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...").
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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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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,...
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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 ...
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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, ...
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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 ...
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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 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"
...
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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 ...
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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 ...
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Prerequisites for Apostol's and Spivak's Calculus
Hi ive 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 ...
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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 ...
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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 ...
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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?
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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(...
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Can I use Friedburg's linear algebra as a *first* course?
I want to use this book as the next step in my math journey. Although I’m not done yet, by the time I plan on starting this book I would have already completed Stewart Calculus and proofs by Jay ...
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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 ...
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Advice on optimizing an objective with many potential cases to track
I am analysing a game based on an extension of the Monty Hall problem and have come across an optimization problem that is just not clicking. I do not currently understand fully whether I should be ...
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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 ...
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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 ...
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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 ...
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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 ...
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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}...
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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 ...
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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 ...
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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 ...
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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 exactly is the converse and the reciprocal of the Pythagorean theorem? [closed]
I think I spotted a translation problem at exercise 12 in Appendix B of Stewart's Calculus, 6th edition, the Portuguese version of the book. Here's the original problem:
(a) Show that the triangle ...
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Is this the right way to think of epsilon-delta proofs when $d = \min(c, e(c))$?
Introduction. This is a check-my-work-type of question. The question itself only appears at the very end and if I made a mistake here, then the question becomes --- what is my thought process that's ...
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How can I think of counterexamples of abstract mathematical objects?
I noticed that I have an intuition for theory (ie making connections between theorems, lemmas, and proving related statements).
However, when a problem gives me the choice between proving or finding ...
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I want to learn mathematics of physics without going near proof writing
I am self-studying physics, and I just finished Linear Algebra by Howard Anton, Vector Calculus by Susan Jane Colley, and Differential Equations by Boyce DiPrima.
In order the learn the mathematical ...
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How to build a table of trigonometric ratios?
In Appendix D of the 6th edition of Stewart's Calculus, we find example 3 which tells us to find the exact trigonometric ratios for $t = 2\pi/3$. The solution says --- from Figure 10 we see that a ...
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Methodology for solving graduate mathematics problems
Recently, I have been introduced to graduate mathematics, and I am doing graduate courses, in these courses we have homework and the problems tend to be challenging.
In comparison to undergraduate ...
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Advice on making reflections about an axis
I can reflect a simple graph (such as $x^2$, $|x|$ et cetera) about the y-axis, x-axis, but I seem to struggle and make mistakes when I try to reflect about $y = x$ and other less standard lines or ...
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Learning more advanced math to solve differential equations
I am looking to expand my toolkit for solving and understanding differential equations.
I often come across results and methods such as the possibility of solution by quadrature of ODEs, ...
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How to study a book like Gallian?
I just finished chapter 3 of the book and I'm not sure whether I'm doing it right.
The chapter has 10 pages. After the chapter there are 92 exercises.
Do people do all of these or do they pick some? ...
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Book recommendation and advice needed.
My question is regarding which texts to follow for Geometry and Combinatorics for Olympiad Preparation.
I have done Geometry at a high school level and have a fair share of problem solving experience ...
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I need an exam of complete undergraduate mathematics courses. [closed]
I have an important exam in which I am responsible for undergraduate level of
Calculus, Advanced Calculus, Linear Algebra, Differential Equations, Abstract Algebra and Real Analysis.
Do you know any ...
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Could you give me advice on self-study for topology, measure theory and functional analysis?
I would really love to understand measure theory, as I want to become better at probability and statistics.
I heard that in order to delve into measure theory I need to first study functional analysis ...
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Show that this joint density function of X and Y is in fact a density
We have this density are asked to verify if the double integral over $R^2$ of the density evaluates to $1$ (the second part of the problem asks to find the expectation of $X$). The density given is $f(...
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I m struggling to understand math, please give me advice
I'm desperate! I need your advice. I score A's on all math courses in high school. But I'm very depressed, because I find myself still bad at math. Reason for that is because I'm forced to rely on ...
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Logic: Proving a Negated Disjunction is a Conjunction of Negations
~ = Not
V = Disjunction
& = Conjunction
A and B are stand ins for more complex formula but I know how to derive the whole derivation if I just had their negations.
So I know that ~(A V B) = ~A &...
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Advice on choosing universities to apply to for PhD in Geometry/Topology [closed]
I'm a mathematics Master's student and I'm applying to Ph.D. programs this semester. I want to study in a field related to Geometry/Topology and I'm trying to come up with a list of possible ...
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Preparing for a rigorous multivariable calculus course after a period of absence [duplicate]
CONTEXT:
I am mathematics and software engineering student, currently in my second year of study. Due to personal circumstances I had to take a leave of absence from my studies for a period of 1.5 ...
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