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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0
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2answers
35 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 ...
9
votes
1answer
315 views

Balancing Coursework with original research

I am a first-year graduate student in a US university pursuing a PhD in mathematics. I am a bit frustrated in trying to balance coursework with original research. I saw students who spend most of ...
5
votes
1answer
168 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 ...
4
votes
1answer
153 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 ...
3
votes
1answer
74 views

Suggestions for calculus review for mGRE

I'm currently studying for the mGRE that will be given in October of this year and I'm having trouble deciding which books to use for the calculus review. I'm currently brushing up in Stewart's ...
3
votes
1answer
171 views

Changing streams in PhD

I've a masters degree from a reputed Indian university in pure mathematics, with a specialization in Algebraic Number Theory. However, I'd like to apply for a PhD in computational math/theoretical ...
3
votes
1answer
171 views

Literature on Chern-Weil Theory and the Chern-Gauß-Bonnet Theorem

At my university there are plans for a graduate seminar on Chern-Weil Theory and Chern's generalisation of the Gauß-Bonnet Theorem. Unfortunately I am having a though time in finding adequate and ...
3
votes
1answer
234 views

Learning roadmap for mathematical biology

Which courses (undergrad level but also master's level) in mathematics and statistics should be taken by a student aiming for a PhD in mathematical biology? The basics I imagine are: Calculus ...
2
votes
1answer
52 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...
1
vote
1answer
224 views

Will I have learned the prerequisites for self learning stochastic calculus and monte carlo method?

I'm an undergraduate econ major, and my main focus is in actuarial sciences, which as you may or may not know it's pretty mathematical. Some of the topics I will have to learn at some point on my own ...
1
vote
1answer
111 views

prove normality of famlity of analytic functions

I already proved normality for meromorphic functions that omit 3 values. I'm trying now to prove normality of family of analytic functions that omit two values. Is there any way to deduce any one of ...
0
votes
1answer
76 views

Intuition or wisdom for stability and instability properties of locally linear system. Boyce, p513, Table 9.3.1

Our instructor requires us to memorize this table for our differential equations exam. So I wonder if anyone has some deeper intuition or observation to help with this? For example, I noticed ...
11
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0answers
605 views

Prerequisite of Projective Geometry for Algebraic Geometry

I studied Euclidean Geometry in high-school, and I have not studied anything relates to geometry since I started studying in university. I am now intending to study Algebraic Geometry, however, I ...
6
votes
0answers
88 views

Strategy for self-studying after M.S.

For someone who has finished their M.S. degree in pure mathematics, what is a good way to keep learning mathematics within your specialization? Would you suggest reading research articles from ...
6
votes
0answers
197 views

What is the best way to go about learning math?

I know this is a very subjective question, but after struggling on my own for a while I figured I might as well ask it. I did all the normal math classes in college (LinAlg, MultiVariable Calc, ...
5
votes
0answers
267 views

Analysis or (abstract) algebra first?

Which one would you recommend? I only know calculus and linear algebra when it comes to university-level mathematics. Is one required to understand the other?
5
votes
0answers
90 views

Is there a proper etiquette for asking an author for their (mathematical) software?

This may not be the correct place to ask such a question. I have read a mathematical paper on multiclass total variation clustering. I wish to use the algorithm in the contents to compare with another ...
5
votes
0answers
874 views

which branch of maths studies Standard Logical Matrices

In classical logic you have truthtables like: & | T | F ---|---|--- T | T | F F | F | F In many valued logic you have tables like: (this one is ...
5
votes
0answers
105 views

A partial ordering on textbooks

After college, it has been very difficult to continue learning math as a hobby, I have the time for it, but I get incredibly frustrated when I run into something that it feels like I will never ever ...
5
votes
0answers
200 views

Recommendation textbooks on D-module

I am going to take part in a seminar on D-module and applications, the textbooks that will be used are : D-modules, Perverse Sheaves, and Representation Theory, and A Primer of Algebraic D-Modules ...
4
votes
0answers
57 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 ...
4
votes
0answers
201 views

How to balance learning and researching as a new PhD student?

