Questions tagged [advice]
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...").
934 questions
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Looking for guidance: academic career prospects [closed]
I’m writing here because I could really use some advice. I got my bachelor’s and master’s degrees in math from a small university in the EU. Following the advice of some good professors, I came to UC ...
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Textbook for self study of Graduate Level Linear algebra [duplicate]
Having just finished my masters, with my dissertation being heavily applied, but more than half of my credits in various abstract algebra courses(Modules, Semigroups, Number Theory etc.), I was ...
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How you started your research career, and can you do it alone? [closed]
I am applying to this scholarship to study Master's in Math, and it requires "Research plan", now such a request is weird because the bachelor level of math is just ABC.., its learning the ...
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How to study math to really understand it and have a healthy lifestyle with free time? [closed]
Here's my issue I faced;
I worked really hard studying Math, so because of that, I started to realised that I understand things better. However, that comes at a big cost:
In the last few years, I had ...
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Switching to numerical analysis/applied math [closed]
I am a 2nd year Computer science PhD student who is at a crossroads in regards of what should I do with my career.
My research has been on accelerating astrophysical codes. I have generally enjoyed it ...
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Too old to start math [closed]
I'm sorry if this question goes against the meta for posting questions - I attached all the "beware, this is a soft-question" tags I could.
This is a question I've been asking myself now for some ...
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Struggling to retain mathematical knowledge as a self-learner.
I’m a self-learner who studies mathematics because of a deep passion for the subject. However, I’ve been facing a persistent issue that has started to seriously affect both my progress and motivation, ...
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How to find existing solutions to problems
It is pretty often that I think of an interesting math problem, and similarly often that I get stuck. Historically I have found it difficult to locate solutions online, since I don't really know what ...
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How should I approach the exercises in "Theory of Numbers by Niven, Zuckerman, and Montgomery"? [closed]
I’m currently self-studying number theory using An Introduction to the Theory of Numbers by Ivan Niven, Herbert S. Zuckerman, and Hugh L. Montgomery. The book includes a large number of exercises, ...
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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 ...
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Find all roots of a Lipschitz function
I'm looking for advice to pick a numerical method to find all roots of a univariate function $f$ on a finite interval:
$f$ is Lipschitz-continuous with unknown $L$ (without that assumption, it is ...
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"Advice to young mathematicians" [closed]
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 ...
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Tips on how to find $K_{3,3}$ or $K_{5}$ minors
I am looking for general advice on how to find graph minors (for example $K_{3,3}$ or $K_{5}$) efficiently. I often struggle applying the Kuratowski-Wagner theorem for non-planarity, but want to ...
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Minimize checkmarks function - Advice for optimization algorithm
I'm looking for advice to pick a numerical optimization method for the following case:
find global minimum of a univariate function $f$ on a finite interval
$f$ is a black box, no derivatives known
$...
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How do I sell out with abstract algebra?
My plan as an undergraduate was unequivocally to be a pure mathematician, working as an algebraist as a bigshot professor at a bigshot university. I'm graduating this month, and I didn't get into ...
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What are some of the Websites/web-tools which must be a part of every mathematician's arsenal?
What are some of the web-tools which must be a part of every mathematician's arsenal? Tools which help mathematicians research, solve problems or even collaborate together!
Here is a list I gathered. ...
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How to develop patience in mathematics?
How to develop the patience in mathematics?
When you read the books like Rudin, Conway, etc., it takes a lot of time for one problem; sometimes $10$ hours each.
I usually devote one problem for $...
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How do you describe your mathematical research in layman's terms?
"You do research in mathematics! Can you explain your research to me?"
If you're a research mathematician, and you have any contact with people outside of the mathematics community, I'm sure you've ...
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Building Foundations for Geometric Analysis: Advice and Strategies?
I am a first-year graduate student, and I aim to shift my focus to geometric analysis because I have recently realized that it is likely the field I want to pursue. In the past, I was more focused on ...
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How Can I Truly Understand Mathematics Instead of Just Following Rules?"
I want to ask a somewhat philosophical question. I’m a 10th-grade student currently studying systems of linear equations. I’ve learned to solve both simple and relatively complex equations. However, I’...
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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 ...
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Prerequisites for understanding Maryna's Proof on sphere packing problem in dimension 8
I am a Math enthusiast pursuing a Minor in Mathematics (UG). I was always fascinated by elliptic curves and modular forms, and how they are used in proofs of these legendary problems.
For context, I ...
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Why is construction required in geometry?
I don't know if this is a good question to ask but I need some advice, anything is appreciated.
(Contruction here, doesn't imply geometric construction tools one)
Q1:In solving problems in geometry, ...
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I want to do mathematics similar to style of Grothendieck. How is that possible? [closed]
I am a person who enjoys math. Out of interest, I would like to ask a (soft) question. One of the reasons that I am posting this question is because in doing mathematics, it is hard to get rid of the ...
