Senin, 27 Februari 2012

KISAH HIDUP LEONHARD EULER PENEMU RUMUS MATEMATIKA


Leonhard Euler lahir 15 April 1707 di Basel, Swiss. Dia diterima di Universitas Basel pada tahun 1720 saat berusia 13 tahun. Dan mendapat gelar sarjana pada usia 17 tahun.
Pada mulanya, Euler mempelajari tentang teologi, yaitu ilmu yang mempelajari segala sesuatu yang berkaitan dengan keyakinan beragama. Tetapi, tidak lama ia kemudian pindah ke mata pelajaran matematika.
Saat usianya 21 tahun, Euler sudah menerima undangan Catherine I dari Rusia untuk bergabung dalam Akademi Ilmu Pengetahuan di St. Peterburg. Pada usia 23 tahun, dia menjadi guru besar fisika dan matematika. Ia dipandang sebagai matematikawan terbesar di sepanjang masa bersama Archimedes, Gauss, dan Newton. Ia secara genius melanggar dasar teori Einstein. Ia juga menemukan berbagai notasi matematika termasuk konsep fungsi dan cara menuliskannya sebagai f(x), singkatan fungsi trigonometri, ‘e’ sebagai dasar logaritma alami (the Euler Constant), huruf Yunani Sigma untuk penjumlahan dan huruf ‘i’ untuk unit imajiner, serta simbol ‘pi’ untuk rasio keliling lingkaran dengan diameternya dan masih banyak lagi. Semua itu adalah yang memainkan peranan besar pada matematika modern, sampai saat ini. Selain itu, ia juga memecahkan Tujuh Jembatan masalah Koenigsberg dalam teori graph, menemukan Kerakteristik Euler untuk menggabungkan jumlah simpul, sisi dan wajah objek, dan sebagainya. Ia juga memecahkan banyak teori matematika ilmuan lain. Selain itu, ia terus mengembangkan kalkulus, topologi, teori bilangan, analisis dari teori graph serta masih banyak lagi. Dia juga memperkenalkan terminologi dan notasi matematika modern, terutama analisis matematika, seperti konsep fungsi matematika. Dia juga dikenal dengan karya-karyanya dalam bidang mekanika, dinamika fungsi, optika dan astronomi.
Hasil karya Euler mempengaruhi penggunaan semua bidang fisika dan di banyak bidang rekayasa. Dia menulis 32 buku lengkap, banyak diantaranya terdiri dari 2 jilid, ratusan artikel tentang matematika dan ilmu pengetahuan. Banyak yang bilang bahwa kumpulan tulisan-tulisan ilmiahnya terdiri dari 70 jilid.
Pada saat usianya 26 tahun, Euler ditunjuk untuk menggantikan posisi ketua matematika yang sebelumnya diduduki oleh matematikus Daniel Bernoulli. Namun, 2 tahun kemudian salah satu matanya kehilangan penglihatan. Tapi ia tidak patah semangat. Euler terus bekerja dan berkarya menghasilkan artikel-artikel yang brilian.
Tahun 1741, Federick Yang Agung dari Prusia membujuk Euler agar meninggalkan Rusia dan memintanya bergabung ke dalam Akademi Ilmu Pengetahuan di Berlin. Dian tinggal di Berlin selama dua puluh lima tahun dan kembali ke Rusia pada tahun 1766.
Namun, tidak lama kemudian di terkena musibah. Kedua matanya tidak bisa melihat lagi. Meski tidak bisa melihat, Euler tetap bekerja melakukan penyelidikan dan berkarya. Euler memiliki kemampuan spektakuler dalam hal mental aritmatika.
Euler wafat pada 18 September 1783 di St. Peterburg (sekarang bernama Leningrad) di usia 76 tahun. Meskipun demikian, Euler tetap saja terus mengeluarkan kertas kerja kelas ringgi di bidang matematika. Euler menikah dua kali dan mempunyai tiga belas anak, delapan diantaranya mati muda.
Untuk menghormatnya, nama salah satu asteroid, 2002 Euler berasal dari namanya. Dia juga dikenang oleh Gereja Lutheran pada kalender para Santa Lutheran pada tanggal 24 Mei. Euler merupakan penganut agama kristen dan mempercayai bahwa alkitab bersih dari segala kesalahan dan berargumen sengit melawan para atheis ternama pada zamannya.

