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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30
votes
10answers
2k views

How do mathematicians find formulas?

How do mathematicians find formulas? For instance, the area of a triangle is $$\mathrm{area}=\frac{\mathrm{base}\times \mathrm{height}}{2}.\tag{1}$$ When I study maths, the book I am using tells ...
1
vote
2answers
52 views

How can I start to learn proof theory?

I'm studying computer science and I realized that I have problems in working with mathematical proofs. They are for example part of my class Formal Systems and Automata. I'm really interested in ...
2
votes
1answer
36 views

Does set theory help understand machine learning or make new machine learning algorithms?

When I was in a university, I didn't major in math but took some math classes. However, I dropped out of math classes pretty quick. Some person recommended that I learn some set theory because it'll ...
0
votes
2answers
56 views

How to remember various set operations very easily?

I need an way to remember the set operations very easily. Does anybody have any idea? For example, how do you remember the distinction between Set-Intersection and Set-difference? I regularly mess ...
2
votes
2answers
66 views

Prove that $\mathbb{Q}(r+s\sqrt{t})=\mathbb{Q}(\sqrt{t})$.

Let $r,s,t\in\mathbb{Q}$. Prove that $\mathbb{Q}(r+s\sqrt{t})=\mathbb{Q}(\sqrt{t})$. Ok. So I've fallen a little behind in my algebra class, and I'm a bit confused on how to approach this ...
0
votes
0answers
57 views

How to understand Differential Equations?

I'm taking Differential Equations -II course this semestre and I'm in a big trouble. The problem is, I don't know how can we find the solutions, how can we be sure whether the solution(s) exist or ...
0
votes
0answers
11 views

Formula to convert currencies

I know this currency exchange rates: 1.000000 USD = 0.943837 EUR 1.000000 USD = 0.683463 GBP What would be the formula to find: 245 EUR = ??? GBP
1
vote
1answer
64 views

Learning mathematical concepts

Our teacher loves to test us on pure concept based questions and test if we really know what we are doing when learning a particular lesson. For example, when we first started learning about ...
1
vote
0answers
35 views

Is there a companion to the book 'A Synopsis of Elementary Results in Pure and Applied Mathematics' by George S. Carr?

A Synopsis of Elementary Results in Pure and Applied Mathematics by George S. Carr is as most of you probably know a book that was famously used by the great mathematician Ramanujan. It is said he ...
8
votes
1answer
71 views

Importance of Exercises in Mathematics for Self-Studying

I am a high school student wanting to major in Mathematics in the future. I started to like Mathematics recently, starting a year ago and I watched some interesting math videos on YouTube for fun (ex: ...
0
votes
2answers
69 views

High school looking to prepare for university

I am a high student and doing the general math course at my high school, it will cover: Geometry Graphs and Relations Matrices Statistics Next year I want to enroll in a science degree and major ...
378
votes
25answers
73k 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 ...
19
votes
7answers
3k views

Mathematical Career Advice to a young 16 year wannabe mathematician [closed]

I am high school math enthusiast I am very much interested in mathematics. I try to learn stuffs from the internet but I can't seem to find the resources and am also confused about where to start. I ...
0
votes
2answers
30 views

How to say when the integral converge and when diverge?

I have the following integral. $$I=\int_a^b |x|^{-p} dx$$ where $a<b$ are finite real numbers and $p\leq 0$ is a non-negative real number. If we start solving the integral we will come up the ...
0
votes
1answer
242 views

Does one necessarily need an MS in Math before taking a PhD in Math? [closed]

I finished bachelor's in mathematical finance and am nearly finished with master's in mathematical finance (I am already done with thesis), and I plan to pursue a PhD not in mathematical finance but ...
3
votes
0answers
352 views

Can I get a PhD in Stochastic Analysis given this limited background?

General advice on PhD apps welcome Given my limited background in stochastic analysis and other information (below), can I apply for a PhD with stochastic analysis for my dissertation topic? 1/4 I ...
1
vote
2answers
54 views

Are there any databases for PhD dissertations?

I just know ProQuest which supplies some PhD dissertations. However, it's hard to find some the dissertations of French and German. So are there any other good databases for dissertations of French, ...
3
votes
1answer
132 views

Advice on mathematical cources and profession

I am a class 9 student studying in India. I deeply love mathematics and I am aspiring to become a mathematician ( I am aiming for research and development). My hobbies include learning and trying to ...
74
votes
9answers
6k 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 ...
1
vote
0answers
22 views

Partial Differential Equations Methodology

I am currently studying PDE's i got an almost standard methodology for the First order PDe's mostly using the characteristic's Method.Now Im on the Second order Pde's .So i wanted to get some things ...
43
votes
12answers
4k views

I almost quit self-studying mathematics, but should I continue?

Before I move on to the main idea of this post, I need to tell you some background information about myself. Hopefully, it proves useful for you in giving me advice. I'm a 16 year old high school ...
6
votes
2answers
261 views

How should one go about obtaining “mathematical maturity”?

tl;dr: Is mathematical maturity better obtained by doing hard subjects slightly out of your reach, or by doing more simple subjects to gain experience? The end of the semester is close, and I ...
4
votes
2answers
96 views

Quality of Videos Lectures and Lectures vs Textbooks

I am a student trying to learn different subjects by watching video lectures and reading on my own time. I was wondering if the lectures from ICTP and nptelhrd are a great use of my time. I tried ICTP ...
1
vote
0answers
23 views

Book Suggestion, Analysis (Multivariable Calculus)

I am doing my 4th Analysis course. Now we are doing functions from $\mathbb{R}^{n}$ to $\mathbb{R}^{m}$ And we are talking about differentiabiity . I have a lot of problems understanding the course ...
3
votes
4answers
122 views

Good way to convince a young kid that $0*0 = 0$?

