Do complex numbers really exist?
Complex numbers involve the square root of negative one, and most non-mathematicians find it hard to accept that such a number is meaningful. In contrast, they feel that real numbers have an obvious...
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,...
View Article"Negative" versus "Minus"
As a math educator, do you think it is appropriate to insist that students say "negative $0.8$" andnot"minus $0.8$" to denote $-0.8$?The so called "textbook answer" regarding this question reads:A...
View ArticleShould a high school introductory calculus class teach $\varepsilon$-$\delta$...
It seems to me that most high school students are comfortable with the intuitive notion of a limit ("as $x$ gets arbitrarily close to $c$, $f(x)$ gets arbitrarily close to $L$") and gain little insight...
View ArticleRole of imaginary part of non trivial zeros of Riemann Zeta function on prime...
Simple terminology, for my convenience:$b$ = imaginary part of a non trivial zero of Riemann Zeta function (for example $14.134...$ for the first zero); for me the fact that every zero has real part...
View ArticleStudying representation theory of $H$ by restricting characters from $G\ge H$
Suppose we have finite groups $H \le G$, and we know a lot about $G$'s representation theory over $\Bbb C$. Every isomorphism class of $H$-irreps appears in a restriction of some $G$-irrep.To an...
View ArticleIs it possible that every algorithm with a linear running complexity can be...
Can we prove or if it has been proved (if it is possible) that an algorithm with linear computational complexity does have mathematical representation using the clever manipulation of elementary...
View ArticleTechniques for using set theoretical universes effectively outside of set...
It is well known that it is not possible to define the "set of all sets" in standard ZF set theory without contradiction, as it breaks the axiom of foundation. However, I find this to be surprisingly...
View ArticleWhat are the prerequisites in general to study linear Programming \...
Please check if the following required prerequisite knowledge points are complete？Is the learning sequence reasonable?Below is the mathematical knowledge needed before studying Linear Programming,...
View ArticleSmart Pen For Math Writing [closed]
Next month I will begin to learn in the university, and I am not sure if to buy smart pen such as Livescribe or Logitech IO 1/2 to write math with.(handwriting is not an option)The problem is that I am...
View ArticleIs it possible to create a self evident mathematical foundation without using...
Let me clarify: $\mathsf {ZF}$ and other fundational theories often use logic to define the basic concepts like $\implies, \exists$ etc... even if they are a circular definition.My question is: it...
View ArticleIntuitive reasoning why are quintics unsolvable
I know that quintics in general are unsolvable, whereas lower-degree equations are solvable and the formal explanation is very hard. I would like to have an intuitive reasoning of why it is so,...
View Articlesymbolic computation program/software
What is your recommended symbolic computation program/software for free and commercial respectively?What are its strength and weakness? For example, efficiency, comprehensiveness, etcThanks!
View ArticleStriking applications of integration by parts
What are your favorite applications of integration by parts?(The answers can be as lowbrow or highbrow as you wish. I'd just like to get a bunch of these in one place!)Thanks for your contributions, in...
View ArticleExamples of functions which grow faster than their computational complexity.
A good example of this would be the function $f$ defined as follows, $f(n) = (10^n-1)$. While in this form it's equation is exponential, it is easy to note that $$f(n) = 99...9 \,(n \text{ times}).$$...
View Article$d(dx)$ exterior derivative in simple language?
I’m only learning the basics of analysis, so I have no understanding of exterior derivatives. I simply need clarification on my misconception using simple words.I’m reading about second degree...
View ArticleFormal statement of theorem about perfect numbers?
I cannot seem to find the formal statement of the theorem if there are infinite perfect numbers in Wikipedia or online. I searched this site but the closest is the generalization of perfect numbers...
View ArticleMnemonic for platykurtic and leptokurtic
I keep confusing terms leptokurtic and platykurtic. Is there a good mnemonic to help remember which is which?"Lepto" means "little", "platy" means "flat", and both are equally unrelated to thickness of...
View ArticleBooks recommendation: differentiable manifolds, Banach manifolds
I'm looking for good books in English about differentiable manifolds in finite dimensional spaces, as well as Banach manifolds (optionally, containing some information about calculus in Banach spaces)....
View ArticleReference on Infinite Dimensional Manifold
I am studying manifold. For comprehension, I read the site http://en.wikipedia.org/wiki/Manifold, and there is some information about infinite dimensional manifold. Now I have two questions or...
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