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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1
vote
1answer
204 views

Taking Differential Topology concurrently with Analysis

So I'm trying to finalize my schedule for this semester. I can't decide whether I should enroll in a grad level Differential Topology (Milnor) class or just the undergrad general topology one. The ...
33
votes
7answers
3k views

What are some good math specific study habits?

What are/ were some of your good mathematician's study habits that you found really worked for you? I'm a CS major at a respected school and have a solid GPA... However, I definitely lack when it ...
15
votes
2answers
294 views

How long should I insist?

While studying math, I usually get stuck on some topics, how long should I insist trying to understand it alone? What are the strategies for when this happens?
21
votes
6answers
1k views

What am I losing if I decide to perform all math by computer?

I solve mathematical problems every day, some by hand and some with the computer. I wonder: What will I lose if I start doing the mathematical problems only by computer? I've read this text and the ...
11
votes
3answers
388 views

Module Theory for the Working Student

Question: What level of familiarity and comfort with modules should someone looking to work through Hatcher's Algebraic Topology possess? Motivation: I am taking my first graduate course in ...
75
votes
9answers
7k views

Math and mental fatigue

Just a soft-question that has been bugging me for a long time: How does one deal with mental fatigue when studying math? I am interested in Mathematics, but when studying say Galois Theory and ...
6
votes
3answers
8k views

Math Textbooks for High School

I'm a high school student who is trying to figure out a complete course of self study for each year of high school. Is there a way to self learn grades of math without devoting too much time? For ...
7
votes
4answers
4k views

Advanced Linear Algebra courses in graduate schools

After studying general a linear algebra course, how would an advanced linear algebra course differ from the general course? And would an advanced linear algebra course be taught in graduate schools? ...
3
votes
2answers
414 views

Advice for study plan.

I'm studying math by myself, and now I'm wondering what is the most appropriate for me to study. I think my interest goes to rather pure mathematics than applied math or math for engineers. So far I ...
75
votes
23answers
19k views

Complete course of self-study

I am about $16$ years old and I have just started studying some college mathematics. I may never manage to get into a proper or good university (I do not trust fate) but I want to really study ...
41
votes
3answers
4k views

Motivation and methods for self-study

First, a little background: Beginning with calculus in my first semester of college, I fell in love with mathematics. That was the point at which the concepts became interesting to me, and I started ...
9
votes
1answer
875 views

How to address mistakes in published papers?

I have recently discovered some mistakes in a published maths article. I have contacted the author pointing out politely my concerns, but I got no specific answer, just a "polite" one, that the ...
11
votes
3answers
8k views

I want to start mathematics from scratch. What should I begin with?

I've just finished high school but I don't feel my knowledge of mathematics is good enough. I'd like to start again from scratch, possibly adding a bit (a lot) of problem solving to it. What is the ...
2
votes
0answers
353 views

Schaum's Outlines for self-study

I wish to learn Physics via self-study. I realize that I have a long way to go as far as Mathematics prerequisites: I will need to begin with Precalculus(I took that course many years ago, so I am ...
5
votes
0answers
194 views

Recommendation textbooks on D-module

I am going to take part in a seminar on D-module and applications, the textbooks that will be used are : D-modules, Perverse Sheaves, and Representation Theory, and A Primer of Algebraic D-Modules ...
5
votes
1answer
652 views

How to select an field of study?

As my question implies, I am a young, developing mathematician, with concerns about my future math career. In particular, I'd like to know how to select a future field of study. Through my courses ...
19
votes
5answers
5k views

Graduate school self-doubt (currently an undergraduate)

I don't know if this is the right place for such a question, so please redirect me to a more appropriate place if necessary. My main question is, if you go to a small school, are you doomed to fail ...
50
votes
7answers
2k views

Am I too young to learn more advanced math and get a teacher?

I am still 15 years old, but I am very interested in pure math. I have been teaching myself though books, from the internet and from others for the past year or so. I haven't mastered all the topics ...
14
votes
7answers
2k views

Teaching abstract maths concepts to young children.

I am interested in opinions and, if possible, references for published research, about the pros and cons of teaching abstract maths concepts to young children. My younger brother (five years old) ...
6
votes
2answers
460 views

Recommendations for real analysis

I have completed two courses in real analysis that covered up to chapter 9 in Rudin's Principle of Mathematical Analysis (and one on complex analysis). So if I am interested in continuing on in ...
9
votes
1answer
2k views

Tips and examples for a poster presentation in pure mathematics

I will be presenting a poster in a few weeks but have no experience with them. I've seen and given plenty of talks, read and written papers, but I have never made or even seen a poster in pure ...
18
votes
2answers
2k views

Spotting crankery

Underwood Dudley published a book called mathematical cranks that talks about faux proofs throughout history. While it seems to be mostly for entertainment than anything else, I feel it has become ...
10
votes
4answers
2k 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 ...
47
votes
5answers
2k 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
179 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 ...
7
votes
1answer
782 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 ...
14
votes
8answers
2k views

What math should a programmer know?

I am an application programmer focussing on Line Of Business (LOB) applications. I am from non-mathematics and non-CS background. What mathematics should I learn which help me improve my programming ...
5
votes
2answers
609 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? ...
2
votes
2answers
2k 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
votes
3answers
283 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
994 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 ...
20
votes
4answers
1k 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
201 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 ...
9
votes
3answers
2k 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 ...
4
votes
1answer
728 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
296 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
126 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 ...
64
votes
7answers
6k 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
625 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 ...
25
votes
5answers
4k 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 ... ...
3
votes
1answer
222 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 ...
10
votes
0answers
579 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
283 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
218 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
2k 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
383 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 ...
8
votes
2answers
1k 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 ...
30
votes
4answers
4k 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, ...
4
votes
0answers
657 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 ...
3
votes
4answers
351 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 ...