriented university. We received 261 applications for the position and will phone interview about 5% of these applicants. Many of these applicants have 5 or more years of experience past the Ph.D. The academic job market in ...


5

Another possible aspect of the situation is that the invitation to speak at the seminar is a way to fund a short visit on your part, in which you could discuss more with that professor. If that is the case, the topic of your talk wouldn't necessarily need to be the same as you discussed.


5

Really, the answer to this is very simple. Everything that you can find on the internet has already been done by someone else. What you are required to do in PhD research is something which has not been done by anyone else yet. Of course, the web may still give you good ideas about techniques, etc. But SE or (any other web forum) isn't actually going to "...


5

The existing answers all seem to focus on the US job market, so I will try to put a perspective for the European job market and the differences here. Most US maths jobs are posted on MathJobs and one can apply there. This is convenient but also means that it is very easy to apply for a lot of jobs and so this is what people do. Math jobs in Europe are not ...


4

This is a really really important question, and it's really important that the correct answer is option 2. Most graduate students interpret it to mean 1, and this puts them at a disadvantage. You should list any people in the department who might be interested in serving a postdoc mentor for you. You should always list someone. There are two main reasons ...


3

Generally speaking, the choice of one form over another is better done on a case-by-case basis, according to readability. If I have to specify a speed of 5 meters per second, I'll write v = 5 m/s rather than v = 5 m·s-1, because for most people the first form is more readable than the latter. However, if I have to label the axis of a quantity with some ...


3

This is not really an answer but a (somewhat) relevant anecdote that's too long for a comment. About 20 years ago, I chaired my department's graduate admissions committee. The college had a requirement that new graduate students whose undergrad degree is from outside the U.S. must participate in an orientation before the start of their first semester of ...


2

You can just carry on with this approach through graduate school and well into your career as a professional mathematician. For instance I have at least one series of papers that started because of answers I got to a mathoverflow post when I was confused about something.


2

I assumed that chalkboards were last used when dinosaurs ruled the Earth. Anyway, write slowly and with large figures. Practice. It will probably get better with practice. But. The reason for the chalkboard - dinosaur allusion is that the technology is terrible. It was used at a time when there were few options and no better ones. It was difficult and ...


2

Yes, it will be a plus. And no, you won't need to go into details. But get a letter of recommendation from a superior. But part of its being a plus is that it is closely related to your academic trajectory and not something different. And, with permission from the DoD, you can probably say some things, even if not especially detailed. You can, for ...


2

Undergraduate math has a wide variety of free or cheap resources online. Youtube, udemy, and khan academy are your best friend. You will quickly learn how to spot a good teacher / course. Some books are public and many are available at libraries or online. And of course stackexchange is an option when you feel stuck. As you said, you have a number of years ...


2

if I am writing a proof of a theorem and I need to refer a lemma that comes later in the same later. What is the proper way to say that? Many approaches are possible, it depends on the precise setting. E.g., when the lemma is relevant to that particular theorem, you could write: \begin{theorem}\label{mytheorem} ... \end{theorem} \begin{proof} ..., by ...


2

The proper way here is to rearrange your paper so that this does not happen. It might be possible to put the theorem into the paper twice. Once in the introduction, possibly without some technical details but with more context and intuition around it and once after the required lemmata a proven with all the technical details. The main reason is that the ...


2

Try to have a good attitude about it. And make use of any technology available. In undergrad, one of my profs would write on slides directly on the overhead projector. It meant he could produce his stuff in fairly normal sized printing on the slide, and he could even be sitting down when he did it. He had a tall stool by the projector. It means he can be ...


2

I was a teacher for 2 years. After the first month or so you get comfortable using your arms to write more / larger. If you are a teacher / lecturer than the best two options are Do a practice lecture or a component of it depending on the length before hand. Particularly practice any diagrams ahead of time. Just ask your students. Everyone has different ...


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