My little brother (6 years old) asked me a question ("What is $0*0$?") and gave an answer to his own question which I found ridiculous so I refuted it but he still thinks he is right. He says that ...
2
votes
0answers
53 views

What topics should I study to understand this document?

Background I'm trying to understand a document I found online. The reason I'm reading it is because I need to translate the Nedelec element into code for my research. Problem My background is in Food ...
6
votes
3answers
223 views

Career advice: Mathematical neuroscience

I need some advice about my career. Currently, I'm an undergraduate student of math. Since I can remember, I wanted to be a scientist, so I decided to go for applied math. The field that I'm ...
1
vote
1answer
146 views

What should I study to understand this paper? [closed]

I study computer science on bachlour level and I will soon start to write my thesis. I found a project and my intended supervisor sended me some papers to read[1]. I understand nothing when I read it ...
23
votes
4answers
3k views

Math GRE Subject Exam

I am studying for the GRE Mathematics subject exam [1]. I am looking for tips regarding how to more effectively study for it. Does anyone know of any good study materials or have any tips in general? ...
1
vote
1answer
107 views

In balancing effort and advancement in what concerns learning

What's new besides showing modern advancements in modern mathematics as well as eloquently written notes also contains some good advice to young people like me in this room (career advice:!). in ...
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 ...
6
votes
2answers
469 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 ...
2
votes
1answer
44 views

Ackermann Function - Book recommendation

What books would you recommend me for the topic "Ackermann Function" ?? I will have a presentation at the end of the semester for this topic and I would get some information...
9
votes
1answer
105 views

Mathematical Research seems daunting [closed]

Suppose you are a research mathematician. I imagine your problems are generally unlike the problems of fellow scientists in the physical sciences, because you deal with proofs, and proofs demand ...
3
votes
0answers
36 views

Advice on methods to capture lecture board and add notes [closed]

I am looking for a method to save the lecture materials, and examples without hand copying from the boards during the lectures. Unfortunately some courses don't have the material available, and ...
1
vote
1answer
192 views

Late summer 2015 opportunities for undergraduate [closed]

I am an undergraduate who was just accepted into an REU (yay!), but it only runs through July meaning I will have all of August free. As such, I am looking for some opportunities appropriate for 3rd ...
44
votes
15answers
4k views

How do I motivate myself to do math again?

I have been thinking of asking for help for a few months now but posting in a public forum like this is intimidating. Still, I am currently in a university studying mathematics as an undergrad. I took ...
1
vote
2answers
120 views

Book: Functional Calculus

Is there a good book that investigates in detail the various kinds of functional calculus? I'm having now some knowledge about unbounded operators and integration but I would like to understand ...
3
votes
1answer
69 views

Opportunities for Mathematicians to Work in Biological/Disease Areas

Yesterday, I was reading some of the question Can I Use My Powers for Good? and it got me thinking. It's quite an old question (3 years), so I don't want to resurrect it and also my own question's ...
46
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 ...
31
votes
10answers
3k views

How to be a successful math undergraduate student?

I am an undergratuate student in my first year of combined bachelor of electrical engineering and bachelor of mathematics. For my mathematics degree, this year I am supposed to take two math courses ...
3
votes
1answer
89 views

Can you succeed in undergraduate math, if you can't create proofs unseen and new to you? [closed]

TL & DR. Here I only mean proofs that I personally never stumbled across, either in a book, lecture, or practice question, NOT proofs that are too hard for even the best math undergrads. I ask an ...
16
votes
3answers
279 views

Good examples of mathematical writing (structural organization, style, typesetting, and so on)

A very famous question on MathOveflow asks for examples of good mathematical writing. Here, I'd like to narrow down the topic and ask: $\color{#c00}{\text{Question:}}$ Could you point ...
9
votes
2answers
392 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 ...
0
votes
2answers
67 views

Question about proving something is a group: in general not a specific structure

I could use some clarification, this isn't that difficult of a concept but I feel it's easily screwed up when doing so If you have a structure with a binary operation. First thing to do is check ...
3
votes
2answers
100 views

What is the difference between 'thus', 'hence' and 'therefore'? [closed]

When explaining and writing proofs for certain things in my notes I find myself using these words interchangeably however I'm left to wonder if there is a certain protocol to follow when using them? ...
3
votes
1answer
68 views

Should I drop a class which I may not be ready for in order to pursue more time for personal study [closed]

This is my first time asking for advice on here, but I have seen some great advice given here. I am a first year student in a graduate program and I am currently enrolled in a course on advanced ...
1
vote
1answer
1k views

possible topics for undergraduate project. [closed]

i don't know whether it will be appropriate to ask this question here or not but i need help. we have to a project in either pure or applied mathematics. my supervisor told me that it should not be ...
20
votes
2answers
305 views

How can a beginner researcher or Ph.D. student efficiently and effectively learn new concepts while staying motivated?

I hope this question is appropriate for MSE. The situation is that someone is reading a book (e.g. a monograph), possibly helpful in his/her research, and the content is sufficiently extensive or ...
7
votes
2answers
229 views

Am I wrong for wanting to give up studying analysis? [closed]

I am writing this because I'm having a hard time studying for analysis. This is my second time taking a real-analysis course and from the beginning, somewhere deep down I thought that I might be ...