What to know before solving sequence and series problems?
Talking about How to solve the sequence: $87, 89, 95, 107, ?, 157$ for example, I read the hint: The difference between each term goes like this: 2,6,12. Can you notice any pattern? Based on it, can...
View ArticleSearching unifying formalism for vectors
I’m looking for a beautiful and unifying formalism (which I saw one of professors using and i cant ask him bc he doesn't like me at all 🙃) that elegantly explains and derives concepts like:Vectors,...
View ArticleQuestions about the cardinality section (1.5) of 'Understanding Analysis' by...
I started going through the book Understanding Analysis and kinda don't understand the section about cardinality in the first chapter; imo it leaves a lot of important stuff that is necessary for the...
View ArticleModel theory texts discussing Fraïssé limits and Hrushovski constructions
I am interested in learning about Hrushovski constructions and broadly Fraïssé Limits (see, for example, the wiki page on the Hrushovski construction). There are many resources on Fraïssé limits, but I...
View ArticleAre there any theorems, lemmas, equations or the like named after multiple...
I'm wondering if there are examples of mathematical theorems, lemmas, equations or other mathematical statements that have been named after multiple authors of the same name?For example if two people...
View ArticleWhat to do if I can't do geometry? [closed]
I am 13 years,and I absolutely can't do geometry.I know the theory, but I absolutely can't practice. I can't prove the equality of angles, I can't prove that, for example, a triangle ABC is isosceles....
View ArticleDaleckii-Krein Theorem applied to functions of a quaternion
I wanted to see what would happen if I applied the Daleckii-Krein Theorem to a quaternion function via its $4\times 4$ matrix representation.$\def\h{\odot}\def\k{\otimes}\def\bb{\mathbb}\def\bbC#1{{\bb...
View ArticleExtending Integration by parts
$$\int f g \,dx=f\int g\,dx -\int f'\int g\,dx\,dx$$Note : "first" function is $f$ and "second" function is $g$.$$\int f g h \,dx=?$$$$\int f g h \cdots \,dx=?$$I was trying the Fourier Cosine...
View ArticleCounterexample Math Books
I have been able to find several counterexample books in some math areas. For example:$\bullet$ Counterexamples in Analysis, Bernard R. Gelbaum, John M. H. Olmsted$\bullet$ Counterexamples in Topology,...
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Is there fractal pattern in the plot of the fractional part of $x y$?
For real $x,y$, define $g(x,y)=\{x y\}$ where $\{\cdot\}$denote the fractional part.For a point $(x,y)$ in the plane, color the point as $g(x,y)$ wherezero is black, one is white and smaller is...
View ArticleHow do mathematicians know if a problem is "very difficult"? [closed]
Apparently proving the Collatz conjecture would be one of the greatest achievements in mathematics, because it is extremely hard.How do we know it's hard before it's proved? Why can't it (e.g.) be...
View ArticleHow effective it is to keep attempting to find solutions to a specific math...
For context I've been staring at this specific question that requires me to construct and solve a differential equation for quite a few hours.I've attempted many things and gotten nowhere close. I bit...
View ArticleMath graduate school after a gap of several years [closed]
I studied Mathematics at university and I'm now considering continuing my education with a PhD or Master's degree. The problem is that I have a gap of over four years between when I finished my...
View ArticleWhat are the minimum prerequisites to understand queueing theory?
I have limited mathematical ability, never did calculus and only a tiny bit of linear algebra. Most mathematical notation is lost on me. What are the minimum prerequisite topics that I can familiarize...
View ArticleJames Munkres Elementary Linear Algebra [closed]
Can anyone who has the book give a quick opinion?There are no reviews in any of the websites, and what's weird is the book is freaking expensive, but only 42 pages.Isn't this weird?I know rigorous...
View ArticleWhat math is used in the theory of quantum computing? [closed]
I'd like to know what rung of the math ladder one need be on to grasp how a quantum computer computes.I realize this might not be a simple answer, so I'm just looking for an idea of the broad topics...
View ArticleBook reccomendations on applications of math
I was always fascinated with pure math, but lately I've been increasingly more interested on applications of math (preferably algebra/topology but other fields would be interesting too) in the real...
View ArticleCoordinate independent Taylor expansion of $\det(u + h)$
Let $u$ be an endomorphism of a finite dimensional real vector space $V$ or rank $r$. Put $s = n - r$. For $h$ near $0$ in $\mathrm{End}(V)$ one has$$\det(u + h) = \begin{pmatrix}\text{nontrivial...
View ArticleTranspose method for finding a basis for the row space
My linear algebra textbook outlines a method of finding a basis for the row space of a matrix by finding a basis for the column space of its transpose. Is there any point of using this method? It seems...
View ArticleMathematical induction, is it really a proof of truth?
This soft question is, I think, borderline mathematical philosophy.One of my former professors used to say that induction does not prove that a statement is true, but it merely eliminates the...
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