Questions asking for advice on various mathematical matters. Consider adding the tag (soft-question) as well.

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4
votes
1answer
123 views

What is the correct terminology to say that $\small f(x)=a+bx+cx^2+…$ can be expressed by $\small g(x)=A(1-x)+B(1-x)(2-x)+C(1-x)(2-x)(3-x)+… $

Hm, I do not even know the best formulation for my question in the header. It is not for the math but for the proper writing/terminology. I've come across the term "base change" recently but the ...
57
votes
7answers
4k views

What made you choose your research field?

I was wondering how come modern mathematicians do not seem to discover as many theorems as the older mathematicians seem to have done. Have we reached some kind of saturation limit where all commonly ...
4
votes
1answer
533 views

Video of Terence Tao on Poincaré's Conjecture

Last year, I found a video of Terence Tao on the Poincaré Conjecture, which could be downloaded in mp4 format. I did downloaded it, however I had to format my computer, then I lost it. I searched in ...
1
vote
0answers
395 views

Reading advice: Mathematical finance for a student of pure mathematics

Which books/lecture notes should a student with a background in pure mathematics (in my case it was geared towards algebraic geometry) read in order to do financial math? I have done one basic course ...
23
votes
5answers
3k views

Is a good GRE score enough for a non-math graduate to be accepted in a decent pure mathematics graduate program?

I have a computer engineering degree , and i have studied several mathematics courses like single variable and multiples variables calculus , complex variables , probability , numerical analysis ... ...
2
votes
0answers
169 views

Learning roadmap for mathematical biology

Which courses (undergrad level but also master's level) in mathematics and statistics should be taken by a student aiming for a PhD in mathematical biology? The basics I imagine are: Calculus ...
7
votes
0answers
439 views

Prerequisite of Projective Geometry for Algebraic Geometry

I studied Euclidean Geometry in high-school, and I have not studied anything relates to geometry since I started studying in university. I am now intending to study Algebraic Geometry, however, I ...
2
votes
0answers
232 views

Accesible Area of Discrete Geometry for Undergraduate Research [closed]

This summer I will have a chance to work on a 16-week summer research project under a professor in convex/discrete geometry. I'm a first-year student with a fairly good background for my age and I've ...
4
votes
1answer
254 views

Not in school. Need some help planning my studies post-calculus & intro. abstract algebra.

OK, so I left school (wasn't failing or anything), but I still love math and want to go on with my studies. I want to, first and foremost, cover all the important topics a math education should ...
0
votes
2answers
211 views

Has anyone held an NSERC award before as an undergraduate recently? [closed]

I am a second year math student. I go to a fairly small university with at most 8 profs or so. Seeing I have no chance at all in my university, I am looking to see other universities. However, I am ...
7
votes
4answers
1k views

Citations in Math Papers

I asked a similar question previously, though this is more specific and directed. In the writing of mathematics research papers, when is information cited, such as definitions? I have read that if ...
2
votes
2answers
361 views

Originality of Research [closed]

How can I discover the originality of a field of research or a sub-field of research without divulging the particulars? I am proving some interesting results in a potentially new sub-field of convex ...
6
votes
2answers
810 views

Learning roadmap for Class Field Theory and more

I consider to study Class Field Theory and Advance Number Theory by my self this next semester. However, there are many books, lecture notes... I would like to choose the most comprehensive book to ...
22
votes
4answers
3k views

Learning Roadmap for Algebraic Topology

I am now considering about studying algebraic topology. There are a lot of books about it, and I want to choose the most comprehensive book among them. I have a solid background in Abstract Algebra, ...
2
votes
0answers
254 views

resubmitting a paper to a better journal [closed]

I submitted a paper to quite a low-rated journal a few months ago, partly because I didn't think that my results were particularly good, but also because I neglected to do much research into impact ...
3
votes
0answers
503 views

Topic appropriate for undergraduate research program

This may be not appropriate to ask this kind of question here. But please feel freely helping me. In our Maths faculty, there is not a program like Undergraduate Research Program(URP), however, the ...
2
votes
4answers
302 views

Getting Help in Abstract Math Classes

This semester I am taking abstract algebra, and I am finding the homework to be much more difficult than calculus or linear algebra. The book my class uses is Fraleigh's Abstract Algebra. Although I ...
6
votes
2answers
417 views

What is the best approach when things seem hopeless?

