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Password manager and sync without clouds

First, install the password manager. On windows 10, it is keepass. On linux, the debian package for keepass2 is available in the standard repository. Since strong passwords are needed, either use the keepass password internal generator, or (maybe for the master password), install and use e.g. diceware or xkcdpass: $ sudo pip install xkcdpass $ xkcdpass -w "ita-wiki" -w "ger-anlx" -d ";" It is not difficult to add more words lists, e.

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Dell'uso dell'inglese nelle aule universitarie

A proposito di lingua inglese per le lezioni/esami (e internalizzazione) È di qualche giorno fa la sentenza del Consiglio di Stato N. 00617/2018REG.PROV.COLL. -- N. 05151/2013 REG.RIC, «sul ricorso numero di registro generale 5151 del 2013, proposto da: Ministero dell'Istruzione dell'Università e della Ricerca, in persona del Ministro pro tempore, Politecnico di Milano, in persona del legale rappresentante pro tempore, rappresentati e difesi per legge dall’Avvocatura generale dello Stato. [.

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Gli Esami Non Finiscono Mai

Norme di Riferimento REGIO DECRETO 31 agosto 1933, n. 1592 FONTE Approvazione del testo unico delle leggi sull'istruzione superiore. (033U1592) (GU n.283 del 7-12-1933 - Suppl. Ordinario n. 283 ) note: Entrata in vigore del provvedimento: 22/12/1933 VITTORIO EMANUELE III, PER GRAZIA DI DIO E PER VOLONTA' DELLA NAZIONE RE D'ITALIA Veduto l'art. 70 del R. decreto-legge 4 settembre 1925, n. 1604, col quale il Governo del Re e' autorizzato a riunire in testo unico, provvedendo al loro coordinamento e introducendo, ove occorra, norme integrative; tutte le disposizioni vigenti e quelle da emanarsi eventualmente anche posteriormente alla pubblicazione del decreto stesso in materia d'istruzione superiore e relative a corpi, istituti, stabilimenti, uffici e servizi comunque attinenti all'istruzione e alla cultura superiore;

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Winding Around and Mountains

Just ... ...reading John Roe's book Winding Around. Here: For an extended riff on the idea of mathematics as mountaineering see "Into Thin Air" by Colin Adams, on Mathematical Intelligencer. How much about "mathematics as mountaineering"?

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Fixing MarkDown LaTeX underscore problem

How to fix Markdown underscore with LaTeX problem? Test of a displaystyle formula \( A_k^n = \dfrac{n!}{k!(n-k)!} = \dfrac{n (n-1) \ldots (n-j) \ldots (n-k+1)}{ 1 \ldots j \ldots (k-1) \cdot k } = \dfrac{\prod_ {j=1}^k (n-j+1) }{ \prod_ {j=1}^k j } \) And the same for an inline sum: $\sum_j j^2$. The answer is: in the preamble markup = "mmark" and then just use $$ .. $$ or $ .

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Updating my (Xe)LaTeX vim plugin

After some years, it was time to update my LaTeX vim plugins. My setting was: plain vim, a makefile, some configuration lines. Back-forward search, not much completion. Now, with the vundle plugin. Things to do: I had vundle installed already. I needed to add lervag's vimtex and ajh17's VimCompletesMe. Hence, in .vimrc: " set the runtime path to include Vundle and initialize set rtp+=~/.vim/bundle/Vundle.vim call vundle#rc() " let Vundle manage Vundle, required Plugin 'VundleVim/Vundle.

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Wielandt's proof of Sylow's Theorem

Wieldandt's proof of Sylow's Theorem A brief preparatory combinatorial discussion: [ \binom{n}{k} = \dfrac{n!}{k!(n-k)!} = \dfrac{n (n-1) \ldots (n-j) \ldots (n-k+1)}{ 1 \ldots j \ldots (k-1) \cdot k } = \dfrac{\prod_ {j=1}^k (n-j+1) }{ \prod_ {j=1}^k j } ] and therefore [ \binom{n}{k} = \dfrac{n}{k} \cdot \dfrac{n-1}{1} \ldots \dfrac{n-j}{j} \ldots \dfrac{n-(k-1)}{k-1} = \dfrac{n}{k} \prod_{j=1}^{k-1} \dfrac{n-j}{j} ] Let $p$ be a prime number. Now, if $n$ is an integer divisible by a power of $p$, say $p^\alpha$, then $n=p^\alpha m$.

