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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2
votes
0answers
40 views

Efficient way to rigorously learn AI prerequisites

Question: My formal goal is to be able to rigorously understand the mathematical basis for modern statistical learning methods (ML, deep learning). I am told by math people that this involves: linear ...
-1
votes
0answers
19 views

Bayesian Theory: Is it doable from $0$? [on hold]

How hard is Bayesian Theory? It is listed as a postgraduate course (I'm an undergrad), I haven't done much stats (only a bit of likelihood and liner regression). Is it possible to learn and do it as ...
3
votes
1answer
125 views

Are there any modern mathematicians whose research interest is in “Probability Theory”? [closed]

I have seen professors in universities list "stochastic calculus", "stochastic analysis", "stochastic processes", "stochastic geometry" and "applied probability" as research interests, but are there ...
11
votes
4answers
2k views

Topics on Number theory for undergraduate to do a project [closed]

Im an undergraduate in the mathematics field ..So i wanna be alittle more productive and wanted to do an essay or project mostly on number theory or Algebra(Rings or Groups) and i want to ask if you ...
4
votes
6answers
3k views

Applications of Complex Numbers

For my Complex Analysis course, we are to look up applications of Complex Numbers in the real world. The semester has just started and I am still new to the complex field. I want to get a head start ...
14
votes
3answers
2k views

Does writing a bachelor thesis make sense?

I am a math student in my fourth semester. At my university, it is common to write a bachelor-thesis in the end of the bachelor program in almost all subjects while in the math undergraduate program ...
6
votes
1answer
316 views

Recommended research topics for high school student

I am a high school senior and I am interested in doing a math research. I hope someone can recommend areas or topics of research that are challenging, rewarding, and yet do not exceed my capability. (...
23
votes
11answers
3k views

Gap year to study math

This is a plan in its earliest and thus least concise stage, so either bear with me or don't read the following babble (I bolded some of the important stuff): I am a high school graduate who is about ...
48
votes
6answers
10k views

What is mathematical research like?

I'm planning on applying for a math research program over the summer, but I'm slightly nervous about it just because the name math research sounds strange to me. What does math research entail exactly?...
1
vote
2answers
113 views

Advice for an undergraduate math major [closed]

I've recently switched into the mathematics department at my university preceding my second sophomore semester. My question is the following: What should I study over the summer to best aid my ...
-1
votes
0answers
36 views

Advice on Research topics in Linear Algebra [on hold]

I am a rising senior undergraduate student. I have taken following courses and I have an opportunity to do a project in Applied Linear Algebra at a fairly good Mathematics department. I am trying to ...
3
votes
2answers
43 views

Material to learn some basic combinatorics?

I realize that I'm pretty weak when It comes to basic combinatorics, even with simple things like n choose k I don't feel confident. Furthermore, I've viewed some combinatorics books and the reasoning ...
45
votes
5answers
8k views

What are the work habits of the best mathematicians? [closed]

How hard did Gauss, Euler, Einstein,..., and so on work? How many hours were they spending learning and or thinking about their studies? Do the "best" mathematicians (or scientists) share many similar ...
45
votes
25answers
4k views

What books should I get to self study beyond Calculus for someone about to start undergrad mathematics?

I am struggling to pick out books when it comes to self studying math beyond Calculus. My situation is as follows. I have taken all math courses at my school (up to Calc BC and AP Stats) and I have ...
2
votes
2answers
2k views

what prerequisite classes must I have before I take Abstract Algebra and Real Analysis at the undergrad level?

what prerequisite classes must I have before I take Abstract Algebra and Real Analysis at the undergrad level? Will these prerequisites help me with these two coursea at the graduate level? or do I ...
1
vote
0answers
23 views

To prove: a product of profinite groups is again profinite.

I got stuck on this syllabus about abstract algebra: Let $J$ be a set and $\{ \pi_J \ : \ j \in J\}$ be a collection of profinite groups. Show that $\prod_{j \in J} \pi_j$ is again profinite. ...
5
votes
2answers
301 views

Surveys of Current (last 50 years) Mathematics at Graduate / Research level?

