I have been doing a project about $\operatorname{Ext}^n$ functors for my commutative algebra class. I used the approach via extensions of degree n. Basically I have shown the long exact sequence associated to a short exact sequence for $\operatorname{Hom}_{\mathcal{A}}$ where $\mathcal{A}$ is an abelian category. To apply this construction I have proven the Chinese remainder […]

As the title says, I’m wondering whether there is any known closed-from for the following series: $$\sum_{k=0}^{\infty} \frac{1}{(k!)!}$$ Here I don’t mean the double factorial (treated here) when I’m writing $(k!)!$, but the factorial of the integer $k!$. Trying on WolframAlpha, I get the funny value $2.501388888888888888888890500626459…$, but no closed-form. If you have any reference […]

The main question is in the title. The below are just disclaimers. By puzzle books, I mean just puzzle books and not any math text book. One such good example is Peter Winkler – Mathematical Puzzles A Connoisseur’s Collection. From that, to quote: To appreciate them, and to solve them, it is necessary – but […]

Reading this article I became curious to learn more of (- study more thoroughly and *seriously*$^{\star}$-) the topic. Is / are there some good references – either papers, books and/or other information content / sources – to provide a good (and, if possible, thorough) first introduction? Would be greatly helpful; and greatly appreciated. Sadiq Note: […]

I am looking at buying 1 of the 3 following Linear Algebra texts for my reference. Introduction to Linear Algebra by Gilbert Strang 4th edition Linear Algebra and its Applications by David Lay 4th edition Linear Algebra: A Modern Introduction by David Poole 3rd edition The question I would like to ask is, which book […]

Where exactly (book and page number) can I find the proof that the first hitting time of a Borel set a “Stopping time” (continuous time). My notes say it is a deep theorem, particularly hard to prove but didn’t give any reference. Moreover my prof mentioned that is is so hard to prove that the […]

This question already has an answer here: Where to start learning Linear Algebra? [closed] 16 answers

A proof by H. Iwaniec in ‘On the problem of Jacobsthal, Demonstratio Math. 11, 225–231, (1978)’ shows that: $$j(N) \ll \log^2 (N)$$ where $j(N)$ is the Jacobsthal function. I am very interested in understanding the details of this proof. Would anyone be able to provide a rough outline of the proof and suggest a good […]

I want to find some article or a book which contains all general properties of nets. Of course some of them similar to properties of sequences with almost the same proofs, but I don’t fill the edge, where nets and sequences starts to behave differently. Also it would be nice to find complete survey on […]

I’m interested in finding an online copy of J. Hammersley’s article entitled On the enfeeblement of mathematical skills by Modern Mathematics and by similiar soft intellectual trash in schools and universities, which was published in the Bulletin of the Institute of Mathematics and its Applications, Band 4, 1968, S. 66–85. I’ve searched both the name […]

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