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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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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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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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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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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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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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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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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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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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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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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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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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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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 ...
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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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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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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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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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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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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 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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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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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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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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How to restudy functional analysis
I am re-studying functional analysis to prepare for my next year's PDE courses, I've taken it this year but I feel like I am not very good at it. May I ask what is the study routine/strategy for ...
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Transcendental nature of natural log for proof validity?
I am following Understanding Analysis by Stephen Abott. I read a well bit into the book but I decided to go through and do the exercises through the book because I felt as if I wasn’t being rigorous.
...
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What is the optimal time one should spend on a textbook problem before deciding to seek the solution? [duplicate]
I’ve been grappling with a question that I’ve yet to find an answer to. I love solving math problems and I'm going to college this fall for a degree in computer science. Looking long-term, I would ...
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(Soft-question) Need a guidance and some truth [closed]
I have MS in mathematics. I am 26 years old. I aspire to be a mathematician. Haven't landed phd anywhere. Infact I didn't apply for phd for the following two reasons:
1.) I am not sure I can get ...
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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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Road map to learning about $\ell$-adic representations of $\text{Gal}(\bar{\mathbb{Q}}/\mathbb{Q})$
I am interested in learning about the congruence relations satisfied by the coefficients of modular forms, in particular I am interested in learning more about $\tau(n)$, the coefficients of the ...
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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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Book recommendations and study aid; in need of a little help
Please excuse the placeholder header; I currently don't know what to put up there, yet I might change it in the near future!
Today, I wanted to make a slightly different post and instead of asking a ...
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How to learn necessary concepts for research and avoiding a fake impression of understanding?
As an undergraduate engaged in applied mathematics research, specifically within mathematical programming, my work has quite some intersection with areas like algebraic geometry for polynomial ...
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When I finish an introductory abstract algebra book, where will I be? [closed]
In a few months, I think I'll be done with self-studying Introduction to Abstract Algebra by Nicholson. This book covers things like basic group theory, polynomials, factorization in integral domains, ...
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Advice about a composite book or series on mathematics
My question is mainly about a good book or maybe a series of books which provide me a very a basic understanding of topic of mathematics on an University level. To be specific, is there any series for ...
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What is usually taught after Linear Algebra and Real analysis? [closed]
I am a self-learner who loves pure mathematics. I study mathematics alone without university and I don't have professor or advisor to help me (So I am not sure what I can learn next). I mostly study ...
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Practical advice for balancing intuition and formalism in undergraduate math [closed]
I've recently started my second semester studying Mathematics at an undergraduate level. I'm attempting to find a practical framework through which I can process new mathematical concepts in a way ...
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Seeking Suggestions for PhD Topics in Model Theory, Focused on Combinatorics in NIP Theories and Tameness [closed]
Hello Math Stack Exchange Community,
As I embark on the journey of selecting a PhD research topic in mathematics, my interests are gravitating towards model theory, with a specific focus on ...
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Is there something 'lost' when learning ODEs 'theoretically' as a first-time learner?
I am a freshman (college) math student with semi-decent experience in rigorous maths: I've taught myself / taken courses in real analysis, abstract algebra, measure theory, linear algebra, and of ...
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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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What should I study to prepare for Stochastic Calculus
Context, I am an undergrad looking to take graduate stochastic calculus next semester. Unfortunately I do not have a whole lot of experience with probability theory as a whole. I've taken a first ...
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Help getting through a weird mental loop with mathematics [closed]
Let me start by saying I am not sure if this is the correct place to ask, but I would for sure prefer the question be answered by a mathematician.
I graduated as a physics major in 2021, I always ...
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General mathematics needed to eventually do research in mathematical logic
I am seeking answers from experts in mathematical logic about the amount (if any) of university mathematics I need to know in order to understand mathematical logic and later hopefully do meaningful (...
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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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A better way of presenting mathematical content
Traditionally, mathematical work is presented in a linear fashion. Books, papers and articles are single streams of text meant to be read sequentially, from beginning to end.
However, mathematical ...
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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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How to take maths notes, and generally to work with them, in order to understand as much as you can as best as you can?
I have hit a bit of a roadblock in my undergraduate studies. Our lectures assume that we should be taking notes, and that is entirely understandable: after all, what else can you be doing during a ...
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Symplectic or Poisson geometry first?
I know that symplectic geometry and Poisson geometry are strictly connected and I also know that historically symplectic geometry came first.
I know very very little about this two subbranches of ...
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Suggestions regarding Algebraic topology
I have recently completed my undergraduate degree. Now, I have started reading Algebraic topology Hatcher's book. I have read chapter 0 & 1 . But I am not able to solve excercise.How can I ...
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