Cara yang Benar dalam Belajar Matematika

Banyak orang yang takut dengan pelajaran matematika. Ada juga orang yang sangat benci dengan matematika. Padahal pelajaran ini benar-benar berguna bagi kehidupant kita sehari hari, bahkan bagi orang biasa sekalipun. Matematika adalah kunci dari semua pelajaran sains, baik itu Fisika, Ekonomi, Akuntansi dan Kimia karena pelajaran tersebut tidak akan dapat kita pahami tanpa mempelajari terlebih dahulu dasarnya yaitu matematika. Ada orang yang bilang ” ilmu lain tidak bisa berkembang tanpa matematika, tetapi matematika bisa berkembang tanpa ilmu lain”. Ada juga yang bilang ” kepanjangan dari matematika adalah makin tekun makin tidak karuan”. Namun yang jadi permasalahan sekarang adalah, bagaimana cara belajar yang baik agar kita dapat menguasai ilmu matematika ini?

Harus diingat bahwa tidak ada cara mudah dan cepat untuk menguasai matematika ini. Yang ada adalah Cara yang benar dalam belajar matematika. Dibutuhkan kesabaran dan kegigihan yang tinggi untuk berusaha, tapi dengan niat yang kuat saya yakin kita bisa menguasai pelajaran matematika. Ada beberapa tips yang bisa kita tempuh agar kia bisa menguasai Matematika:

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Leonhard Euler (1707 – 1783)

From `A Short Account of the History of Mathematics’ (4th edition, 1908) by W. W. Rouse Ball.

Leonhard Euler was born at Bâle on April 15, 1707, and died at St. Petersburg on September 7, 1783. he was the son of a Lutheran minister who had settled at Bâle, and was educated in his native town under the direction of John Bernoulli, with whose sons Daniel and Nicholas he formed a lifelong friendship. When, in 1725, the younger Bernoullis went to Russia, on the invitation of the empress, they procured a place there for Euler, which in 1733 he exchanged for the chair of mathematics, then vacated by Daniel Bernoulli. The severity of the climate affected his eyesight, and in 1735 he lost the use of one eye completely. In 1741 he moved to Berlin at the request, or rather command, of Frederick the Great; here he stayed till 1766, when he returned to Russia, and was succeeded at Berlin by Lagrange. Within two or three years of his going back to St. Petersburg he became blind; but in spite of this, and although his house, together with many of his papers, were burnt in 1771, he recast and improved most of his earlier works. He died of apoplexy in 1783. He was married twice.

I think we may sum up Euler’s work by saying that he created a good deal of analysis, and revised almost all the branches of pure mathematics which were then known, filling up the details, adding proofs, and arranging the whole in a consistent form. Such work is very important, and it is fortunate for science when it fall into hands as competent as those of Euler. Continue reading

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A history of Zero

One of the commonest questions which the readers of this archive ask is: Who discovered zero? Why then have we not written an article on zero as one of the first in the archive? The reason is basically because of the difficulty of answering the question in a satisfactory form. If someone had come up with the concept of zero which everyone then saw as a brilliant innovation to enter mathematics from that time on, the question would have a satisfactory answer even if we did not know which genius invented it. The historical record, however, shows quite a different path towards the concept. Zero makes shadowy appearances only to vanish again almost as if mathematicians were searching for it yet did not recognise its fundamental significance even when they saw it.

The first thing to say about zero is that there are two uses of zero which are both extremely important but are somewhat different. One use is as an empty place indicator in our place-value number system. Hence in a number like 2106 the zero is used so that the positions of the 2 and 1 are correct. Clearly 216 means something quite different. The second use of zero is as a number itself in the form we use it as 0. There are also different aspects of zero within these two uses, namely the concept, the notation, and the name. (Our name “zero” derives ultimately from the Arabic sifr which also gives us the word “cipher”.)

Neither of the above uses has an easily described history. It just did not happen that someone invented the ideas, and then everyone started to use them. Also it is fair to say that the number zero is far from an intuitive concept. Mathematical problems started as ‘real’ problems rather than abstract problems. Numbers in early historical times were thought of much more concretely than the abstract concepts which are our numbers today. There are giant mental leaps from 5 horses to 5 “things” and then to the abstract idea of “five”. If ancient peoples solved a problem about how many horses a farmer needed then the problem was not going to have 0 or -23 as an answer. Continue reading

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SEMINAR NASIONAL MATEMATIKA VI

Himpunan Mahasiswa Matematika (HIMATIKA) FMIPA UGM akan mengadakan Seminar Nasional Matematika dengan tema Open Your Mind Through Mathematics Applications. Tema ini dipilih karena matematika yang merupakan  basic science perlu untuk dikaji dan dikenalkan sejak dini. Namun banyak orang yang beranggapan bahwa matematika itu sangat sulit dan aplikasi matematika di kehidupan sehari-hari sangat jarang ditemukan. Hal inilah yang mendasari orang ragu untuk mendalami matematika. Dengan diadakannya acara ini, HIMATIKA FMIPA UGM ingin berusaha membuktikan bahwa matematika tidak sulit untuk dipelajari dan aplikasinya dapat diterapkan dalam kehidupan sehari-hari.

Seminar Nasional Matematika ini merupakan Seminar Nasional Matematika yang ke-6 yang diselenggarakan oleh HIMATIKA FMIPA UGM. Maksud dan tujuan diadakannya acara ini adalah:

  1. Memasyarakatkan matematika sebagai salah satu ilmu dasar yang tidak hanya dipelajari secara teoritis, tetapi juga mempunyai peran besar dalam berbagai bidang
  2. Mengupas aplikasi matematika dalam berbagai aspek kehidupan.
  3. Meningkatkan apresiasi masyarakat terhadap ilmu-ilmu dasar khususnya ilmu matematika Continue reading
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Fibonacci biography

Leonardo Pisano is better known by his nickname Fibonacci. He was the son of Guilielmo and a member of the Bonacci family. Fibonacci himself sometimes used the name Bigollo, which may mean good-for-nothing or a traveller. As stated in [1]:-

Did his countrymen wish to express by this epithet their disdain for a man who concerned himself with questions of no practical value, or does the word in the Tuscan dialect mean a much-travelled man, which he was?

Fibonacci was born in Italy but was educated in North Africa where his father, Guilielmo, held a diplomatic post. His father’s job was to represent the merchants of the Republic of Pisa who were trading in Bugia, later called Bougie and now called Bejaia. Bejaia is a Mediterranean port in northeastern Algeria. The town lies at the mouth of the Wadi Soummam near Mount Gouraya and Cape Carbon. Fibonacci was taught mathematics in Bugia and travelled widely with his father and recognised the enormous advantages of the mathematical systems used in the countries they visited. Fibonacci writes in his famous book Liber abaci (1202):- Continue reading

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