math courses

Phil Courses

I am trying to select the five classes I should take at Tufts for this coming semester.

Math courses taken: multivariable calc, discrete math, complex variables, number theory, and abstract linear algebra, probability

CS taken: data structures, algorithms, intro to CS, and discrete math

I have also educated myself on various topics in philosophy, sociology, history, anthropology and psychology. I wish to do research on AI and on cultural diffusion. I am lacking knowledge in bare bones biological sciences, which I fear may be important for me to take. Additionally, I hope to take a course in modern physics before I graduate. Below I will list courses I am considering taking this coming semester.

  1. nonlinear dynamics and chaos- important in model natural change/growth. Additionally, it will help me for when I want to take my math GRE subject test
  2. real analysis 1-required for my major, and if I want to take a grad course on it senior year
  3. mathematical psychology- a seminar on mathematical models in psychology, I think I will enjoy this seminar thoroughly if I dedicate enough time to it
  4. statistical pattern recognition- a class focusing on bayesians, the class will handle regression and classification problems, model selection, machine learning algorithms, etc. basically a survey into machine learning applications and theory, so I think it would be well worth my time)
  5. Foundations of Rationality- see phil link
  6. philosophy of mind- see phil link
  7. logic103- see phil link

    I have a lot I want to take, and only a little bit of time. I am a rising junior, and I need to decide my trajectory given my goal, which going to a decent graduate school so I can do research. What classes would you recommend for the next semester, and what tips do you have for me moving forward? I am a math major currently. I will take any suggestions. A list of classes I should take by the time I graduate would be wonderful. So would a list of papers to read. Literally any piece of advice that pops into your head I would welcome with open arms. I can’t supply all the links, but googling “Tufts insert given department course descriptions” will bring you to the course description pages in case you for some reason wish to real go deep in advising me.

I am a math postdoc in Europe, and have been a postdoc for the last 6 years. Unfortunetly, I was still not able to obtain a tenure track position
(I was very close to get one, but because of bad luck will have to try again next year).

My current postdoc position ends in a few months. Because I thought that I will get a tenure-track position this year, I did not bother to search for a new post doc position until very late in the year. As a result, in a few months I will not have a postdoc position.

My Phd advisor came to the rescue – He can fund me as a postdoc at the University I did my phd in.

I would like to ask if people will look bad on someone that goes do a postdoc with his advisor in future job searches?

I should mention that I did not work with my advisor at all after my Phd, and am very independent in my research. Still, I am worried about this, and wonder what people think about such a situation.

Thank you

I am a 5th MSc semester mathematics student at a local German university. Since fall, I have been working on my thesis, which is the only remaining task for finishing my studies.

I had not had particular difficulties during my studies, apart from the usual struggling and doubts I suppose every student undergoes: before my masters studies, I had spent 7 semesters at another university on two BScs in physics and mathematics. I am paid by a public scholarship. I had decided to change the university for my master’s half for personal reasons and half in order to have a greater choice in courses held. My average score is 1.5 at the moment, which also had been my final score for the two BScs.

Now that I have started my thesis, nearly everything has changed: I am working with a professor whose courses I took several of, all with good grades, so she did not object to supervising my thesis. Although I have not had severe problems with my studies before, I am getting nowhere with my work now:

For understanding a single paper I am supposed to work on I sometimes need weeks, let alone the questions posed to me to think on, which I sometimes spend weeks without any serious results I could present. I have the impression that I am lacking creativity, intuition and a sufficient knowledge which I think I should have acquainted during my courses.

My problems have driven me into particular personal problems: I have lost contact with most of my former colleagues I used to spend every weekend with, partially because they seem to have lost interest in spending time with me, and partially because my mind is governed by thinking of my inferior scientific performance and the conviction no one wants to have to do with such a poor student. I cannot enjoy leisure time since I permanently have to think of the open problems that haven’t worked out over a long time. I cannot claim to have chosen a university where I am competing with the best.

For 1½ months I have been taking antidepressives and having psychotherapy, which barely helps to soften the biggest peaks of auto-aggression and contemplating self-harm, but have not yet helped me to find another view on what I’m doing.

