Aristarco

Cola

http://en.wikipedia.org/upload/9/9d/Newtonianfig2.jpg

Fig. 1

Math

Math characters:
∫ ∑ ∏ √ − ± ∞
≈ ∝ ≡ ≠ ≤ ≥ →
× · ÷ ∂ ′ ″
∇ ‰ ° ∴ ℵ ø
∈ ∉ ∩ ∪ ⊂ ⊃ ⊆ ⊇
¬ ∧ ∨ ∃ ∀ ⇒ ⇔
→ ↔

&int; &sum; &prod; &radic; &minus; &plusmn; &infin;
&asymp; &prop; &equiv; &ne; &le; &ge; &rarr;
&times; &middot; &divide; &part; &prime; &Prime;
&nabla; &permil; &deg; &there4; &alefsym; &oslash;
&isin; &notin; &cap; &cup; &sub; &sup; &sube; &supe;
&not; &and; &or; &exist; &forall; &rArr; &hArr;
&rarr; &harr;

Caracteres especiales

Tipos de función	Código	Apariencia
Funciones normales (bien)	\sin x + \ln y	$\sin x+\ln y$
Funciones normales (mal)	sin x + ln y	$sinx+lny$
Derivadas	\nabla \partial dx	$\nabla \partial dx$
Conjuntos	x\not\in\empty\subseteq A\cap B\cup \{x,y\}	$x\not \in \emptyset \subseteq A\cap B\cup \{x,y\}$
Funciones lógicas	p\wedge q \rightarrow p\vee q \Rightarrow r	$p\wedge q\rightarrow p\vee q\Rightarrow r$

http://mindprod.com/jgloss/htmlcheat.html

Fuentes

Letras Griegas	\alpha \beta \gamma \Gamma \phi \Phi	$\alpha \beta \gamma \Gamma \phi \Phi$
Conjuntos especiales	x\in\mathbb{R}\sub\mathbb{C}	$x\in \mathbb {R} \subset \mathbb {C}$
Negrita (vectores)	\mathbf{x}\cdot\mathbf{y} = 0	$\mathbf {x} \cdot \mathbf {y} =0$
Fraktur	\mathfrak{a} \mathfrak{B}	${\mathfrak {a}}{\mathfrak {B}}$
Letras hebreas	\aleph	$\aleph$

Notation park

≠

$f(x)=\sum _{r=0}^{n}a_{r}x^{r}$

$F(s)={\mathcal {L}}\ f(s)=\int _{0}^{\infty }e^{-st}f(t)\,dt.$

{\begin{pmatrix}1&4&2\\0&3&4\\0&0&1\\\end{pmatrix}}

$\otimes$ , $\wedge$ , $\Lambda ^{2}V^{*}$

$\varprojlim A_{i}$

$G=\bigcup _{w\in W}BwB$

${\bar {z}}$

\Gamma =SL(2,\mathbb {Z} ),\ {\overline {\Gamma }}=PSL(2,\mathbb {Z} )=SL(2,\mathbb {Z} )/\{\pm I\}

\vdash

\models

{\frac {d}{dx}}(uv)=\left({\frac {du}{dx}}\right)v+u\left({\frac {dv}{dx}}\right)

\prod _{i=1}^{N}x_{i}

Wikipedia:Usando TeX

Grupoide de Brandt

Heinrich Brandt (born November 8, 1886 in Feudingen (Westphalia)) studied mathematics at the University of Goettingen and from 1910 to 1913 at the University of Strasbourg, in 1912 attained a doctorate (Dr. phil. Universität Straßburg 1912 Dissertation: Zur Komposition der quaternären quadratischen Formen Advisor: Heinrich Weber)from 1913 assistant to the TH Karlsruhe. explaining geometry and applied mathematics from 1921 to the TH Aachen. And, from 1930, on the chair for mathematics at the University of Halle. Died 9 October 1954.

External Links

The foundational: "Über eine Verallgemeinerung des Gruppenbegriffes" where Groupoid is defined

Photo and biography (in german)

good references

es:Heinrich Brandt

Grupoide de Brandt

hay que hacerlo YA (con historia) cf. Ronnie Brown o dónde sea

http://www.kcl.ac.uk/ip/jonwilliamson/1999/pai_dc_99_b.doc

http://www.catalogus-professorum-halensis.de/brandtheinrich.html

http://translate.google.com/translate?hl=en&sl=de&u=http://www.catalogus-professorum-halensis.de/brandtheinrich.html&prev=/search%3Fq%3D%2522Heinrich%2BBrandt%2522%26hl%3Den%26lr%3D%26ie%3DUTF-8%26oe%3DISO-8859-1%26domains%3Dhttp://en.wikipedia.org

