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

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7
votes
1answer
55 views

Bad at computations… but not math?

Very generally, the question I'm trying to ask is: Can someone be a good professional mathematician without being particularly good at (or even being - relatively - bad at) computations? More ...
2
votes
0answers
11 views

How to relate two integration contour?

How one can relate two integration contour? For example if I have an integration contour like $\int_{-a}^{a}f(x)dx$ here let say a=infinity. How I can say that the integral $\int_{2}^{3}f(x)dx$ is a ...
1
vote
1answer
44 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 ...
0
votes
0answers
49 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 ...
10
votes
1answer
124 views
+50

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 ...
5
votes
0answers
83 views

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

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 ...
4
votes
0answers
131 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
38 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
52 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
77 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 ...
1
vote
0answers
87 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 ...
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 ...
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 ...
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? ...
10
votes
5answers
159 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 ...
52
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 ...
4
votes
0answers
78 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 ...
0
votes
2answers
55 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
23 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 ...
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, ...
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 ...
2
votes
0answers
80 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 ...
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 ...
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 ...
4
votes
1answer
90 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
31 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 ...
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 ...
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 ...
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 ...
2
votes
0answers
91 views

A Compact Real Analysis book for a graduate student, who is short of time.

I am a Phd student in Computer Science and I want to focus on Machine Learning, especially on statistical methods. My problem is, I always keep hitting the wall when it comes to studying underlying ...
2
votes
2answers
55 views

Combinations: People want a beer, there are certain kinds of beer, but limited numbers of each kind

Four people go to a pub and each wants to drink a pint of either the lager, ale, or porter. However, there are only 2 pints of lager, 1 ale, and 1 porter available to drink. How many combinations of ...
1
vote
0answers
81 views

Learning math vs problem solving

Ok so I am about to start my final year in high school we will be learning calculus this year, but I already know single- and multi-variable calculus and linear algebra so I want to spend my final ...
1
vote
0answers
48 views

Working on strengths vs. weaknesses as an undergraduate student

I realize there's a lot of general advice on this site and elsewhere about studying mathematics, but I couldn't find anything about this, so I've decided to ask: as an undergraduate student, I'm ...
4
votes
2answers
186 views

How much set theory is necessary for serious logic?

I'm currently studying logic at my university and I have been trying to squeeze in as much set theory on the side as possible. Considering that I am spending quite a lot of time studying set theory ...
2
votes
5answers
795 views

How should I self-study calculus?

So I already took Pre-Calc, and ended up with a B both semesters. I am an incoming senior in high school. My special-ed case manager won't let me take it because she doesn't want to see me panic ...
0
votes
2answers
108 views

General question about undergrad math classes? [closed]

I'm currently in Real Analysis 2, and while I'm doing pretty well, it's just so much time and effort to finish all the problem sets and do well on the exams. I only have a few math classes left for ...
2
votes
1answer
63 views

Math required for medical statistics

I have never been good with Math. I talk to many of my medical colleagues and it seems to me that most of them have a poor understanding of statistics. Many of them claim to understand it but actually ...
2
votes
2answers
91 views

Going Back to Grad School After Being Away from Math

I graduated with a degree in Math-Computer Science(dual degree) from a college in the US in 2012, and have been working in the Software industry ever since. From 2012 to mid 2014 I was a software ...
1
vote
1answer
42 views

Progressive division

Given: L: known length of a line which is to be divided S1: known value represening the starting segment, also maximum segment value SN: known value representing the length of ending segment, also ...
12
votes
5answers
362 views

I need help finding a rigorous Pre-calculus textbook

I dislike modern textbooks; their cookie-cutter approach and appearance, over reliance on breaking things down into little boxes, the general spoon-feeding they engender and most of all the poor ...
0
votes
1answer
70 views

Dealing with questions with unknown answers

The vast majority of textbook exercises are worded essentially in the format: This assertion is (true/false). Prove this or find a counterexample. This, of course, is not how mathematics is ...
40
votes
6answers
4k views

What should an amateur do with a proof of an open problem?

Assuming that somebody is not an employee of a university, just a math amateur, and makes a proper proof of some well known open math problem, what should he do with it? Publish on the internet for ...
1
vote
3answers
158 views

Is tutor essential for success in mathematics? [closed]

Everyone in my Pre-Calc - Calc I class is failing, except the kids who go tutor. They get top percentile ranks in the class. Should I drop maths all together so I don't have to invest in a tutor? I ...
5
votes
4answers
234 views

What sequence should I study these topics in?

I will shortly list a series of topics that amount to what is essentially the first two years of an undergraduate degree. I'd like to know what is considered best order in which to study these ...
1
vote
3answers
40 views

What are the concepts that I need to understand before studying Fourier Analysis?

Background ( Long Story Short ) : For some reasons, I am taking a class in my university that focus on Fourier Analysis Laplace Transform, and Partial Diffiential Equations Problem : I have done ...