Skip to main content

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...").

Filter by
Sorted by
Tagged with
0 votes
0 answers
23 views

An integrated math roadmap

Hi I am an electrical engineering undergraduate which want to learn more mathematics along the way. I want a math roadmap consist of books which would help me to integrate different fields of applied ...
Xenogears's user avatar
0 votes
1 answer
51 views

Higher Lemmas and Topics for the International Mathematics Olympiad

I am passionate about mathematics and want to reach IMO camp this year. I have learnt a lot of theorems and lemmas and have learned enough to clear the first 2 levels of IMO in my country.( I have ...
MathsGuy's user avatar
3 votes
0 answers
82 views

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 ...
HIH's user avatar
  • 451
0 votes
0 answers
33 views

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. ...
Co-'s user avatar
  • 1
0 votes
0 answers
27 views

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 ...
ten_to_tenth's user avatar
  • 1,426
1 vote
0 answers
76 views

(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 ...
Debu's user avatar
  • 1
8 votes
5 answers
1k views

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, ...
Krave37's user avatar
  • 543
1 vote
0 answers
70 views

Prerequisites for neukirch algebraic number theory

What topics are prerequisites for studying neukirch‘s book algebraic number theory? I have studied Groups, Rings, Fields, Galois Theory, Linear algebra. But I have no idea what is commutative algebra, ...
Cosimo's user avatar
  • 11
1 vote
0 answers
47 views

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 ...
Takamoto Yuji's user avatar
4 votes
1 answer
176 views

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 ...
John Doe's user avatar
  • 764
1 vote
0 answers
69 views

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 ...
b00nn1e's user avatar
  • 101
3 votes
0 answers
81 views

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 ...
wsz_fantasy's user avatar
  • 1,688
1 vote
1 answer
232 views

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, ...
iwjueph94rgytbhr's user avatar
0 votes
0 answers
82 views

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 ...
Sarban Bhattacharya's user avatar
1 vote
1 answer
401 views

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 ...
pie's user avatar
  • 6,456
2 votes
0 answers
81 views

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 ...
Amitai's user avatar
  • 351
3 votes
0 answers
145 views

Seeking Suggestions for PhD Topics in Model Theory, Focused on Combinatorics in NIP Theories and Tameness

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 ...
Shostak8's user avatar
  • 159
2 votes
1 answer
123 views

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 ...
adam dhalla's user avatar
4 votes
2 answers
240 views

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 ...
Connorlindquist's user avatar
1 vote
0 answers
57 views

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 ...
person's user avatar
  • 1,503
1 vote
1 answer
80 views

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 ...
cazanova's user avatar
  • 321
0 votes
1 answer
151 views

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 (...
user56417's user avatar
7 votes
3 answers
3k views

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 ...
pie's user avatar
  • 6,456
7 votes
2 answers
245 views

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 ...
Alex's user avatar
  • 943
0 votes
3 answers
815 views

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 ...
pie's user avatar
  • 6,456
0 votes
0 answers
136 views

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 ...
Barbatulka's user avatar
1 vote
0 answers
62 views

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 ...
Kandinskij's user avatar
  • 3,536
0 votes
0 answers
108 views

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 ...
Nope's user avatar
  • 1,222
2 votes
4 answers
131 views

Soft question - meta-thinking and problem solving internal dialogue. [closed]

For context, I am currently a first year Undergraduate student, and am currently trying to be more reflective of my mental dialogue and thought processes whenever I practice solving problems. Recently,...
Jason Xu's user avatar
  • 637
0 votes
1 answer
157 views

Real Analysis (Book Advice)

When I first decided to begin real analysis I had a look at the much recommended book 'Principles Of Mathematical Analysis' by Rudin, however I found it very complicated and understood very little of ...
Maximus's user avatar
  • 80
0 votes
0 answers
132 views

How do the contents of Abstract Algebra by I.N Herstein compare to others?

I recently ordered this book, which was much thinner than I expected, only 230 pages (I didn't realize this information was already online!). When I study a math subject I like to understand it well, ...
iwjueph94rgytbhr's user avatar
3 votes
0 answers
112 views

Is there a point where you KNOW a technique won't work?

Every time I'm trying to solve a tough math problem it always seems like I'm overthinking things after like 3-5 (and in one case like 4 days) hours of work (with a few breaks of course) and several ...
iwjueph94rgytbhr's user avatar
6 votes
2 answers
3k views

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 ...
agastya agrawal's user avatar
1 vote
2 answers
110 views

How to self-learn integrals using differentiation (but in reverse)?

i'm having a hard time solving even basic and easy intergral questions highschoolers solve. lets say my question is intergral $(ax+b)^2$ then i think of "what could have been the question" ...
Akab0_0m's user avatar
2 votes
2 answers
819 views

Is "A book of abstract algebra" by Charles C. Pinter enough for Lang's "Algebra"?