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Lettera sulla Polonia (1574-09-25)

Lettera del Cavalier Battista Guarini (1538-1612) al Segretario del Cardinal Luigi d'Este (1538-1586), Monsignor Benedetto Manzuoli (1530-1585). Testo preso dalla raccolta di lettere L'idea del segretario dal signore Bartolomeo Zucchi gentil'huomo di Monza, academico insensato di Perugia. Parte seconda. pubblicato nel 1606 da Bartolomeo Zucchi (1570-1630) a Venezia, presso la Compagnia Minima. ARCHIVE LINK L'ortografia è stata parzialmente adattata a quella moderna. Guarini fu Segretario di Alfonso Secondo d'Este, duca di Ferrara (1533-1597) tra il 1573 e il 1583, e scrive al segretario del Cardinal Luigi d'Este, fratello di Alfonso Secondo d'Este.

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Fundamental group of SO(3) and Dirac's scissors

Topology of $SO(3)$ and fixed-distance pairs of points in $S^2$. Consider the space $X\subset S^2\times S^2$ of all pairs $(A,B)$ of points such that $|A-B|=\sqrt 3$, where the distance is the euclidean distance of $S^2\subset \RR^3$, and $S^2$ is the unit sphere in $\RR^3$. (1) $X\approx SO(3) \approx \PP^3(\RR)$. Proof: The fact that $SO(3) \approx \PP^3(\RR)$ is a not-so-easy elementary exercise (cf. exercise (11.27) and exercise (7.30) of my Geometry Notes, protected by a single-character password: the number of non-zero digits appearing in the password itself; the problem might be ill-posed).

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Homology of (simplicial) spheres and applications

Nullhomotopic odd maps, Borsuk, Lusternik and Schnirelmann Let $\Delta^n$ the standard simplex of dimension $n$ in $\RR^{n+1}$, which is homeomorphic to a $n$-dimensional disk, and $\Sigma^{n}\subset \Delta^{n+1}$ the simplicial $n$-sphere, i.e. the boundary of $\Delta^{n+1}$ (the union of its $n+2$ $n$-dimensional faces), which is homeomorphic to an $n$-dimensional sphere. The homeomorphisms can be more explicit: let $B\in \Delta^{n+1}$ be its barycenter, and $\varphi\from \Sigma^n\subset \Delta^{n+1} \to \RR^{n+2}$ the map defined as $\varphi(x) = \dfrac{x-B}{|x-B|}$.

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Mesh, Barycentric Subdivision and Simplicial Approximation Theorem

Mesh of a euclidean simplicial complex. Let $|K| \subset \RR^k$ an euclidean simplicial complex (i.e., an abstract simplicial complex, where the set of vertices actually is a set of points in $\RR^k$, such that $|K|$ is the disjoint union of the interiors of the convex hulls of the sets of vertices ranging over the set of simplices). A vertex $P$ of $K$ is therefore a point of $\RR^k$. For each simplex $\sigma \subset K$, the diameter of $\sigma$ (or $|\sigma|$ more precisely) is the maximum distance $|x-y|$ as $x,y$ vary in $|\sigma|$.

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Joins and Products of polyhedra

Join $K*L$ of two simplicial complexes Let $K = (X_ K, \Phi_ K)$ and $L = (X_ L, \Phi_ L)$ be two simplicial complexes ($X_ K$ denotes the set of vertices of $K$ and $\Phi_ K$ the set of simplices). Then the join $K*L$ is the simplicial complex defined as follows. Its set of vertices $X=X_ K \cup X_ L$ is the union of the sets of vertices of $K$ and of $L$, and a non-empty subset of $X$ is a simplex of $K*L$ if and only if it is of type $\sigma \cup \tau$, where $\sigma \in \Phi_ K \cup \{ \emptyset \}$ and $\tau \in \Phi_ L \cup \{\emptyset \}$.

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Ranks, Tensors and Abelian Groups

Abelian Groups Given $a\in A$, the homomirphism $i_ a \from \ZZ \to A$ defined by $i_ a(k) = ka$ is mono (injective) iff $a$ has infinite order. Of $S$ is a set, the free Abelian group generated by $S$ is $$ \ZZ[S] = \ZZ S = \bigoplus_ {s \in S} \ZZ, $$ and it is the group of all finite linear combinations (with integer coefficients) of elements in $S$. The elements of $S$ are a basis (base) of $\ZZ[S]$.

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Graphs, trees and simplicial complexes

Graphs and simplicial complexes A one-dimensional simplicial complex is a graph. That is, $K=(X_ K,\Phi_ K)$ where $V(K) = X_ K$ is the set of vertices and $\Phi_ K$ is the set of simplexes, with $\Phi_ K = \Phi^1_ K \cup \Phi^0_ K$, where $E(K) = \Phi^1_ K$ are the 1-dimensional simplexes (termed edges of $K$) and $\Phi^0_ K = \{ \{P\} : P \in X_ K \}$ are the $0$-dimensional simplexes (sometimes termed again vertices of $K$).

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