TL;DR

Although my university performance seemed sufficient for me not to worry much about it, starting working on my master’s thesis has revealed a vast lack of mathematical knowledge and poor mathematical working capabilities. The longer I work on it, the more I lose any self-esteem.

Question: Where should I have foreseen my problems? Which signs did I ignore? Where did I miss to put things on the right track? And: how shall I find value in myself, now that I have found myself incapable of pursuing research, and have lost everything else?

I applied for a postdoc position in Denmark and was invited to an interview. The interview includes a ten minute presentation “of yourself and your research” targeted towards master students (the entire interview is 30 minutes). Presenting my research is expected and not a problem. But what does it mean to give a presentation of myself in such a context?

I have met one of the interviewers during a conference and discussed the position briefly, but the other is not familiar to me.
The interview is through Skype and I assume no master students will ever be exposed to it, in case that matters.

My background is in mathematics, with a main interest in mathematical statistics / biostatistics, and I am considering applying for a PhD position with a quantitative psychology group. The research itself can apparently be made statistically challenging towards the candidate’s interests, which sounds appealing. I am not sure if I want to continue in academia after the PhD, but it would preferably be in mathematical statistics or biostatistics.

Would a PhD research with a quantitative psychology group take away this option or make it more difficult, even if the reseach itself is approached from a mathematical statistics view?

While reflecting on my last research paper (currently in the hands of a referee) I discovered a closely related pair of problems that, as far as I can tell from published record, nobody else has considered.

For those interested in topology, the problems concern a property of
first-category continuous images of the half-open interval of reals.
The property has previously only been of interest in compact spaces,
but I want investigate for other classes of spaces.

A solution to one or both would make for a nice paper I think. I’ve been thinking about them for a couple of weeks with basically no progress.

Should I just tack the problems at the end of my research paper (give up?), or keep them to myself and hope to eventually solve one?

In (mostly) mathematical publications, when proving a theorem that can be generalized to a wider range of parameters, is it generally considered better practice to:

  • Present a special case of a theorem first, and then prove it in a general context, or
  • Prove the general case and then move on to present one (or more) special cases?

The first approach makes understanding the theorem easier, and makes the paper quicker to read. The second one looks more “rigorous”, but is much more difficult to understand for more complex theorems and formulae.

What is generally considered the better practice?

I am writing a math thesis.

I want to provide a result in chapter 2, but formally prove this result in chapter 8. This is because I am introducing a bunch of definitions in between these chapters and they cannot be moved in front of or within chapter 2.

Can I say something like, “as we will see in chapter 8, this result in chapter 2 is true”? In other words, can you allude to the proof of a result that will be given only later in the thesis?

I don’t feel like it is good practice because it sorts of destroys the “surprise factor”, and it also makes the reader jump 100 pages to see the result. How should I handle this?

I am writing a math thesis.

I want to provide a result in chapter 2, but formally prove this result in chapter 8. This is because I am introducing a bunch of definitions in between these chapters and they cannot be moved in front or within chapter 2.

Can I say something like, “as we will see in chapter 8, this result in chapter 2 is true”? In other words, can you allude that a result will be proved later on in the thesis?

I don’t feel like it is good practice because it sorts of destroys the “surprise factor”, and it also makes the reader jump 100 pages to see the result. How should I handle this?

I am a master student in mathematics at a university in the Netherlands and am currently applying for PhD positions as I will be graduating soon. Thus far I have applied for about ten positions (in the Netherlands, Germany, Denmark, Sweden, Switzerland, etcetera) and although I am still waiting on some of my applications, I have been rejected without interview from the ones I have heard back from (which is the majority).

In brief conversations I have had with academics on this issue, they have generally hinted (albeit rather vaguely) that competition is not so high (say, compared with industry) and that I should be hopeful of landing a position. This is in spite of the fact that my grades are quite average and the feedback I received from one failed application was that my grades were too low. My academic advisor, however, advised me that the quality of my thesis (which I am currently writing) was of more importance and downplayed the importance of grades due to how they differ from country to country, university to university (among other reasons).

The problem seems to be that positions are seldom advertised and even if only twenty percent of graduates wish to pursue a doctoral position, that means that there are still a lot of people vying for say only one position.

I was wondering what the general consensus on this was and if I should maybe lower my expectations of getting a doctoral position if it is say only intended for the “best of the best”?