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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14 views

### Specializing in Statistics and Data Science, want advice on where to invest more study time

I want to find out where to focus my attention on mainly in order to become a good mathematician with focus on statistics and data science. A little background. I have bachelors degree in computer ...
246 views

### How does one become a mathematician? [closed]

I mean how someone goes from a student to become a teacher or a professor ? What is that state feel like ? Are you confident of the knowledge you have conquered over the years ?or there is part of ...
20 views

### How do you mathematically formalize standard concepts?

Is there a look-up table or reference of formalizations that describe standard conceptual modules? For example, I'm performing a classification of some set of features and it seems like there must be ...
21 views

### Book recommendations for undergrad stats?

I've taken a two-year break from studying (CompSci) and although I've had a firm foundation in statistics and probability, I've discovered that my memory has somewhat faded over time and I really need ...
47 views

### Self-studying Rudin's Real and Complex Analysis

I am planning to study both Real Analysis and Complex Analysis from Papa Rudin on my own, and I am looking for advice regarding how to do so. I wasn't able to find courses online with solutions to ...
58 views

### vicious circle of a circle area

I want to show that area of a circle $D$ with radius $r$ is $\pi r^2$. To do that I consider inscribed and circumscribed regular $n$-gons $I_n$ and $O_n$. Their areas equals to  S(I_n) = \frac 12 n ...
39 views

### Why is this equation not simplified in this paper?

I am currently reading this paper titled Online Traffic Control through gradient estimation using stochastic fluid models. I like how simple this approach is. To understand the paper, only knowledge ...
68 views

19 views

### Logic check in Peano arithmetic problem

I am trying to prove this theorem I am using induction Working assumptions 6.10 m+n$^{+}=$(m+n)$^{+}$ 6.22 Theorem Let m $\leqslant$ n denote the fact that m ∈ n or m = n. Then the relation is an ...
94 views

### Is there an operation over a finite set of integers (which size is $2^{128}$, or a power of two) that makes a non-abelian group?

I know that there is at least one operation on permutations that makes a non-abelian group: we can "multiply*" them, if we consider them as permutation matrices. And naturals are directly ...
24 views

### Exercise in Peano arithmetic and order relation

Show that if m<n. and k$\ne 0$ that km<kn Working assumptions: 6.22 Theorem Let m $\leqslant$ n denote the fact that m ∈ n or m = n. Then the relation is an order relation in ω. 6.19 Theorem (...
75 views

### Help me decide if I'm ready or not for this research topic

so a bit of background info on me. I'm a math grad student. My undergrad classes were mainly math-theory based stuff. I took Number Theory, Intro to Analysis, Intro to Abstract algebra, and such. I ...
57 views

### Is It Hopeless for Me to Try to Understand the Derivations of All Formulas I Use?

Recently, I've been doing some relatively more advanced math (multivariable and vector calculus) and the derivations of formulas are becoming increasingly complicated. I don't like using a formula if ...
96 views

### i'm 16 years old, what will I have to do from now on in the next few years to become a great mathematician? [closed]

I have 5 months to go to 17 years and I want to finish calculus 1 and in the other 5 months maybe finish lang linear algebra. I don't think I have talent or creativity (I'm so scared) but I want to ...
35 views

### Need help with Peano inequality theorem

The following deals with Peano arithmetic I have trouble dealing with inequalities Working assumptions : 6.22 Theorem Let m $\leqslant$ n denote the fact that m ∈ n or m = n. Then the relation is an ...
47 views

### Prove using induction,if A $\in$ n and n$\in \omega$ Then A$\in \omega$

Prove by induction If A $\in$ n and n $\in$ ω then A$\in$ ω Problem is from Pinter’s a book of set theory 6.1 Definition By the set of the natural numbers we mean the intersection of all the successor ...
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### Prove: if $m \in n$ then $m^+ \subseteq n$.

The following is exercise 5(d), section 6.2, from A book of set theory, by Charles Pinter (pg. 122). 5. Prove the following, where $m, n, p \in \omega$. d) If $m \in n$, then $m^+ \subseteq n$. ...
14 views

### Lookin for equivalent term inZFC

My question is there any equivalent term in ZFC for a p-sequence. I never heard of it. This is taken from Pinter’s:A book of set theory Let A be a partially ordered set such that every chain of A has ...
163 views

### Problem Books in Measure Theory

I'm taking a course in measure theory and the professor isn't following a textbook. Of course, he will be assigning homework problems, but I feel like just doing homework problems is never enough for ...
74 views

### Advance Linear Algebra Textbook Recommendations

Does anyone know of a good textbook that covers the following topics: linear regression, ridge regression, lasso regression, principal component analysis, multi dimensional scaling, perceptron, ...
18 views

### Undergrad major for network analysis and mechanism design

So I have to choose an undergrad major between maths or economics for university. I plan to pursue higher studies in fields of social/economic network analysis, game theory and mechanism design. I ...
43 views

### Getting stuck in self-study in math heavy field: how to look for collaborators?

I have been self-studying some topics in theoretical statistics and find that I often come across questions that are very difficult for me to answer, even with days of work and reading. Sometimes they ...
76 views

### Is analysis all about epsilons? (Inspired by another question from here)

Yesterday, while I was browsing the new questions, I came across this one How is analysis beautiful? -- confusion from an algebraist, which brought up an interesting question, especially for the ...
45 views

### soft question about reference for flow in differential geometry

I was reading Lee's smooth manifold textbook chapter 9 integral curve and flow I can't really handle this chapter, for example: the fundamental theorem for the flow,flowout theorem, canonical form ...
71 views

