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

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7
votes
0answers
64 views

Value in retracing mathematicians' steps (specifically Galois)?

So I'd like to learn Galois Theory, which I am probably not "qualified" for in an ordinary sense (I've never done abstract algebra, and I'm just now learning linear algebra in my vector calculus ...
1
vote
1answer
38 views

Analytic skills in applied math

I am an unexperienced undergraduate student just took few basic math classes. And I have found analysis classes really interesting, like basic analysis, measure theory and functional analysis, and ...
1
vote
1answer
162 views

Is it worth it to start over in math?

Alright, so I wasn't sure where to ask this question but this website seemed the most relevant. I wasn't too good of a math student in middleschool and highschool, I got through my classes, sure, but ...
0
votes
0answers
47 views

Easiest Book to start Manifolds.

Ok, so here is the thing. I do not like analysis,Calculus or topology much, nor are they my strong point, but next week I have an exam on manifolds which I have a course First time in my life. I have ...
157
votes
29answers
16k views

Too old to start math

I'm sorry if this question goes against the meta for posting questions - I attached all the "beware, this is a soft-question" tags I could. This is a question I've been asking myself now for some ...
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 ...
34
votes
3answers
3k 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 ...
68
votes
24answers
13k 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 ...
5
votes
0answers
82 views

What does a day in the life of a mathematician look like? [on hold]

I'm an undergraduate student trying to get into a graduate school for mathematics. Before I apply, however, I wanted to know what a typical day would look for people with PhD in math in various fields ...
1
vote
0answers
36 views

Best way to learn material dealing with cosets, quotient groups and the isomorphism theorems

I'm self studying abstract algebra from Abstract Algebra by Dummit and Foote. I've been able to get through the first few chapters and do problems without any issue, until I hit the material on ...
19
votes
1answer
973 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 ...
4
votes
4answers
333 views

The maths required for an economics degree

I have a degree in computer science and I wanted to do another degree in economics. However, my maths have been weak since high school always scoring slightly above passing rate. During my course of ...
1
vote
0answers
64 views

Math Graduate School (advice needed) [closed]

I'm currently a Senior Mathematics Major at a top 50 private Liberal Arts school. My Major GPA is ~3.5/4.0 and I will be graduating with approximately 13 Mathematics Courses taken (that equates to ...
5
votes
0answers
128 views

Can I use any theorem I know at an IMO? [closed]

What if I happen to know a (fairly well-known) theorem that trivializes a given problem set at a math contest? Could my answer be rejected (unless I provide proof)? For example, see this question on ...
2
votes
0answers
35 views

Typical course of study chart [closed]

I am an undergraduate student in math and am very interested in the field. I have bought a few books and self-studied on my own as i have free time. The next book i found on amazon was riemannian ...
2
votes
0answers
49 views

self-study hints

A question to those who took rigirous courses like math 25 (Harvard), MATH 295-396 Michigan and etc Being not able to collectively discuss problem sets from the course, as those who involved in ...
4
votes
0answers
75 views

should i try to continue in academia?

I actually have 2 questions. 1.What are my chances of going to grad school, 2.Should i go to grad school If I decide to go to grad school, what are my chances if: I got a C in Algebra first ...
-2
votes
3answers
418 views

I have a proof of the Collatz conjecture . Where should I submit my proof? [closed]

I have been working on the Collatz conjecture starting around 10 years ago. I would like to submit my proof for analysis. I would like advice on where to submit my proof.
50
votes
11answers
9k views

Am I just not smart enough? [closed]

When I was doing math, let us say for example, introductory number theory, it seems to take me a lot of time to fully understand a theorem. By understanding, I mean, both intuitively and also ...
2
votes
0answers
86 views

Soft question: Pure mathematics problem [closed]

I am having some serious trouble as a mathematics major. I am getting a degree in pure math, but I am must awful at taking the tests. I seem to be fine with understanding a theorem, definition or ...
326
votes
24answers
63k 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 ...
0
votes
0answers
44 views

Prime Gap Conjectures

There are many conjectures which can be proven by proving a tight enough upper bound for the prime gap above $n$. Some of these conjectures are stronger than other conjectures and imply the weaker ...
10
votes
5answers
157 views

Algebraic topology in high school?

This winter I am planning on teaching a small seminar (20 lectures 45 minutes each) for high school students. I was was given the freedom to choose the topic of the seminar, but it is supposed to be ...
1
vote
1answer
69 views

What is the best way to share findings?

I have discovered something. I have some things written in pencil on paper which prove some very important things in number theory. So I want to ask how to write a proof? How do I share my findings? ...
2
votes
1answer
52 views

Career counselling undergraduation underconfidence

I don't know whether this is the right place to ask this, but I expect you to help me. I am a third year undergraduate student in the Indian Statistical Institute, Bangalore. After completing two ...
18
votes
11answers
2k views

Gap year to study math

This is a plan in its earliest and thus least concise stage, so either bear with me or don't read the following babble (I bolded some of the important stuff): I am a high school graduate who is about ...
5
votes
1answer
139 views

Struggling with Topology. Any advice?

