Prime numbers.

There is a video of the Prime numbers.

Uses of integration in real life

1. Applications of the Indefinite Integral shows how to find displacement (from velocity) and velocity (from acceleration) using the indefinite integral. There are also some electronics applications.

In primary school, we learnt how to find areas of shapes with straight sides (e.g. area of a triangle or rectangle). But how do you find areas when the sides are curved? e.g.

2. Area under a Curve and
3. Area in between the two curves. Answer is by Integration.
4. Volume of Solid of Revolution explains how to use integration to find the volume of an object with curved sides, e.g. wine barrels.
5. Centroid of an Area means the cenetr of mass. We see how to use integration to find the centroid of an area with curved sides.
6. Moments of Inertia explain how to find the resistance of a rotating body. We use integration when the shape has curved sides.
7. Work by a Variable Force shows how to find the work done on an object when the force is not constant.
8. Electric Charges have a force between them that varies depending on the amount of charge and the distance between the charges. We use integration to calculate the work done when charges are separated.
9. Average Value of a curve can be calculated using integration.

Interview with a mathematician, Aurora Morena.

Well, today I will interview a mathematician, who was teacher of my brother, my sister and already mine, when we were in primary school. She was a demanding teacher with high expectations for us. She never lost hope in us, she always gave us more strenght to continue every single day. Her aim was that one day, we can achieve our goals, or even think of maths on another way, that we like to do.

Question: What do you like of Maths? How do you hooked at Maths?

Answer: When I was 14 years old I have already a tremendous desire to learn about Maths, but my real fascination was generated when I read "A course in Pure Mathematics". When I was reading this book I tried to solve their problems one bye one, I think this is a fantastic book and every student that like Maths should know about it.



Question: Is there creavity in mathematics?

Answer: It is creavity itself! When one person is doing mathematics he or she is creating new problems and then they can resolve it. But just look of the amount of international journals dedicated to publishing mathematicians research.


Question: Mathematics is a science study or art?

Answer: It's a science activity, but when the mathematical theory is armed or we can see a brilliant demostration, the result is like looking at a building, may be of such beauty that is pure expression
artistic.


Question: Anything else to add?

A: I think math attract a lot if we apply the logic to follow steps, then everything fits and it goes well. Just try to follow it.

Number ZERO.

Today i'm going to talk about de number ZERO.

The number zero appears about 17,000 years ago, but it hasn't been incorporated until 1,500 years ago in the mathematics. Zero is the only number in the numerical system that is neither positive nor negative. This concept was hard to grasp because they couldn't understand the idea of "having nothing (zero) to the value of something."

The number zero has 2 uses: 

-The first one is the empty place indicator in our place-value number.

-The second one is, as a number itself.

The Babylonians did not have the characteristic of the number zero in their number system, until 400 BC that was when they introduce the number zero. Once the Babylonians started using the zero, Greeks began their contributions to mathematics, but they didn't adopt this use, because they didn't have to name the numbers, because they worked with the numbers as lenghts of a line. The first use of the number zero, was attributed to the Greek astronomy, but it has different explications about that, such as the attribution of zero to 'obol' or 'omicron'. And then we move to India, where its use began to evolve, because there was where the number and the different numerical systems were born. It is important to note at this point that there was another civilization which developed a numerical value to the zero position. Were the Mayans, who lived in Central America. 

Why the Romans didn't use the number zero? 

- The Romans didn't use the number zero because they used an additive system, it was the transcription of what we have.

Additive systems, using methods such as the abacus, can become more advanced systems such as positional. The Romans never used the arithmetic for doing calculations. Additive systems need special symbols for order numbers greater in magnitude than the base number, indeed, having an additive system, the Romans didn't need the zero. For its part, the first civilizations with positional systems use holes in the script, but that brought up many misunderstandings, and gradually was creating zero as we know it.

Nowadays, we use the Arab numbers, thanks to the Arab mathematician al-Khwarizmi, who adopted and introduced in Europe. 

This is the fascinating story of why the Romans did not use zero. It is certainly very interesting and makes us understand a little more work today as our numbers, and also the importance of zero in mathematics.

Mathematical operations with zero.

Zero sum:

In addition, zero is the neutral element, any number a added to 0 restores to a. 

Zero in multiplication:

In the product, the absorbent element is zero, any number operated with 0 gives 0.

Zero in the division:

Among the controversies that exist about zero, one of them is about the possibility of dividing by it, until reaches zero doubt about whether you can divide another number. The problem is that you use the same word, division, to refer to different things.

THIS IS THE EXPLANATION OF THE NUMBER ZERO, I THINK PERSONALLY THAT IT'S STORY IS SO INTERESTING, AND NOWADAYS THE NUMBER ZERO IS SO IMPORTANT IN OUR DAILY LIFE, BECAUSE JUST WHEN WE HAVE BORN THE NUMBER ZERO HAS REALLY EXISTED. 

TARTAGLIA TRIANGLE.

So, there I'm going to talk about the Triangle Tartaglia.

• The triangle Tartaglia combinatorial numbers or Pascal (because it was the mathematician who popularized it) is a triangle of integers, infinite and symmetric.
• Pascal's triangle Tartaglia will be very useful for calculating the Newton's binomial coefecientes. (Formula which provides development nth power of n -n being positive integer- of a binomial.)
• It is associated with the name of the mathematician Pascal because he wrote the first treatise of the triangle and Tartaglia because the italian, was the first who published it in Europe.

                  

• The properties of this triangle were known many years before Pascal formulate, by chinese, indian, persian mathematicians ... but it was he who organized all the information together.

          For example, in China there isn't Pascal's triangle, there is Yang Hui's triangle. (You can see it at the picture below.)

                           

• The construction of the Tartaglia triangle is like that and following:

                            

• Some numbers, such as - 1 2 1 - y - 1 3 3 1 - are the coefficients of the identities below:

         (a + b)² = a² + 2 · a · b + b²

        (a + b)³ = a³ + 3 · a² · b + 3 · a · b² + b³

Mathematics in real life.

Now, I'm going to talk about mathematics in real life. Nowadays, a big number of students think that maths will not appeared in their futures, that maths won't be a problem because of the advances in technology, or the uses of calculators, but they're wrong. Maths is in every step we take, because every day we should resolve many numeral problems in each situation.

We can use Maths in situations such us:

When we are doing the shopping, when they look for the lowest price, or calculating the discount that are marked; In the kitchen, when we make a recipe, changing the units of measurement; With the money, when you calculate the amount of money that the other have to give you, or to count the coins that you need to buy a product; In trips, to calculate the estimated time of arrival...

This are many situations in life that required the use of the mathematics, so I think that we have to learn it for the best in our future, as you can see, every single day we use it!

INTRODUCTION.

• This blog has been created with the goal of learning, is a way to learn about the subjects of Calculus, Algebra and Communication skills in engineering and create a blog.
• This entry will address a specific topic, calculus.
• Calculus refers to the result for the action to calculate or count. Calculate, is to perform the operations necessary to predict the outcome or know the consequences of a previously known data. 

                 - The most common use of the term calculation is the logical-mathematical. From this perspective, the calculation is a mechanical process where we know the consequences of a previously known data.

                 - The calculation is natural for human when we start to relate things together, in logical-mathematical sense appears when reason begins to formalize.

• Today we can say that the calculus is a binary system, which has great computing power achieved by computers, its calculation speed is inhuman, millions of operations per second.