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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0answers
23 views

do Carmo or Pressley as introduction to Differential Geometry?

I'm choosing between these authors for self-studying Differential Geometry. The contents seem pretty similar for both books and I was wondering which book I should choose. The level of these books ...
4
votes
0answers
61 views

A discontinuous function $f: X \rightarrow Y$ satisfying: for each closed ball $B$ of $Y, f^{-1}(B)$ is closed in $X$

Find a function $f: X \rightarrow Y$ between metric spaces $X$ and $Y$ that is not continuous but has the property that for each closed ball $B$ of $Y, f^{-1}(B)$ is closed in $X$ Solution Attempt: ...
5
votes
3answers
453 views

What is the pre-requisite knowledge for generating my own integer sequence?

I've recently come across the On-Line Encyclopedia of Integer Sequences and I'm completely fascinated by it; something about how easy integers are to grasp and yet how complex the sequences are. I ...
1
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1answer
95 views

Advice for a math grad student needing a sixth year [closed]

I am a doctoral student (pure math) who might need a sixth year to complete his PhD. My school might lack the funds to allow me another year as a teaching assistant. At least, there is no guarantee of ...
0
votes
1answer
66 views

Background for Graduate Real Analysis I Class [on hold]

This semester, I have signed up for a graduate Real Analysis I course (really a course in measure theory/Hilbert Spaces/Lebesgue integration) and have thus far attended two lectures. However, from ...
-2
votes
0answers
14 views

Some difference in notation in a project report [on hold]

I am focusing on a specific model in my study. When I am writing my project paper, for describing the estimation procedure, can I describe it more generally with some difference in notation than my ...
3
votes
1answer
105 views

Undergraduate mathematics competitions

I am a freshman (math undergraduate) here in Argentina and I am deeply interested in mathematical olympiads but I really need some advice. Right now, my problem solving skills are good but not that ...
6
votes
1answer
110 views

Jobs in industry for pure mathematicians

While I love research and academia and would prefer to continue there, I've found myself in industry and haven't felt it's a good match for my interests. Moreover, I'm constantly frustrated by the ...
0
votes
0answers
12 views

Unit Impulse response vs Impulse response in ODE

I'm was watching MIT OCW lectures for Differential Equations and in lecture 23, the professor goes over impulse inputs where impulse is $\int_a^b{f(t)dt}$ where $f(t)$ can vary or be constant. He ...
4
votes
1answer
112 views

Bridge between High School Mathematics and University-level Mathematics?

I've graduated from High School and I am going to major in math at a local University. I've finished High School Calculus and I've self-studied very very basic Multivariable Calculus, Linear Algebra, ...
2
votes
1answer
101 views

Failed Calc 2. It's the Algebra, stupid

Well, I took "Multidimensional Math" w/ Linear Algebra and Calculus 2 at the same time over a 6 week period for the Summer session. It was a disaster. I don't think my Algebra and Trig are good ...
0
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2answers
68 views

Next step to learn mathematics for a high school student? [on hold]

I am a high school student. I would like to study mathematics at university. Because I want to be successful in my studies and in productive research so I want to learn and practice more mathematics ...
3
votes
1answer
83 views

Troubling questions about probability

Suppose we have some random phenomena. Is it true that any event concerning the phenomena has a fixed "correct" probability? That is, the correct probability is the relative number of occurrences of ...
3
votes
1answer
59 views

Probability question from GRE subject test

I ran across the following problem while practicing for the GRE math subject test: Suppose $X$ is a discrete random variable on the set of positive integers such that for each positive integer $n$, ...
20
votes
2answers
310 views

Is there a profitable way to read mathematical proofs

Mathematical proofs are often presented in a sequential way, i.e., presenting definitions, building lemmas based on these definitions, building further results on these lemmas and finally invoking a ...
0
votes
2answers
60 views

Rudin's Chain Rule

Rudin's chain rule theorem goes like this: Suppose $f$ is continuous on ${[a,b]}$, $f'(x)$ exists at some point $x\in [a,b], g$ is defined on an interval $I$ which contains the range of $f$, and ...
1
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0answers
32 views

Dihedral group and symmetry group of icosahedron

I am studying abstract algebra at the moment, but I have several troubles picturing the dihedral group $D_n$ and the symmetric group of the icosahedron. For instance, I find it really hard to solve ...
1
vote
1answer
42 views

research in special function with Lie algebra

First of all, I don't know if this is the right place to ask about this. If not, please direct me somewhere I can get more help. I have to research in the field of special functions with a lie ...
2
votes
1answer
55 views

literature on advanced calculus [closed]

I need your opinions on this particular textbook: Advanced Calculus by Robert C. Buck. In my first year in college I finished two semesters of single-variable calculus and now I'm looking for a proper ...
0
votes
0answers
47 views

How to effectively learn from and use Ramanujan's notebooks? [duplicate]

I will come back and elaborate on the question if necessary (I must be off for a while...). But I'll try being specific. I have all four of Ramanujan's notebooks, with their respective Errata ...
8
votes
1answer
175 views

Do Electrical Engineering Researchers Usually Know Higher Math? e.g. Measure and Distribution Theory, Functional Analysis

I am an EE undergraduate student, and I recently took two courses in signals and systems. We were exposed to things like the Dirac delta (without mention of distributions), Fourier series (without ...
0
votes
0answers
48 views

What journals/websites do mathematicians have to check frequently?