From what I understand, the book "A book of abstract algebra" by Charles C. Pinter is fairly elementary. On the other hand, the book "Algebra" by Serge Lang is very advanced. I'm ...
MSEU's user avatar
  • 1,148
0 votes
1 answer
104 views

How to decrease the randomness when solving a math problem? [closed]

When I try to solve a hard problem, I have no idea on what to do before I write anything on the paper: apparently, only after I spent hours on a particular problem I find the key idea by just a ...
pie's user avatar
  • 6,456
2 votes
0 answers
371 views

Prerequisites for Apostol's and Spivak's Calculus

I've just finished A levels in maths, further maths and physics and intend on going to uni to do maths and physics joint but I feel that A levels haven't prepared me enough. So my plan is over the ...
LEO's user avatar
  • 21
0 votes
0 answers
205 views

Abstract rigorous Multivariable Calc textbook

I just finished a theoretical calc3 course, the main text for the course was Spivak's Manifolds. I supplemented with Munkres, Analysis on Manifolds. The course heavily focused on the geometry of ...
Liza Struleva's user avatar
3 votes
0 answers
128 views

Am I doing math the right way? [closed]

I'm an undergrad and I will be completing my Master's Thesis the next year,based on elliptic curves.However coming to the end of my undergrad career as math major,I don't feel the same enthusiasm I ...
user631874's user avatar
3 votes
0 answers
131 views

Amount of mathematical knowledge required for starting Ph.D. in pure mathematics

How much mathematics should one know before starting a Ph.D. program in pure mathematics? For example what topics one must understand well to pursue a Ph.D. in Number Theory?
SARTHAK GUPTA's user avatar
0 votes
0 answers
60 views

Markov inequality when r-th momentum of $x$ exists.

Thank you for taking the time to read my post. I greatly value any advice you might be able to provide. I've recently learned about Markov inequalities in my probability and statistics course. $P\left(...
Woosung Jung's user avatar
1 vote
0 answers
236 views

How do you solve all exercise problems from a book if they are hard to do

I am reading Atiyah MacDonald's Introduction to Commutative Algebra book. Now I am enjoying reading the book but when I am doing the exercises I feel it is hard to do. In 20 problems almost 5-6 I can ...
Soham Chatterjee's user avatar
4 votes
6 answers
232 views

Explaining the concept of identities in Math to a grade 8 student

I was tutoring a student in the quadratic formula today, and wanted them to see different ways of solving $8x^2 - 64$. Suppose we want to solve $8x^2 - 64 = 0$ using the quadratic formula. I then told ...
John's user avatar
  • 1,950
1 vote
2 answers
430 views

How can I improve my comprehension of mathematical notation and avoid getting lost in the details, when there's no obvious visualization to rely on?

For context, I'm an engineering student nearing the end of my degree and I've been tutoring algebra, calculus, and statistics for years, so I'm not a newbie to math. It's only really been an issue in ...
Mikayla Eckel Cifrese's user avatar
1 vote
1 answer
248 views

How to develop mathematical ingenuity besides practicing problems(advice for Cambridge STEP Exams)?

I have been preparing for the STEP II and III exams administered by the University of Cambridge by solving several papers (I've done hundreds of problems). I am quite good at interpreting and using ...
Boson's user avatar
  • 43
1 vote
2 answers
219 views

Which Concepts to master before studying about large cardinals?

I am a undergraduate student interested in large cardinals since I've watched a youtube video called "How to count past infinity", and the concept of inaccessible cardinal that is introduced ...
Seungjun Wang's user avatar
1 vote
0 answers
92 views

A problem on the divisibility of central binomial coefficient

Erdos proved that, $$\gcd\left(\binom{2n}{n},pq\right)=1$$ For infinitely many $n\in\mathbf{N}$. Where $p,q$ are primes. Later the following idea was conjectured by Graham, That, $$\gcd\left(\binom{2n}...
RAHUL 's user avatar
  • 1,521
0 votes
0 answers
69 views

Finding Burton's elementery number theory tough, any lower level book suggestion

I am studying number theory from David Burton's book elementary analysis and second chapter on primes, in that exercise I had no idea how to start attempting questions on primes. The first chapter was ...
Olivia's user avatar
  • 167
3 votes
0 answers
81 views

Instructions on rigour for a beginner

I've just finished High School and I've always been very interested in math. Yesterday I was proving some very basic theorems on Geometry (Pythagorean/Hero's, sine/cosine laws/). At some point I ...
Nobody's user avatar
  • 323
1 vote
0 answers
93 views

The Summer Before University: Self-Studying for Proofwriting skill vs. Comprehensiveness

Apologies for the soft question. I have been puzzling over what to spend my time studying. I'm a high school senior, who only recently (during the pandemic) became interested in mathematics. I've ...
adam dhalla's user avatar

1
2 3 4 5
19