Interview; What´s mathematics and algebra for you?

For the present interview, I could ask a 4th year student in mathematics and informatics double degree student of the Polytechnic university of Madrid about his career and how he sees things inside it. The name of the student is Alejandro Ortega de los Ríos and he offered himself to respond all the questions I had about his passion: mathematics.

Me: Hello Alejandro, first off I will like to thank you because of giving me your time in order to answer my questions.

Alejandro: No problem.

Me: Well so first of all, I would like to ask you why mathematics.

Alejandro: Since I was a little kid, mathematics were a field that impassioned me so much. Of course I am not going to lie, I had doubts since we only live once and I did not want to commit to something I would not like in the future... that is why I had to decide between engineerings and mathematics... but at the very end, I let my heart decide and I studied what I love, and not thinking about the future... and so far I think I chose correctly.

Me: Why you think mathematics are no so interesting for kids of our days?

Alejandro: How mathematics are taught in schools... I do not think is the way to make them appreciate it. You go to a student, tell him: You have to do this or you will not pass, and repeat the course and see you next year... it is not the way to do it. I am not saying I got the key, but when I was in school, I had good and bad teachers. This last ones made me think this subject was hateful, but the first one made me think the opposite. Mathematics has to be taught as a tool for life... something we all need to use if we want to success, not just as a tool for passing or failing exams, because this is not the way to learn. Making kids feel mathematics is the alternative way.

Me: What would you do in order to change this?

As I said, I do not have the key... but I repeat, making kids feel mathematics, showing them that it is an useful tool for life... just as an example, I´ve been watching a series called "Breaking Bad" for the last months. In this series, the main character is a school chemistry teacher. During the episodes, he shows how he has the biggest weapon no one has: knowledge in the fields of mathematics and chemistry, which lets him get whatever he wants with simple formulas he applies. He is able to fabricate artificial bombs, batteries for cars, electrical systems... this is the way of teaching kids, showing how useful it can be for them in the future.

Me: Well, and now let´s get deeper into the topic. What´s algebra for you?

Alejandro: Algebra is just a branch of mathematics... let´s call it the advanced mathematics. For me, algebra is the key for understanding absolutely everything, from simple mechanisms to the laws that rule in the universe.

Algebra Picture.

Me: Why is it so important knowing about algebra?

Alejandro: Without algebra, the world we know nowadays would not be the same. Computers for instance are programmed with algebraic equations and systems. Mobile phones, structures... absolutely everything, even those investigations scientists do out of the Earth to learn about the outer space... I repeat, absolutely everything is algebra, and is the tool humans use for developing.

Me: How you see yourself in the future=

Alejandro: Buff... not really sure, but hope involved in big projects.

Me: Ok Alejandro, thanks you for giving me your time.

Alejandro: Do not worry, it has been a pleasure. Bye.

My video about absolute value of complex number

And what is algebra for?

Algebra as well as explained in previous posts, works for many different fields, and are the key for human development in the 21st century. In this post, I could find two different videos that explain both whats algebra for and how we feel it in our day to day:

For both videos, it is important to put english subtitles since both of them, from the same channel, speak in spanish.

As well as we could see in both videos, algebra is technology, computers, advance... everything around us is constructed through algebraic structures.

The history of algebra

Until the 19th century, Algebra was simply the theory of equations, but not until before the algebra we know in our days was the same. In fact, it is a branch of mathematics, that began being known as the work of an expert mathematician of the 16th century, François Viète.

François Viete.

But how did interest for Algebra started?

In Ancient Egypt,  people learned to solve linear (ax = b) and quadratic (ax² + bx = c) equations. They also could solve some indeterminate equations, which give us an answer for the previous question.

From the past, we can observe that ancient civilizations wrote out algebraic expressions using only occasional abbreviations, and by medieval times, Islamic mathematicians were able to talk of the unknown “x”, and work out the basic algebra of polynomials.

Back again with the 16th century, mathematicians such as René Descartes wrote Book III of La géometrie (1637)which looks much like a modern algebra text. This and references we can obtain from François Viète show us that algebra started being founded at around this century.

René Descartes.

By the time of Gauss, algebra could be finally named as in modern state. Attention mathematicians had focused on polynomial equations changed into studying the structure of abstract mathematical systems who’s axioms were base don the behavior of mathematical objects i.e.: complex numbers, algebraic groups…

Later, XIX-XX century, algebra shifted again with the discovery of quaternions; complex numbers of the form a + bi changed into a + bi + cj + dk. After this discovery, mathematicians started investigating vectors, and this bring us to our days, where algebra, in a continuous develop, has occupied importance and an role in every field, and not only in mathematics.

Algebra Introduction

Short time ago, I read an article about why is Algebra so important in our days if we do not see it, we do not feel it, we do not know how it exactly works. Well, in this article, algebra was named as the gatekeeper subject. Used by professionals ranging from electricians to architects to computer scientists. It fills every field, explains the relationships of our universe: algebra are de advanced maths we need to success. "It is no less than a civil right", says Robert Moses, founder of the Algebra project, which advocates for math literacy in public schools.

Algebra is more than what we study in university after preparing for around 18 years in primary school. Is a way of reordering our mind, and finding different ways of thinking. In conclusion, Algebra is, in short, the gateway to success in the 21st century. What's more, when students make the transition from concrete arithmetic to the symbolic language of algebra, they develop abstract reasoning skills necessary to excel in math and science.

Interview with Dr.Abrahamson

The Tortoise and Achilles

Zeno of Elea (c. 450 BCE) is credited with creating several famous paradoxes, and perhaps the best known is the paradox of the Tortoise and Achilles. 

This paradox ca be only applied in the branch of mathematics, because its complexity cannot be understood in other ones, for instance, physics.

The paradox consist on a race between Achilles and a tortoise. At the beginning, the Tortoise asks Achilles to give her a small head start. Achilles, laughing, answers 10 meters, knowing for sure he will win even though the tortoise begins "x" meters ahead, in this case, 10. 

Once the race was going to start, Achilles, annoyed by the tortoise´s laugh, asked her: "How can you be so happy when you will lose for sure?" "Because I won´t, and I´m sure about it" answered the tortoise. "How come?" replied Achilles "Well look, if I start, for instance 10 meters ahead, How long will take you to catch me?" asked smoothly the tortoise." One or two seconds, I mean, almost nothing" answered in a brave way Achilles."but... think about it, in these 2 seconds, I will not be there anymore, I´ll be ahead again." "Well, then I will catch you again in less than a second""but again... I will not be there, maybe 1 or less than one steps from you, but still ahead; therefore, I´m sorry Achilles, but you will never catch me" Achilles, surprised, answer"Yeah... but... but... oh no, you are right, as always" replied in a sad way.

This paradox obviously cannot happen in real life, but demonstrates that mathematics rules applied in non-mathematical situations can give us strange results; in this case, it give us one of the principals of an infinity limit.