After the elementary school Brandt occurred the Praeparandenanstalt Holzwickede, from 1904 to 1907 visited he the teacher seminar stove corner. 1907/08 he worked as a people school teacher, 1909 put it the Abitur starting from 1909/10 studied Brandt mathematics and natural sciences at the University of Goettingen and from 1910 to 1913 at the University of Strasbourg, 1912 attained a doctorate he there to the Dr. phil. it put the examination for the higher teaching profession (mathematics, physics, Botanik, Zoologie) to 1913 starting from 1913 became it an assistant to the TH Karlsruhe. it carried military for 1913/14 out -, then war service. In October 1914 it was wounded and distinguished with the iron cross IITH class. Until 1916 had to remain Brandt in the military hospital, it became 70 % disabled to dismiss (beinamputiert). Returned to Karlsruhe, habilitierte it itself 1917 for the fan mathematics and mechanics. it received a tidy Professur for explaining geometry and applied mathematics to 1921 to the TH Aachen. it took a call to 1930 on the chair for mathematics at the university resounds to 1950 emeritiert, continued to teach it up to its death. After the Second World War Brandt was selected to the dekan.

Organizations: NSKOV, NSV, promoting member of the SS.

Sources:UAH Pa 4853 Brandt; Rep. 6 NR. 1407; DBE Bd. 2, P. 69.

born: 8. November 1886 Feudingen (Westphalia)

died: 9. October 1954 resounds

Denomination: Evangelist

Father: People school rector

buena biblio al final

Emmy Noether cf.final nota 12

I having beginning of May in resound spoken; then still was in Leipzig. Deuring have recently in attaining spoken; in addition in resounds at the same time with mir.1Àlso good-bye and best Gr¨usse!Ihre Emmy Noether.hatte the title: systems in its relations with commutative Algebraund with the Zahlentheorie?.11Hasse has then nevertheless only in January 1933 in the G¨ottinger mathematical society vorgetragen.1Ìn resounds affected since 1930 Heinrich Brandt, that the?Brandtschen Gruppoide?zur¨uckgehen; they serve the ideal theory in the maximum orders one-simple algebra for the description. In Leipzig van the Waerden worked, with the Noether in close contact conditions. In attaining was Wolfgang Krull and F. K. Schmidt.6

Grupoide de Brandt

Grupoide

http://www.fernuni-hagen.de/TOPOLOGIE/documents/glos1305.pdf

http://134.76.163.65/servlet/digbib?template=view.html&id=27941&startpage=364&endpage=370&image-path=http%3A%2F%2F134%2E76%2E176%2E141%3A80%2Fcontentserver%2Fservlet%2Fcontentserver%2F1379&image-subpath=1379&pagenumber=364&zoom-factor=null&imageset-id=1379&hlinfo=771

http://134.76.163.65/servlet/digbib?template=view.html&id=29227&startpage=304&endpage=319&image-path=http://134.76.176.141/cgi-bin/letgifsfly.cgi&image-subpath=/1414&image-subpath=1414&pagenumber=304&imageset-id=1414

http://faculty.colostate-pueblo.edu/karla.oty/groupoids/1900.htm

http://faculty.colostate-pueblo.edu/karla.oty/groupoids/1961.htm

http://www.bangor.ac.uk/~mas010/

http://www.bangor.ac.uk/~mas010/gpds.htm

http://www.bangor.ac.uk/~mas010/nonlnpub.htm

http://www.bangor.ac.uk/~mas010/hdaweb2.htm

As Grothendieck wrote in 1985:

"The idea of making systematic use of groupoids (notably fundamental groupoids of spaces, based on a given set of base points), however evident as it may look today, is to be seen as a significant conceptual advance, which has spread into the most manifold areas of mathematics. ... In my own work in algebraic geometry, I have made extensive use of groupoids - the first one being the theory of the passage to quotient by a ``pre-equivalence relation (which may be viewed as being no more, no less than a groupoid in the category one is working in, the category of schemes say), which at once led me to the notion (nowadays quite popular) of the nerve of a category. The last time has been in my work on the Teichmüller tower, where working with a ``Teichmüller groupoid (rather than a ``Teichmüller group) is a must, and part of the very crux of the matter ...."

http://genealogy.math.ndsu.nodak.edu/html/id.phtml?id=47792

Grupoide 1

empezamos con http://www.ams.org/notices/199607/weinstein.pdf y seguimos con http://math.berkeley.edu/%7Eacannas/notes_latest.pdf Parte VI pero daremos un tratamiento tan sencillo que pueda usarse de base para toda la matemática (abstracta).

http://www.unirioja.es/dptos/dmc/luhernan/hfolder/htp.pdf

http://www.gt.matfun.ull.es/GRUPO/tesis/T-David.pdf

http://www.math.ist.utl.pt/~molmos/papers/trabajouno.pdf