This blog has been created by Sonia Agüera Artero as an integrated project for Biomedical Engineering at the Polithechnic School of the "Universidad Europea de Madrid", Academic Year 2013/2014.

jueves, 31 de octubre de 2013

The Jacobian


     


        


        In vector calculus , the Jacobian or Jacobian determinant called the determinant of the Jacobian matrix . Both the Jacobian matrix and the Jacobian determinant are named after the mathematician Carl Gustav Jacobi .


        Carl Gustav Jacobi was born in Potsdam in 1804 within a Jewish family in Germany .                                                                                                                Jacobi Niels Henrik Abel established with the Theory of Elliptic Functions . Demonstrated the solution by applying elliptic integrals of functions, exponential series introduced himself.
       He worked mainly on differential equations and determinants, studying , among other things, the concept that today is known as Jacobian . He published the result of these years on the formation and properties of determinants .
       Jacobi had the reputation of being an excellent teacher , attracted many students. Seminar introduced a method to teach students the latest mathematicians.
\begin{bmatrix}
\cfrac{\partial y_1}{\partial x_1} & \cdots & \cfrac{\partial y_1}{\partial x_n} \\
\vdots & \ddots & \vdots \\
\cfrac{\partial y_m}{\partial x_1} & \cdots & \cfrac{\partial y_m}{\partial x_n}  \end{bmatrix}


       The Jacobian is simply determining which serves to move or transform from one coordinate system to another. Also called functional determinant .

jueves, 17 de octubre de 2013

Why no Nobel Prize in Mathematics ?




          Nobel Prizes are given to people who have excelled in certain areas by sufficiently important contributions to society. It is awarded annually on December 10 ( the date on which Alfred Nobel died ) in Stockholm and the fields that are awarded are Physics, Chemistry, Medicine , Literature , Peace and Economics. So , as you can see, there is Nobel Prize of Mathematics .... why? .

          There are a couple of legends to explain this.One of them says that when Nobel thought in prizes, he asked advice from specialists who might deserve each .
In the category of Mathematics told that Mittag - Leffler , Swedish mathematician , would be suitable to receive it. But Nobel took wrong with him , and declined to give award at this branch for not giving it to him . And the other is even more pink : it is said that such Mittag - Leffler had an affair with the wife of Nobel and thus not established the prize for this science .

          But they are just that : legends. There is no record that had references from this Nobel Swedish mathematician , in fact it seems that barely knew , so there might be wrong with him. The other story is easily removed : Nobel never married .

          The reason why there is no Nobel Prize in Mathematics is that Nobel did not consider this science as important for life on the practicality and elected branches awards did consider important to the advancement of society . As we all know obviously wrong in this reasoning as mathematics are essential in our life. But Nobel did not consider that.

           Yet this has been and mathematicians who have been awarded the Nobel Prize in any category in which they are delivered. A couple of examples are John Forbes Nash, Nobel laureate in economics and José Echegaray , Literature Nobel Prize .

         But mathematicians are not exempt from specific awards for us. As I said in this post there is a prize , say, equivalent to the Nobel designed to mathematicians the Fields Medal , which is awarded every four years to one or more outstanding mathematicians in this period that would meet the condition of not exceeding 40 years old. It is the highest honor a mathematician can receive and next, as I said , will Grigori Perelman .





Presentation!!

I am Sonia Aguera, I am student of biomedical engineering at the Polytechnic of the European University of Madrid. And this will be my first blog related to mathematics, and the second I do.
The first thing that comes to my mind when I do a blog is that this blog might be interesting, at least. It is very difficult by the fact of being a math blog,where we study especially in "integrals" in this course.
I will leave a link to a page trying to help you  in mathematics. http://www.webmath.com/