What is the “main” axiomatic system in geometry at the moment?
At the moment we have many different systems of axioms and from observations we most often use Euclidean ones, so everything else can not even be considered as the correct answer. After Euclid's...
View ArticleAxiomatic/ non-constructive integration book recommendation?
I have taken both courses on Riemann integration (single and multiple cases) and one course in measure and Lebesgue integration that didn't progress far. We covered a chapter on measure, measurable...
View ArticleFun but serious mathematics books to gift advanced undergraduates.
I am looking for fun, interesting mathematics textbooks which would make good studious holiday gifts for advanced mathematics undergraduates or beginning graduate students. They should be serious but...
View ArticleMore information about "parallel maths"
I came across a version of maths on a site (it requires you to sign up to read the article), where addition is defined as the reciprocal of the sum of the reciprocals. In the below article, the author...
View ArticleWhich system of axioms is used most often in modern geometry?
We have many different systems of axioms in geometry and from observations we most often use Euclidean ones. Euclid's postulates are insufficient, but the Hilbert system seems overloaded and redundant....
View ArticleQuadratic ODE systems
Linear ODE systems $x'=Ax$ are well understood. Suppose I have a quadratic ODE system where each component satisfies $x_i'=x^T A_i x$ for given matrix $A_i$. What resources, textbooks or papers, are...
View ArticleFooling myself with confidence intervals [closed]
This is labeled as soft-question, because I'm aware that I did not do enough work by myself. (I did, years ago and forgot nearly all of it).I am doing a Bernoulli trial with a given number of trials,...
View ArticleErrors of Euler interpretation?
To complement the recent post on Euler's errors, I would pose the following question: what common errors of Euler interpetation appear in the literature? What errors are attributed to Euler's work in...
View ArticleCollection of surprising identities and equations.
What are some surprising equations/identities that you have seen, which you would not have expected?This could be complex numbers, trigonometric identities, combinatorial results, algebraic results,...
View ArticleGreat books on all different types of integration techniques
It's coming up to Christmas so I can ask to have all the books I can't afford from begrudging relatives! I'm really interested (mainly from looking at some of the answers cleo and other fantastic...
View ArticleVivid examples of vector spaces?
When teaching abstract vector spaces for the first time, it is handy to have some really weird examples at hand, or even some really weird non-examples that may illustrate the concept. For example, a...
View ArticleAny other uses of K-Theory of $\mathrm{C}^{*}$-algebras aside from...
I have recently become very interested in K-theory of $\mathrm{C}^{*}$-algebras due to several of the interesting properties one can derive about a $\mathrm{C}^{*}$-algebra $A$ relative to its...
View Articlewhat is an algebra? [closed]
In the context of BN-algebra introduced by C.B. Kim and H.S. Kim. I'm doing an undergraduate thesis where I seek homomorphisms and isomorphisms. My professor asked me what is an algebra. He won't allow...
View ArticleDifference between topology and sigma-algebra axioms.
One distinct difference between axioms of topology and sigma algebra is the asymmetry between union and intersection; meaning topology is closed under finite intersections sigma-algebra closed under...
View ArticleUnexpected examples of natural logarithm
Quite often, mathematics students become surprised by the fact that for a mathematician, the term “logarithm” and the expression $\log$ nearly always mean natural logarithm instead of the common...
View ArticleDesigning a non-elementary integral yielding an answer
How can I reverse-engineer the process of designing a definite integral with no elementary antiderivative yet a fixed solution?To make this concrete, assume I want to design a function $f$ such that...
View ArticleWhat other tricks and techniques can I use in integration?
So far, I know and can use a reasonable number of 'tricks' or techniques when I solve integrals. Below are the tricks/techniques that I know for indefinite and definite integrals separately.Indefinite...
View ArticleExamples for Hilbert's Quote
Hilbert once said, “The art of doing mathematics consists in finding that special case which contains all the germs of generality.”What would be (relatively) simple examples?
View ArticleWhy can we treat differential operators as if they behave like algebraic...
In college, I've come across many instances where we multiply a derivative by a function i.e $\frac{d}{dx}\times f=\frac{df}{dx}$, and the result somehow becomes the derivative of the function — as if...
View ArticleReferences for "equational" calculi for specific propositional logics.
I am interested in references for equational proof calculi (in the sense described below) for specific propositional logics. I am especially interested in references that deal with mundane or practical...
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