### How to determine your field of research?

This is probably going to be a long post, but its something I've always wanted to know and I believe many could profit from it. How do you determine a field of research? Of course, this question can ...
68 views

### What should I study next if I enjoy thinking about problems such as these?

So, until now I have studied a fair amount of linear algebra(matrices and determinants mostly, but some vector spaces too), abstract algebra(groups-up to topics such as the Sylow Theorems, FTFGAG, ...
55 views

### Courses to take as a maths undergraduate planning to go to grad school

I hope this is an appropriate place to ask this question. I don't have anyone else to ask this. I am starting my second year in university as a maths undergraduate. Right now, we have a curriculum ...
114 views

### How to become more creative in problem solving? [closed]

I am 16 years old and I am doing everything to improve in mathematics and one day try to do something important as I want to become a mathematician. Many say that the fundamental character for being a ...
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### For those familiar with Folland's real analysis, may I skip chapters 4 and 5 to continue pure measure theoretic topics?

So i'm self-studying measure theory and i'm finishing up chapter 3. I don't have much time before my semester begins and I wanted to continue pure measure theory topics (namely L^p spaces and radon ...
139 views

### How can I prevent silly,frustrating mistakes while solving math problems. [closed]

I face this problem since a long time ago,and it really annoys me. I am “relatively” good at mathematic , but would always get “relatively” low grades in math tests I mainly lose grades because I ...
122 views

### How to learn math at a high pace/volume?

Background: I am a graduate student in a mid-tier U.S. university, and I am struggling. I feel like I during my undergrad, I haven't aquired the neccesary skills to keep up with the high volume/pace ...
79 views

### How do you efficiently take notes? [closed]

I've recently realized how ineffective my notetaking strategy is, especially in proof-based classes. Generally, I copy every word that professors write on the board, but this is not allowing me to ...
50 views

### Some questions about prime number research

I'm an undergraduate who is studying for determination of prime number with my academic advisor. Before I meet her, I want to prepare more hardly. So, I'd like to ask you some questions that I'm most ...
73 views

### Is it useful for an engineer to study projective geometry? [closed]

I'm an engineering student, is there any application of projective geometry that can be a useful skill to have?
17 views

### Book Recommendation for Proving Inverse Laplace Transform using Fourier Transform

What is your recommendation to understand proof of Inverse Laplace Transform using Fourier Transform in detail? By the way i found one book that talked about it from Mathematical Methods for ...
56 views

### Geometric Measure Theory prerequisites

What are topics good to familiarize oneself with, if one wants to study geometric measure theory? I've learned exterior algebra (Grassmann algebra), and I want to know if I should seek anything next, ...
411 views

### Restart mathematics

I am 73 yo who has not been to a math class for 50 years. I know there is a completely new mind set needed to approach math problems and I need a starting point. What is the best Algebra book ...
25 views

### What should I do if I can't see through abstractions in complex shapes

I am recently solving Problems & Solutions in Euclidean Geometry. I have learnt a lot of facts regarding to parallelogram, triangles, areas etc etc and solve quite a lot of questions. For the most ...
52 views

### Galois theory or algebraic topology for advanced probability theory

I am an undergraduate student interested in probability theory.I have an option to take either Galois theory or Algebraic topology as part of my course.I want to know which one will be more useful if ...
116 views

### Can High school student take Putnam contest? [closed]

I am a Canadian High school student and intend to take Putnam contest this year, a well-known annual mathematics competition for undergraduate students. According to the Mathematical Association of ...
130 views

### How to study mathematics [closed]

I've been self studying math for 6 months, i'm a computer engineering student and I just know a little bit of calculus, linear algebra, abstract algebra, logic, set theory, but not much at all, my ...
80 views

### Active research on the subject of general topology

I've lately been told that the subject of general topology, like what Hausdorff and Kolmogorov dealt with, is a a dead subject research wise. I have been wondering however whether this is indeed true, ...
175 views

### Will only studying Serge Lang's Basic Mathematics be enough to start single variable calculus from MIT OCW? [closed]

I wasn't the best at math and mostly learned by memorization. I have manged to graduate with a degree in computer science but I performed with C's and B's in most of my maths classes. I would like to ...
354 views

### How may I teach myself pure mathematics “from scratch”? [closed]

I'm in my 19's and I keen on becoming a mathematician yet currently I can't fund going to university. I am to work as a customer service representative in order to linger. I harness mornings to study ...
163 views

### Just finished Highschool and I am starting my degree in math after the summer, but in the mean time what subjects should I try and study?

Hi I just finished Highschool, I'm starting a degree in math when the summer is over but I want to do a bit of self-studying just for fun. As you might expect I am not very knowledgeable of college ...
68 views

### Exercises for Calculus and Analysis for Graduate School Entrance Exam for Tokyo and Taiwan University

Can anyone recommend exercise books for the following topic? I am applying for entrance exam to a few places in Taiwan and Japan for graduate studies in maths, statistics and data sciences, as their ...
67 views

So I have become familiar with the basics. I have read both GRAPH THEORY WITH APPLICATIONS by Bondy and murty and Richard J. Trudeau - Introduction to Graph Theory. How do I take graph theory to the ...
91 views

### Proof Preparation [closed]

I'm planning on taking Abstract Algebra and Real Analysis in the future, but I realize I am very lacking in "mathematical maturity". Having only taken a computational linear algebra class (...
Well I am preparing for the $\textbf{IMO}$ and I had this really small doubt actually. For geometry I'm basically following $\textbf{EGMO}$ ( I understand going thru it wont make me a pro but its ...