Questions tagged [advice]

Questions asking for advice on various mathematical matters. Be careful that your question is answerable, and also that it is not a polling question (e.g. "What is the best / your favorite way to...").

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12
votes
4answers
4k views

Math for computer science?

Math for computer science? I'm a computer science major and just completed linear algebra. Many courses are available to take now. Of particular interest: number theory and abstract algebra (Modern ...
55
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4answers
3k views

How does one give a mathematical talk?

Sometime tomorrow morning I will be presenting a mathematics talk on something related to commutative algebra. The people present there will probably be two mathematicians (an algebraic geometer and a ...
3
votes
2answers
226 views

Question on mathematical writing

I am now writing my graduate thesis, it includes some basics mathematical theorems/propositions. I got a trouble in writing, more concretely, I do not know when can I state a mathematical claim as a ...
9
votes
1answer
2k views

Independent undergraduate research — what to do?

I hope this question is within the scope of this website. I am currently a rising senior, and need to decide on a topic for my independent undergraduate research/thesis. I was hoping to get some ...
5
votes
2answers
792 views

Math for a high school junior?

I don't find the math taught at my school too challenging so out of personal interest I teach myself other fields of math. I was wondering if you could recommend some areas with a bit more complexity? ...
5
votes
2answers
8k views

What makes Probability so difficult to get it right in the first place? [closed]

I took two classes of Probability, I did very well and was confident on the subject. Now I meet it again in my Combinatorial Algorithm course, and guess what? I feel completely blank again! I have to ...
4
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3answers
343 views

I need some advice for $ \; “ \; 3xy+y-6x-2=0 \;”\, $

PS: I edited the title again and I think, it's better now... :) Actually, almost the whole solving way is wrong but, I understood why... :D :) You can check that or add some more useful links about ...
3
votes
1answer
1k views

Learning Math On my own

I'm a physics major and I'm pretty sure that I'm interested in theoretical physics research. However, I haven't been able to take math courses in a systematic way (as a math major would) due to ...
29
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4answers
4k views

Perspectives on Riemann Surfaces

So, I have come to a somewhat impasse concerning my class selection for next term, and I have exhausted all the 'biased' sources. So, I was wondering if anyone in this fantastic mathematical community ...
5
votes
3answers
259 views

Dealing with many entities that need a symbol

What does one do when one needs a lot of symbols and one has exhausted the useful symbols of the latin and greek alphabets? (I say useful symbols because letters like iota (ι) and upsilon (υ) seem too ...
12
votes
3answers
5k views

Is Foundational Research a Dead Field?

I'm a second year mathematics major at a pretty good school. Ever since I became a math major I have been most interested in set theory and logic, which I guess can be lumped into the category of ...
3
votes
1answer
1k views

1 or 2 Year Master's Program [closed]

I have been admitted to two Master's Programs in math (both with funding). One is 1 year long and the other is 2 years long. I plan on obtaining a PhD directly afterwards. The 1 year option lets me ...
8
votes
1answer
397 views

Where to get peer-reviewed before submitting a paper to journal?

As a student where should he first approach for review of his paper, even more so a first one, before submitting to peer reviewed journal? Teachers tend to be busy with school and personal work, ...
4
votes
1answer
140 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 ...
92
votes
8answers
13k 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 ...
5
votes
1answer
915 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 ...
65
votes
2answers
26k views

What is the proper way to study (more advanced) math?

Here's what happens. I get stuck on some proof or some mathematical construction and I end up staring at the problem for hours, sometimes not making any progress. I do this because sometimes I think ...
3
votes
0answers
659 views

Can I research in complex analysis, PDE and differential geometry without exposure to mathematical physics?

I love mathematics, but physics is far away from my interest. I see that recent mathematics research is strongly connected to mathematical physics which is something doesn't interest me! I love ...
31
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6answers
7k 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 ... ...
6
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1answer
461 views

Learning roadmap for mathematical biology

Which courses (at an undergrad level or master's level) in mathematics or statistics should be taken by a student aiming for a PhD in mathematical biology? The basics I imagine are calculus courses, ...
14
votes
1answer
1k 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 ...
5
votes
1answer
368 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 ...
9
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4answers
5k 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
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2answers
461 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 ...
13
votes
2answers
3k 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 ...
51
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4answers
13k 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, ...
13
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4answers
1k views

Visual research problems in geometry

I am considering doing research in mathematics to be my career (and my life) someday. I'm a visually oriented person in general; for example, I prefer chess over cards because when I play chess, I ...
5
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0answers
1k 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 ...
4
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4answers
438 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 ...
9
votes
2answers
582 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. What is the best thing to do when it feels impossible to get caught up in the literal sense. Being "caught ...
26
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4answers
1k 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 ...
32
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2answers
2k views

Efficient ways to read and learn a new topic [closed]

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 ...
5
votes
1answer
1k views

Self-study: part 2

So I'm thinking of doing the following course progression: Baby Rudin Finite dimensional vector spaces Halmos Abstract Algebra Herstein Big Rudin (Real and complex analysis). Is this a good ...
12
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4answers
2k 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 ...
15
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6answers
6k views

What to self-study, after studying AP Calculus BC and finishing Rudin's Principles of Mathematical Analysis?

I am a senior in high school who has taught myself Calculus BC and I got a 5. However, I have taken all the math I can at my school. I also taught myself multi-variable calculus and much of ...
3
votes
1answer
663 views

Study Order for high school math

Here in Brasil math is "divided" on fundamental, average and superior, where superior is the math that you learn on universities, like calculus, integrals, limits, derivates, etc. My question is ...
7
votes
5answers
2k views

How might I refresh high school level mathematics and extend it much further?

I did well at Mathematics at school (top 0.1% in the country, approximately), however I stopped studying it when I was 16. Since then I've studied a couple of highly specific mathematics modules in ...
5
votes
5answers
2k 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. I'...
738
votes
27answers
174k views

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

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 ...
9
votes
2answers
701 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 ...
22
votes
4answers
2k views

What are some good math study methods for a high school sophomore?

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
1k views

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

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: ...
14
votes
3answers
2k views

Preparation for Putnam?

Currently, my math training includes Calc 1-3, linear algebra, and some introduction to set theory/discrete math. What would you recommend that I study over summer in preparation for the Putnam? Real ...
17
votes
6answers
596 views

Are there any generic thinking approaches for providing mathematical proofs to a given theorem

To produce mathematical proofs for theorems we should have the required knowledge in that area. But even having adequate knowledge, people like me struggle a lot for writing down the proofs for any ...
7
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8answers
2k views

Most important elementary math skills [closed]

Barring very elementary arithmetic, which skills from elementary school are essential for understanding the world better?
3
votes
3answers
259 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 ...
88
votes
9answers
28k views

Learning mathematics as if an absolute beginner? [closed]

I dread mathematics, and I believe it's because I have come to associate mathematics with the experience of terrible teachers. All of my math teachers have been grumpy, but one in particular was the ...
14
votes
6answers
11k views

In what order should the following areas of mathematics be learned?

I am in a biological field (medicine) but I have genuine passion for mathematics. I want to learn it on my own , in my spare time. Mathematics , as I gather, is learned best when you have grasped ...
11
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6answers
1k views

Suggestions for topics in a public talk about art and mathematics [closed]

I've been giving a public talk about Art and Mathematics for a few years now as part of my University's outreach program. Audience members are usually well-educated but may not have much knowledge of ...
1
vote
2answers
136 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. ...