I'm finding that I am getting to the point of being hopelessly behind in one of my courses (Fourier Analysis). What is the best thing to do when it feels impossible to get caught up in the literal ...
17
votes
3answers
1k views

Career advice in mathematics

First of all, I don't know if this is the right place to ask about careers. If not, please direct me somewhere I can get more help. So, I'm in my first year of university, majoring in applied ...
23
votes
4answers
919 views

Are there any common practices in mathematics to guard against mistakes?

It occurred to me that math is somewhat like programming (or vice-versa, if you prefer) because, in both, it is easy to make mistakes or overlook them, and the smallest error or misguided assumption ...
18
votes
1answer
890 views

Efficient ways to read and learn a new topic

I started reading the book "Topology without tears" by Sidney A Morris and lecture notes on "Elementary Number Theory" by WWL.Chen. To get the maximum out of the book and understand the material ...
7
votes
3answers
562 views

Where can one find (freely, online) mathematical articles with a fighting chance to be understood by high school students and undergraduates?

I am an undergraduate non-math major. I just finished my university's engineering calculus series, looking forward to linear algebra in the coming semester. To be frank, I always despised math because ...
10
votes
5answers
3k views

Advice for Self-Study

I am a senior in high school who has taught myself through Calculus BC and I got a 5 on the exam. However, I have taken all the math I can at my school. I have also taught myself multi-variable ...
5
votes
5answers
1k views

What's wrong with me? [closed]

Over the past few days I have been pondering about this: I enjoy technical things (like programming and stuff) and try to find the patterns and algorithms in everything. My life is number oriented. ...
310
votes
24answers
60k views

How to study math to really understand it and have a healthy lifestyle with free time?

Here's my problem. I'm studying math and when I really work hard, I think I understand things very good, but that comes at a big cost: in the last few years, I've had practically zero physical ...
8
votes
2answers
421 views

What jobs apply mathematics to ecology, outside of academia?

What kinds of jobs exist that blend mathematics and ecology, outside of academia? Are they in government and if so, what agencies? Are they in consulting? Private industry? I have a master's in ...
19
votes
7answers
2k views

Mathematical Career Advice to a young 16 year wannabe mathematician

I am a '94 born aspiring mathematician, programmer and a little bit of drummer from Nepal. I have been an avid follower and lover of mathematics since my seventh grade. Although I do not even consider ...
16
votes
4answers
970 views

Grasping mathematics

First, I'm not trying to make this sound like a "poor-me" story. I understand fully that every decision I've made leading to this is my fault. I am genuinely looking for advice. So, I am a high ...
8
votes
3answers
586 views

Which of these courses to take if one intends to go to grad school in pure math (rank please)

could you rank these classes in terms of necessity to take if I intend to pursue a Ph.D in pure math? I don't know if I can fit everything, but I want to make sure I take the most important ones: ...
11
votes
2answers
1k views

Preparation for Putnam?

If all the training I have right now is Calc 1-3, Linear Algebra and some introduction to set theory/discrete math, what would you recommend focusing on over summer in preparation to Putnam? Real ...
6
votes
8answers
1k views

Most important elementary math skills

Barring very elementary arithmetic, which skills from elementary school are essential for understanding the world better?
2
votes
3answers
243 views

Large-scale Coordinated Research in Mathematics

I've long dreamt of an occasion where hundreds or thousands of mathematicians work on a single problem in a truly coordinated way. Well, now that I'm nearing my doctoral defense in mathematics, I've ...
22
votes
5answers
2k views

Math GRE Subject Exam

I am studying for the GRE Mathematics subject exam [1]. I am looking for tips regarding how to more effectively study for it. Does anyone know of any good study materials or have any tips in general? ...
0
votes
2answers
103 views

how can I present an idea about the difference between two functions clearly?

I have a presentation in which I want to point out a difference between two functions. Instead of putting the two functions on a slide and pointing to the differences, I want to do something simple. ...
13
votes
11answers
5k views

Which 4 maths courses to take as an Economics PhD student?

I am doing a PhD in economics and I have the chance of taking one subject a semester in the maths department (I would like to do more, but "unfortunately" I have to work on my thesis). I want to have ...