Video by solving a problem of Homomorphism

http://youtu.be/sE40dp0lrSY

This is the link to go to  homomorphism's exercise.

And with this video and this post
I end the blog of algebra, I hope to approve, even such an abstract subject that sometimes you do not know where to start to solve the exercises on a test.
Always have to try again and again to reach the top.!!

Mathematician’s Interview

Alejandro Sánchez, mathematical engineer. He studied in Madrid and continues its path specializing in statistics. And Algebra teacher devotion and eager to show their skills.

When did you discover you wanted to be a teacher?

 At 14, I explained algebra to my classmates and at 17 started giving my first lessons. Since then I grew fond of the teaching of mathematics and every day more of them own studio.

Are you studying to teach better every day?

. I think the study should not be teaching, I think that teaching is applied, then I study math every day for my own knowledge. Although it is true that it helps me to be more loose in every mathematical resolution. But my studies are usually higher than what I teach.  And I hope to improve my knowledge of mathematics.

 Why you think that students do not approve more math?

Do not hesitate to say, that mathematics learning are not entirely clean and do not analyze in detail all points, mathematics is something deeper than numbers and letters. And many times we try to explain something more difficult than it is.

What strategy and best practices could be implemented to improve math education?As I said not ignore anything an explanation and always explain everything in the easiest way, in order to reach a proper or formal way. But the problem of failure in mathematics is the wrong base.

Very well thank you very much for your answers.

An endomorphism

Is a morphism (or homomorphism) from a mathematical object to itself.

For example, an endomorphism of a vector space V is a linear mapƒ: V → V, and an endomorphism of a group G is a group homomorphism ƒ: G → G. In general, we can talk about endomorphisms in any category. In the category of sets, endomorphisms are functions from a set S to itself.

In any category, the composition of any two endomorphisms of X is again an endomorphism of X. It follows that the set of all endomorphisms of X forms a monoid, denoted End(X).

An invertible endomorphism of X is called an automorphism. The set of all automorphisms is a subset of End(X) with a group structure, called the automorphism group of X and denoted Aut(X).

In the following diagram, the arrows denote implication:

Any two endomorphisms of an abelian group A can be added together by the rule (ƒ + g)(a) = ƒ(a) + g(a). Under this addition, the endomorphisms of an abelian group form a ring(the endomorphism ring).

 For example, the set of endomorphisms of Zⁿ is the ring of all n × n matrices with integer entries. The endomorphisms of a vector space or module also form a ring, as do the endomorphisms of any object in a preadditive category.

The endomorphisms of a nonabelian group generate an algebraic structure known as a near-ring. Every ring with one is the endomorphism ring of its regular module, and so is a subring of an endomorphism ring of an abelian group, however there are rings which are not the endomorphism ring of any abelian group.