Sumber :

Nama  : Rizki Yudhi Pratiwi
NIM     : 10305144020

Selasa, 03 Januari 2012

Mengembangkan Nilai-Nilai Filosofis matematika dalam Pembelajaran Matematika Menuju Era Global


By : Rizki Yudhi Pratiwi
10305144020
MATEMATIKA SWADANA 2010
(http://akuyudhipblg.blogspot.com/)

The development of mathematics education can be conducted on two level, i.e. in macro and micro. In the macro means the development of mathematics should be able to renew and develop their vision of education as well as scrape out paradigm constraints for education by maintaining and improving the quality and profesionalisma and community empowerment towards new, namely Indonesia Indonesia open, democratic and unified. For a teacher, educational development at the macro level for some of the stuff is outside the range of thought and the capability. However, given the guru is what determines the success of education, the teacher can cast the object and subject of the development of education by improving the ability of the educating and managing class.
The value of mathematics can be seen from the context of ontologism, epistemological and axiological, within the limits of extrinsic and intrinsic value, systemic. For math, then student the value of the lowest math is if used only for yourself, a higher value is if the math can be used for the public interest. But, in fact the highest mathematical score is a mathematical value is systemic can be used for the wider interests. But the mathematical values developed should be coupled with critical thinking, because math is not another critical thinking itself.
In the field of education, teachers need to continuously evaluate the lack or excess to teach in order to obtain information for improvement to teach, if need to learn new techniques that are more interesting and effective. To that end, teachers need to get a boost from the parties concerned especially the principal and School owners, so that they can bring about a good teaching. A teacher can reflect the style of teaching is good and flexible if teachers were mastered how to organise the class, make use of learning resources, the achievement of the purpose of teaching the student accordingly, development capability evaluation system, handling individual differences, and embody a particular style as required.

Kegiatan Penelitian sebagai Usaha untuk Meningkatkan Profesionalisme Guru Matematika


By : Rizki Yudhi Pratiwi
10305144020
MATEMATIKA SWADANA 2010
(http://akuyudhipblg.blogspot.com/)

If the teacher wants the reform of mathematics education, mathematics education research will be a need. Aside from the legal aspects of formal mathematics education activities either then by teachers, lecturers and teachers will be member many benefits. With research mathematics education we can know the existence of differences in individual or group in the study of mathematics, we can determine the position of students in a group, can compare the results of learning between groups. We can also conduct an examination for compliance with the goals of learning outcomes from, do a basic standard of competency or competency has been achieved or not. The results of research can be used for refinement of the program, guidance, provision of information to the public. In addition, we can also make a comparison between performance and criteria for each program as well as the refinement of the program dimension and penyimpulan results of the mathematics education as a whole. Next we can conduct studies on the implementation of the program, curriculum or syllabus of study results, and ultimately used for the improvement of mathematics education program in its entirety.

Pembelajaran Matematika Berbantuan Kalkulator : Studi Kasus Penggunaan Kalkulator Texas Instrument TI 89 pada PBM Matematika di SMK MUHAMMADIYAH IV YOGYAKARTA


By : Rizki Yudhi Pratiwi
10305144020
MATEMATIKA SWADANA 2010
(http://akuyudhipblg.blogspot.com/)

In developed countries, the role of y6ang calculator is important in the process of learning math. This type of Calculator experience rapid growth. Types consist of two kinds, namely ordinary scientific calculator and a calculator. One example is the calculator graphic scientific calculator that can solve math problems quickly and display it in the form of graphs, and can also be used to create a program that can solve a math problem.
From research conducted on PBM Math class I SMK Muhammaditah IV, can be inferred that the utilization of the calculator as a tool in the study can be done in four phases, namely :
1.       The stage of understanding of the significance of the graphic calculator.
2.       Stages of understanding the theory and use of calculators in graph equations solve problems and inequality.
3.       Stage of entering data into the calculator graphic problem.
4.       The interpretation of the display screen calculator chart and draw conclusions.
From penelotian there are also several aspects of the utilization graph Calculator in mathematics learning, namely :
1.       Chart Calculators aimed at determining and match image graphics.
2.       Chart Calculators useful for determining and match answers the set resolution.
3.       Calculator charts to give you real experience about the graphic image.
4.       The settlement of the question of equality and inequality can use the command, the manipulation of symbolic and graphing.
5.       Chart Calculators useful to give an answer that was previously calculated without a calculator and speed up the completion of a math problem.
6.       Constraints experienced by students in using the calculator graphic is a membahasakan in mathematical expressions into the calculator and reveal any screen display calculators into mathematical expressions.
7.       The graph Calculator in the teaching of mathematics, mathematics became more attractive and easier solution to math problems.
8.       If the use of graph without offset calculator the ability to understand the operating procedures and mathematical thinking it can lead to a high level of dependence, loss of self-confidence, and lazy thought.