As a new PhD student, how to balance learning and researching? I am in Australia and here we don't have any course in PhD period. I know I need to learn something about my programme, but sometimes ...
4
votes
0answers
297 views

Isolation and self-study

A little background: I am currently a sophomore (studying mathematics) at an unknown university in the Middle East. My mother is European so it does not make sense to study mathematics in the Middle ...
4
votes
0answers
295 views

start studying advanced topics in number theory

I am a first year undergrad and have had elementary course in Number Theory which includes only basic introductory topics like: divisibility,gcd-lcm,primes,congruences, number theoretic functions etc. ...
4
votes
0answers
696 views

Topic appropriate for undergraduate research program

This may be not appropriate to ask this kind of question here. But please feel freely helping me. In our Maths faculty, there is not a program like Undergraduate Research Program(URP), however, the ...
3
votes
0answers
38 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 ...
3
votes
0answers
498 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 ...
3
votes
0answers
113 views

Group Theory Research Topics [advice]

I'm currently a Senior Mathematics student in the US. I'm interested in Abstract Algebra, specifically Group Theory (I've taken a course that dealt entirely with Fields, but I enjoy Groups a bit more) ...
3
votes
0answers
44 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 ...
3
votes
0answers
278 views

Which is the best transitional mathematics book for self-teaching among the ones listed?

What is Mathematics, An Elementary Approach to Ideas and Methods - Courant Robbins Stewart How to Solve It, A New Aspect of Mathematical Solving - Polya Introductory Mathematics, Algebra and Analysis ...
3
votes
0answers
53 views

What should one do if one works on a problem and submits a paper only to find that it is already in some book?

What should one do if one works on a problem and submits a paper only to find from the editor, that the work is already in some book? The work is is not really easy to find on the internet and was ...
3
votes
0answers
107 views

My first simple direct proof (very simple theorem on real numbers). Please mark/grade.

What do you think about my first simple direct proof? What mark/grade would you give me? Besides, I am curious about whether you like the style. Theorem Let $I = [a,b]$ be a non-empty closed ...
3
votes
0answers
297 views

Bachelor Thesis - Galois Theory Research Topics?

I'm on the last semester of my bachelor's degree (undergrad degree) and I will be writing my thesis next semester. I have talked to a professor at my university and one of the topics he suggested was ...
3
votes
0answers
94 views

What is the most relavant math for statistics students?

As they say "the more math you learn the better". Unfortunately, I did not have a lot of mathematical training in my undergraduate. Now I am doing a master in mathematics, mainly to make up some ...
2
votes
0answers
57 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 ...
2
votes
0answers
39 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 ...
2
votes
0answers
93 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 ...
2
votes
0answers
281 views

How to Read Michael Artin's Algebra

I am currently reading Algebra by Michael Artin (for self study). I'm finding the book pretty interesting, but I'm still not sure how I should study the book. For example, should I try to prove every ...
2
votes
0answers
192 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
0answers
373 views

Schaum's Outlines for self-study

I wish to learn Physics via self-study. I realize that I have a long way to go as far as Mathematics prerequisites: I will need to begin with Precalculus(I took that course many years ago, so I am ...
1
vote
0answers
30 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
0answers
54 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 ...
1
vote
0answers
50 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 ...
1
vote
0answers
26 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 ...
1
vote
0answers
36 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 ...
1
vote
0answers
299 views

Partial Differential Equations Course And Differential Geometry Prerequisites

Is the ordinary differential equations course a prerequisite for the partial differential equations course for a person who has passed the integral calculus course? Is it really required to have ...
0
votes
0answers
23 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 ...
0
votes
0answers
43 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 ...
0
votes
0answers
22 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 ...
0
votes
0answers
15 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