What books or broad survey articles survey the mathematics of the last 50-100 years? The ones I've read do a good job conveying mathematics from the ground up but typically assume a complete beginner ...
3
votes
0answers
64 views

Which books or subjects would you recommend for undergrads for grad school? [closed]

I am an undergraduate mathematics student in my third year. Most undergrad programs don't completely prepare you for grad school. I know Ph.D. students are telling me that there is a lot of crucial ...
86
votes
23answers
34k views

Complete course of self-study [closed]

I am about $16$ years old and I have just started studying some college mathematics. I may never manage to get into a proper or good university (I do not trust fate) but I want to really study ...
5
votes
3answers
1k views

start mathematics from scratch

I'm sorry if this question goes against the site. I have completed my engineering in computer science; we were taught to get degrees only in our university :(. I love mathematics but time passed ...
1
vote
0answers
41 views

Is it wise to select a research topic first and then choose an advisor? [closed]

I am a student of Pure Mathematics. I am interested in Linear Algebra and Abstract Algebra. As I was browsing the Internet for some good research topics which contains a flavor of linear algebra ...
81
votes
9answers
26k views

Learning mathematics as if an absolute beginner? [closed]

I dread mathematics, and I believe it's because I have come to associate mathematics with the experience of terrible teachers. All of my math teachers have been grumpy, but one in particular was the ...
6
votes
1answer
184 views

How to know if you are “tough enough” to study Algebraic Topology [closed]

I am graduating with a BA this summer and I am very interested in topology. I admit it, I never went that deep into topology and all I know is about point-set topology (metric spaces etc.) but from ...
20
votes
4answers
862 views

How do I tell if I am able to go to graduate school in math? [closed]

This is my first question on this site, and this question may sound disturbing. My apologies, but I truly need some advice on this. I am a sophomore math major at a fairly good math department (top ...
4
votes
2answers
282 views

Too “young” for advanced mathematics?

Is it harmful to try to learn an advanced topic that is way beyond your mathematical maturity, even if you're really interested in it? Should I focus only on standard material for undergraduates and ...
2
votes
0answers
49 views

GRE Math Resources

I am planning to give the MATH GRE. I intend to go to physics graduate schools but I may have to given the MATH GRE according to my college's requirement. I very much like maths, but I'm overloaded ...
0
votes
1answer
27 views

Number theory text.And advices.

What do you suggest as a must number theory text maybe leaning towards diophantine equations.I think im gonna do a project as an undergraduate.And my topic i think it will be " Aplications of ...
0
votes
1answer
130 views

Any advice to help visualizing/understanding theorems in Real Analysis?

I am currently taking a real analysis course and sometimes I can't really get the complete meaning/details of certain theorems. For example, one of the statements in the Heine-Borel Theorem saying ...
3
votes
2answers
674 views

Two sets can be separated by a hyperplane iff their convex hulls do not intersect

So I am supposed to prove that two sets of points in $\mathbb{R}^n$ are linearly separable in an n-dimensional space if and only if their convex hulls do not intersect. I understand the concept ...
1
vote
1answer
53 views

Spivak's Calculus for a soon to be physics undergraduate.

I'll soon start my undergrad. studies in physics and because of that I picked up Spivak's Calculus a while ago to get a solid foundation in single-variable calculus before I start my studies. However, ...
2
votes
2answers
80 views

Studying mathematics as an Undergraduate [closed]

This is not a question related to a certain topic in mathematics, but more a question about studying mathematics generally. (please forgive me if my vocabulary isn't appropiate, I'm not a native ...
3
votes
1answer
63 views

Calculus by Spivak - looking for a piece of advice from someone who has been through it.