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Defining the "Finest" Equivalence Relation as an Extensional Equivalence Relation in Constructive Logic with forgotten Intensional Equality
Suppose we're working in a constructive setting where we don't have access to a notion of intensional equality. In other words, we are in a theory $T$ where there is no symbol that relates to the ...
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Generalizing Gâteaux derivatives and/or Clifford Analysis to $R$-Modules
I've been studying the intersection of Algebra and Analysis for a while. I read about Gâteaux derivatives, Clifford analysis, and generalized "structural" derivatives.
I am not following the ...
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Structuring/Planning Your First Original Research Project (graph theory/combinatorics - seeking advice)
thank you for taking the time to read this post.
Some Context on My Background: I am an undergraduate student in mathematics, and I recently coauthored my first paper with my summer mentor. While ...
user1497245
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How to study algebraic topology? [closed]
I'm graduate student in second semester
Since the class uses Hatcher's book, I read it and tried to solve exercises, But it's too hard for me.
The reason first is that it's hard to read. I'm reading ...
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Problem book recomemendations for a math major freshman who's behind [algebra/precalculus/geometry]
I'm in a marginally specific position, and need recommendations for problem books related to algebra, precalculus or geometry (any or all), that cover more difficulties than basic to intermediate ...
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What are the essential skills and abilities for pure mathematics? [closed]
I am interested in learning pure mathematics and I want to be better at it so I want to know what skills and abilities are most important for this field so I can improve them. I have asked two related ...
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Prerequisites and Stepping Stones to Study Advanced Number Theory [closed]
I just finished an undergraduate course on elementary number theory. I covered the following topics:
Divisibility, GCD, Euclidean Algorithm, Linear Diophantine Equations
Primes, Fundamental Theorem ...
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Trouble with 'elementary questions' as a beginner math student (Soft Question)
I've tried to make it clear that this is a soft question. I wanted to express a few of my questions/concerns on what I call 'elementary questions,' hoping to find some answers.
I don't have a set ...
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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?...
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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 ...
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How can I get faster at doing math? [closed]
In general, my level of mathematics is good with respect to the competitions that I need to appear in.
However, no matter what the competition is, whether it is an easier level or a more difficult ...
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How to get back to math and study abstract algebra? [closed]
I graduated (undergrad) with a math degree in 2023 and have been working in finance industry for a year (NOT quant trading, so not much math in my day to day). When I was in college, I tried to take ...
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What are some general guidelines or tips to reading a mathematics textbook? [closed]
I am an undergraduate who started down the math educator path but found pure math to be very intriguing. As I enrolled in higher math courses, I found reading the textbook to be ever more important. ...
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What made you choose your research field?
I was wondering how come modern mathematicians do not seem to discover as many theorems as the older mathematicians seem to have done. Have we reached some kind of saturation limit where all commonly ...
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Advice on problem solving in mathematics [closed]
I am in need of some advice on how to improve my problem solving in mathematics.
I have been taking calculus for a while now, and I have noticed something, I have never been able to actually come up ...
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Am I just not smart enough? [closed]
When I was doing math, let us say for example, introductory number theory, it seems to take me a lot of time to fully understand a theorem. By understanding, I mean, both intuitively and also ...
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How to retain mathematical understanding and gain more [closed]
I am going through a stage where my mathematical intuition(Olympiad perspective)is taking a hit and the problems that I had solved seem unapproachable now.I had for 2 months quit a lot of proof based ...
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Math and mental fatigue [closed]
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 ...
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What should an amateur do with a proof of an open problem?
Assuming that somebody is not an employee of a university, just a math amateur, and makes a proper proof of some well known open math problem, what should he do with it? Publish on the internet for ...
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How to efficiently find articles/theory/books on topics I want to learn more about
Thank you for taking the time to open this post.
My question is as follows: how do I efficiently find papers/books/talks/any academic resources that have been published about topics that I find myself ...
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GRE Subject Test - Past Papers, Books, Advice
This is not for the Maths part of the General GRE. This is for the GRE Subject Test in Maths. Feel free to add or comment.
How do I know the definition of rings or of anything on the GRE given that ...
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what is expected from a PhD student?
As a PhD student in applied mathematics or mathematics in general, are you expected to be able to prove every problem, for example, in an elementary real analysis book? I know it sounds silly but I am ...
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What to do with "half-learned" material
I have somewhat often found myself in the following situation, especially when self-studying a mathematical subject:
I'm reading a book on a certain topic, and at certain parts I don't immediately ...
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Nobody told me that self teaching could be so damaging... [closed]
Even though I've been teaching myself math for a couple of years now I only just started (a month ago) at the university. My experience is rather mixed.
For starters, I'd like to mention that I'm 21 ...
user195750
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Soft Question - Book Techniques with notes
Do you guys have any concrete techniques for consuming and extracting material and concepts from math texts quickly? My library is growing and I have a set trajectory of the texts I will read, but the ...
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How to be good at math :- Book recommendation or sources that help me to improve my mental arithmetic skill and mental mathematics skill
I am interested in improving my mathematical abilities and understanding. I wonder what it means to be good at mathematics and what skills are essential for to be good at mathematics in general . of ...
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