I'm a Junior Mathematics major at a small Liberal Arts college. I'm currently taking first semester topology (Munkres text). I feel like I'm barely able to tread water in this course. I was able to ...
1
vote
2answers
64 views

Enlightening ideas and methods that change one's appoach to problems, theorems or mathematics as a whole

I would like to collect a "big-list" of ideas and methods from different areas (although I'm particularly interested in elementary number theory, algebra, calculus, linear algebra, geometry, physics, ...
12
votes
3answers
1k 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 ...
4
votes
0answers
74 views

Learning linear algebra within the context of abstract algebra

I'm currently a freshman in college in a proof-based vector calculus course that teaches linear algebra concurrently with multivariable calculus, and given that the direct linear algebra instruction ...
6
votes
3answers
147 views

Books that you think you should have read during your undergraduate years

A quite popular question here is "If you could go back in time and tell yourself to read a specific book at the beginning of your career as a mathematician, which book would it be?" I would like to ...
0
votes
2answers
54 views

What is the relation between two integrals?

Let us suppose that we have two integrals, $I_1$ and $I_2$ with the same non negative integrand. The integration contour of $I_1$ is a subset of the the integration contour for $I_2$. What can we say ...
0
votes
0answers
22 views

How to select the integration contour

In the following two figures which describe sets, How many possible integration contour we have for the figure 1 and how many integration contour we have for figure 2.
1
vote
1answer
47 views

Interesting and not too difficult topics in geometry

I was asked to give a talk to a mixture of undergraduate and graduate students on a topic of my choosing from differential geometry. The students will mostly not be in geometry; however, I believe I ...
2
votes
0answers
79 views

How do I finish my problem sets on time? (The way I'm solving problems right now is very inefficient)

I'm embarrassed to say this. I'm an Applied Math major, I've been in college for three years, and I've never finished a problem set in my math classes. Despite this, I've only did well enough to least ...
4
votes
1answer
288 views

Is Abstract Algebra Necessary For A Thorough Understanding of Real Analysis?

Background Info: I have been studying (self-study) Real Analysis for a few weeks now, and with the help of people from here I have, comfortably, made it 3/4 of the way through the first chapter on ...
5
votes
3answers
188 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 ...
3
votes
0answers
90 views

What is set theory about? [closed]

What is the subject set theory about? What knowledge is required? I am thinking about what subjects I will choose, but I am not sure if I should take this one. That is the course content: Brief ...
1
vote
2answers
583 views

Ask your professor your questions?

Most questions occur to me outside of class, when I'm reading a textbook or working on an assignment, so I e-mail my math professors with questions. Otherwise the alternative is wait until next class ...
3
votes
0answers
34 views

My attempt to gather mathematical spaces in a drawing

There are many spaces (Sobolev, inner product spaces, etc.) that I am not using on a daily basis, but have to recall their definition from time to time. So I decided to draw a synthetic scheme of the ...
0
votes
1answer
34 views

Program that calculates pentagon, given the side lengths

Can you suggest me a free online program, that calculates the area of an irregular pentagon, given the side lengths? Any suggestions would be appreciated! That is the pentagon I am talking about: ...
2
votes
1answer
62 views

How to conceptualize unintuitive topology?

I found Project Origami: Activities for Exploring Mathematics in my university's library the other day and quickly FUBAR'd (folded-up beyond all recognition) the couple sheets of paper I had with me ...
2
votes
1answer
135 views

Rudin: Problem Chp3.11 and need advice.

I am working on the following problems and I have a couple of questions. Suppose $a_n>0, s_n = \sum_{i = 1}^{n}$ and $\Sigma a_n$ diverges. RTP (a) $\Sigma \frac{a_n}{1+a_n}$ ...
4
votes
1answer
86 views

How important is the “prestige” of your university for undergraduate mathematics?

I go to a university in Canada. It's not really considered a top university (it is one of the best universities in the province but is ranked really low nationally). I study mathematics here and ...
-4
votes
1answer
29 views

advanced algebra function word problem [duplicate]

can you please explain the answer and why you got it? the distance in feet $d(t)$ a dropped object falls in $t$ seconds is given by the function $d(t)=16t^2$. suppose you drop a ball from a height of ...
9
votes
3answers
280 views

How do you go about formalizing a concept?

I am reading Godel Escher Bach. I love it. In the first few chapters, the author shows what a formal system is and gives examples that eventually lead to a typographical formal system of strings that ...
10
votes
2answers
1k views

I'm feeling demotivated in my undergraduate course

I was a very good math student in high school. I was in the national level Olympiad team. Now I'm studying at the best college in my country with really good mathematicians. I've all almost all of my ...
6
votes
4answers
2k views

What are the prerequisites for taking introductory abstract algebra?

I am a maths student in my second year of university. I have taken and done quite well in Calculus I, II, III as well as a linear algebra (application focused) class. I have not worked much with ...
1
vote
1answer
103 views

How substantial an advance must be to justify publication in pure mathematics?

In order to publish a paper in pure mathematics, specifically functional analysis, do we really need to come out something which improves a lot of existing work in the field? I ask this because I ...
0
votes
0answers
43 views

Advices on which to choose, uncertainty or certainty?

Currently I am doing my final year project(FYP) on Large-Scale Distributed Storage System, where I apply finite field and coding theory to design new codes which can improve existing codes. I plan to ...