I am currently self-studying Calculus by M. Spivak and before I started I was well aware of the fact that it is not an easy read. Right now I am going through the problems at the end of the very first ...
1
vote
4answers
73 views

Mathematics for Guidance, navigation and control

I'm finishing my math degree this week and have been looking for some subject to practice and study on my own while I'm doing some work as a programmer. I'm interested in getting my master's later but ...
0
votes
0answers
5 views

Reference for $L$ functions

What is the best possible reference to study $L$ functions for a beginner in this field? I have studied up to the Chebotarev Density Theorem in Algebraic Number Theory. Depending on that, which book/...
26
votes
4answers
2k views

How much time is too much (to put into a single problem)?

As a self-studier, I have no due dates and no time pressure. This is partly a good thing since I do have a life outside of my pursuit of mathematics. However, the lack of pressure is also a bad ...
3
votes
2answers
75 views

Dissertation on Integrals

I'm considering doing a dissertation on Integrals: Riemann, Henstock-Kurzweil, Lebesgue and more I'm wondering if I can do it. This is usually a masters level dissertation (while I'm an undergraduate ...
54
votes
6answers
3k views

Am I too young to learn more advanced math and get a teacher?

I am still 15 years old, but I am very interested in pure math. I have been teaching myself though books, from the internet and from others for the past year or so. I haven't mastered all the topics ...
0
votes
1answer
93 views

How to do complicated problem without messy mind?

I have trouble when doing complicated problem, when I look at a problem with so much information. (e.g. deal with some concrete example such as proving a 'ugly' space is homeomorphic to another 'ugly' ...
4
votes
0answers
70 views

Concrete Mathematics: Not taught how to solve problems.

I've read and studied the first 3 paragraphs from Concrete Mathematics and now I've made the first couple of problems. When I got to the actual homework problems I was lost because I tried to solve ...
20
votes
5answers
2k views

Bad at computations… but not math?

Very generally, the question I'm trying to ask is: Can someone be a good professional mathematician without being particularly good at (or even being - relatively - bad at) computations? More ...
9
votes
4answers
1k views

Where can one find (freely, online) mathematical articles with a fighting chance to be understood by high school students and undergraduates?

I am an undergraduate non-math major. I just finished my university's engineering calculus series, looking forward to linear algebra in the coming semester. To be frank, I always despised math because ...
14
votes
8answers
1k 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 ...
93
votes
5answers
4k views

“Advice to young mathematicians”

I have been suggested to read the Advice to a Young Mathematician section of the Princeton Companion to Mathematics, the short paper Ten Lessons I wish I had been Taught by Gian-Carlo Rota, and the ...
5
votes
3answers
10k views

What is the most effective way of teaching mathematics to my 7 year old kid? [closed]

I want to help my kid excel in Math. I can see she has some trouble with additions,subtraction, multiplication and division. Will it help if I let her memorize the multiplication table? or use ...
2
votes
2answers
79 views

Will conquering the two basic actuary exams, p and fm, be too difficult to do alone? [closed]

I'm currently a PhD student in mathematics at a decent sized graduate school, but I've been questioning my desire to continue on and finish my doctorate after I achieve my master's, which will occur ...
1
vote
3answers
4k views

James R. Munkres' TOPOLOGY, 2nd edition: How to check my work?

I'm trying to learn, or revise, some topology from James R. Munkres' TOPOLOGY, 2nd edition. I'm working alone; that is, I'm self-learning. It is quite fun. But the problem is how do I check if I've ...
1
vote
0answers
52 views

Good books on Algorithms for a math major without any programming experience?

I couldn't find this question anywhere else so it may not be apt. I am an undergraduate mathematics major and during my discrete math class I really enjoyed the study of algorithms and recursive ...
2
votes
1answer
309 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 ...
3
votes
0answers
25 views

Looking for references for learning the words and sentences used in proofs

I'm familiar with textbooks on logic, proof techniques, and sets. But I have yet to encounter a textbook that dives into the language used w/ definitions and sentence structure used in proofs, for ...