There are so many news and publications updated online everyday. What are some must-read journals or websites? Such as AMS notices, or Arxiv.org? On one hand, I want some comprehensive news and the ...
3
votes
0answers
41 views

Classical geometry vs. p-adic geometry

I am interested in learning more about $p$-adic analysis and some of the geometric theories that are commonly used. However, it seems that many of the tools there are developed from analogous ...
12
votes
8answers
930 views

When trying to learn analysis from bottom up, what numbers should I first construct?

I am interested in studying more analysis and related topics. However, I want to make sure I do so well and without making too many broad jumps in my learning. In some books I have seen, the author ...
2
votes
1answer
65 views

How far can I get with graph theory?

I am an undergraduate who had recently finished his $2$nd year. I was wondering how far can I get with Graph Theory this summer. I am studying from Bondy & Murty's book. I already finished ...
1
vote
0answers
69 views

Kline, Lang, Silverman…which author provides thorough and rigorous Calculus up Multivariate & Advanced Calculus?

I know this question may appear subjective, but it is not, let me explain; note to mods --> please don't close this if it is considered too subjective, please alert me and I'll try to reword it. I ...
0
votes
0answers
29 views

How to Begin Learning/Doing Sport Statistics?

I would like to start playing fantasy sports using a statistical approach to help with picking players, setting line ups etc. I have a particular interest in football but am also interested in hockey ...
1
vote
1answer
31 views

Proving triangular inequality in general

I want some advice on approaching proofs of the triangular inequality for various metrics. I have a suspicion the answer is simply 'improve mathematical maturity' but hopefully there is a general ...
2
votes
3answers
109 views

How do I figure out my math aspirations? [closed]

I am really confused. Here's my present situation: I'm 18. I am about to start a computer science degree this August--going there only coz my parents want me to. I know most teachers for undergrads ...
0
votes
2answers
114 views

How important is it to learn latex?

So I am currently in my senior year (Undergraduate mathematics). And I am thinking to continue on and do my masters and PHD in mathematics. I need to now how important it is to learn latex and how ...
0
votes
1answer
75 views

Is the infinitesimal approach good.

I have heard of an infinitesimal approach to calculus. Is it better than the normal approach or is it the other way around.
7
votes
1answer
108 views

Would the professor take me seriously? [closed]

I'm a pure mathematics undergraduate. I have been working since a long time, and I am finally done with my little book. It handles a particular subject (which I won't mention). It is a collection of ...
4
votes
0answers
63 views

Matrix Calculus

My school offers Matrix Calculus class next semester. I have never heard about this subject before and got intrigued. After a short chat with professor I found myself unable to get rid of suspicion ...
2
votes
1answer
61 views

Confusion about ODE

so I am in a class for ODE and for me is is moving a bit quick. I am one year behind most of the class but thats note anything rare. But I am feeling very stumped on something now. Because, usually I ...
160
votes
14answers
10k views

Identification of a quadrilateral as a trapezoid, rectangle, or square

Yesterday I was tutoring a student, and the following question arose (number 76): My student believed the answer to be J: square. I reasoned with her that the information given only allows us to ...
1
vote
1answer
100 views

Is it ill-advised to read books casually for entertainment? [closed]

I'm a student who has about a year (and a few months) to go before entering a university and I've been reading some math books recently. I'm on Chapter 6 on Rudin's PMA, Chapter 5 in Munkres' Analysis ...
3
votes
2answers
150 views

Prerequisite of Algebraic Geometry

Algebraic geometry, as far as I know, is a very important branch of mathematics, which is also very difficult. I am going to take a try to taste that. Before really going into the field, I have two ...
2
votes
2answers
81 views

How do I get good grades in an exam?

I study hard throughout the year and I am able to solve most problems in the text assigned to us and I am frequently the only one who can solve the hardest problems in the assignments or the problem ...
5
votes
1answer
66 views

How to get the most out of attending a conference talk or a research presentation?

I'll say up front that I imagine there's a resource for this somewhere, but I was unable to find it. I've been attending conference talks and research presentations for about a year at my university, ...
1
vote
2answers
98 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 ...
4
votes
2answers
153 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 ...
2
votes
2answers
75 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
16 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
82 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 ...
0
votes
2answers
84 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 ...
11
votes
2answers
299 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: ...
1
vote
0answers
53 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 ...
0
votes
2answers
84 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 ...
0
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2answers
36 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
331 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 ...