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
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1answer
71 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
190 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 ...
56
votes
11answers
10k 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 ...
0
votes
2answers
58 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
60 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
66 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, ...
8
votes
3answers
197 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
99 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
36 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
2answers
43 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
71 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
112 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 ...
-5
votes
1answer
41 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
290 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
104 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
46 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
120 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
1answer
101 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
54 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
195 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 ...
4
votes
6answers
1k 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
123 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
66 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
111 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
44 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 ...
13
votes
5answers
446 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
91 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
161 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
264 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
42 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 ...
6
votes
1answer
216 views

How much mathematics should a student of mathematical logic know?

I would like to know what areas of mathematic are directly related to mathematical logic, besides the usual courses on model theory, proof theory and computability. If you suggest only one book on ...
3
votes
0answers
84 views

In what order should I study?

I would like to study the basic fundamentals of mathematics from the beginning and move on from there as my understanding of the subject is lacking. In what order should I study? Arithmetic ...
2
votes
3answers
137 views

What is so special about $a*b^{ -1}$ equivalence?

This equivalent is used often in group theory. For example, using this equivalnce you prove Lagranges theroem and also this equivalence gives you the cosets and other things. This equivalence also ...
1
vote
1answer
87 views

A tenth grader's starting point on mathematics

This question primarily concerns the elementary books a Canadian high school student could read and work through to gain further insight into mathematics and be attracted to it. My brother, who has ...
1
vote
1answer
29 views

Is $g$ increasing?

Suppose $f:[a,b]\rightarrow\mathbb{R}$ and define $g:[a,b]\rightarrow\mathbb{R}$ as follows $$ g(x)=\sup\{f(t):a\leq t\leq x\}, $$ with $x\in[a,b]$. Someone told me that $g$ is an increasing ...
10
votes
3answers
385 views

A question from an engineering undergraduate

My question primarily concerns the necessary transition from an undergraduate program in electrical engineering to graduate program in applied mathematics or pure mathematics. I'm an electrical ...
3
votes
1answer
120 views

Actuarial Science or Financial Mathematics?

I’m a second year undergraduate student of Actuarial Science that equally loves finance and pure mathematics. I only knew of Actuarial Science as a career that suited best these two requirements ...
3
votes
2answers
52 views

Favorite Textbooks for introducing a subject?

I'm interested in learning more about number theory, about fractal geometry, and about probability. Anyone have any good recommendations? I've taken calculus and statistics at university if that helps ...
2
votes
1answer
88 views

How to see 4th dimension? [closed]

Anyone has tricks or methods? Great help, thank you. P.S.: Abstractly of course, not actually seeing 4D, which I don't think is possible.
3
votes
1answer
56 views

Re professional mathematicians working on several problems at once. Source needed.

Recently I read a quote from a working mathematician where he pointed out that professionals have to get used to carrying around several unsolved problems at once. Can anyone help me with the source ...
0
votes
0answers
57 views

Is it necessary to know all the details in proofs of theorems you study in PDE's?

I've been studying PDE from the book by L.Evans for some time now. I came across some statements in the proofs which I couldn't justify. But to complete the exercises I didn't need to know all these ...
36
votes
5answers
6k views

How hard should a mathematician work? [closed]

Of course I would never compare myself to, and don't expect to be, one of the great mathematicians. However, I am curious as to how my work habits, dedication and passion differs from theirs. How ...
6
votes
2answers
259 views

The best balance in studying Mathematics?

I'm a student studying Mathematics at a university level. I've completed Single Variable Calculus, Differential Equations, Multivariable Caculus, Real/Complex Analysis, and Linear Algebra and I've ...
2
votes
4answers
371 views

Should I read about Manifolds or Algebraic Topology?

I really enjoy doing maths and it fills quite a lot of my spare time. I'm starting my first year in the university on october and I probably won't have that much time for independent reading once ...
4
votes
0answers
106 views

Problem solving strategy?

This question has always bothered me, and I've never had a maths coach to guide me along the way and show me what to do next. Nevertheless, I did make top 50 nationally in my national mathematics ...
0
votes
5answers
136 views

Some examples of applications of Game Theory

I'm approaching my junior year of HS now, and I'm looking for a good science fair project to do. I love mathematics, so I decided to a category of mathematics that can help base logical conclusions to ...