Ahli Matematika

Carl Friedrich Gauss

Carl Fredrich Gauss memiliki nama asli Johann Carl Friedrich Gauss lahir di Braunschweig, pada tanggal 30 April 1777 dan wafat di Göttingen, 23 Februari 1855 pada umurnya yang ke 77 tahun. Adalah seorang matematikawan, astronom, dan fisikawan Jerman yang memberikan beragam kontribusi.

Saat umurnya belum genap 3 tahun, ia sudah mampu mengoreksi kesalahan daftar gaji tukang batu ayahnya. Pada umur 10 tahun, ia sudah membuat gurunya terkagum-kagum dengan memberikan rumus untuk menghitung jumlah suatu deret aritmatika berupa penghitungan deret 1+2+3+...+100. Meski cerita ini hampir sepenuhnya benar, soal yang diberikan gurunya sebenarnya lebih sulit dari itu. Gauss melakukan penelitiannya di observatorium astronomi di gottingen, kota kecil di jantung jerman. Yang dengan segera menciptakan tradisi matematis yang membuat Gottingen dan universitasnya menjadi pusat matematika dunia.

Di universitas Gottingen, karya Gauss dapat diperbandingkan dengan karya para matematikawan lain dan hasilnya memang mencolok. Semakin dia membandingkan akhirnya dia menyadari bahwa dia adalah seorang matematikawan besar. Gauss selalu menyimpan semua penemuannya dan menyesal bahwa tidak seorangpun dapat berdiskusi tentang teori-teori yang menarik hatinya. Salah seorang teman baiknya di universitas adalah Wolfgang Bolyai, bangsawan Hongaria yang kelak anak lakinya [Janos Bolyai] menemukan geometri non-Euclidian.

Kemampuan intelektual Gauss menarik perhatian dari Duke of Brunswick, yang mengirimnya ke Collegium Carolinum (sekarang Braunschweig University of Technology ), yang dihadiri 1792-1795, dan ke Universitas Göttingen 1795-1798. Sementara di universitas, Gauss secara mandiri menemukan kembali beberapa teorema penting.

Nama Gauss mulai terkenal sehingga merencanakan menggunakan bahan-bahan dalam buku itu untuk disertasi doktoral, namun pihak penerbit menolak. Dicari judul lain sebelum akhirnya didapat judul panjang, Demonstratio nova theorematis omnem functionem algebraicam rationalem integram unius variabilis in factores reales primi vel secundi gradus revolvi posse yang terbit lebih awal, tahun 1799. Isi tesis doktoral adalah membuktikan theorema dasar aljabar – membuktikan bahwa polinomial pangkat n (kuadrat adalah pangkat 2 dan kubik adalah pangkat 3, quartik adalah pangkat 4 dan seterusnya) mempunyai (hasil) akar pangkat n juga. Hal tersebut baru valid (sahih) apabila perlakuan terhadap bilangan imajiner sama seperti bilangan riil.

Bidang analisis dan geometri mengandung banyak sekali sumbangan-sumbangan pikiran Gauss, ide geometri non Euclidis ia garap pada 1797. Kemudian pada tahun 1799 ia  menyumbangkan tesis doktornya mengenai Teorema Dasar Aljabar. Pada 1800 berhasil menciptakan metode kuadrat terkecil.

Pada 1801 berhasil menjawab pertanyaan yang berusia 2000 tahun dengan membuat polygon 17 sisi dengan memakai penggaris dan kompas. Di tahun ini ia juga menerbitkan Disquisitiones Arithmeticae, sebuah karya klasik tentang teori bilangan yang paling berpengaruh sepanjang masa.

Gauss adalah ilmuwan dalam berbagai bidang antara lain matematika, fisika, dan astronomi. Bidang analisis dan geometri menyumbang banyak sekali sumbangan-sumbangan pikiran Gauss dalam matematika. Kalkulus (termasuk limit) ialah salah satu bidang analisis yang juga menarik perhatiannya.

Referensi:

https://blogpenemu.blogspot.co.id/2014/06/biografi-carl-friedrich-gauss-penemu-Teori-Bilangan.html

http://www.biografiku.com/2009/01/biografi-carl-friedrich-gauss.html

Komentar:

Gauss adalah ilmuan yang sangat cerdas, terbukti pada saat berusia 3 tahun ia sudah bisa mengerti kesalahan tentang gaji. Padahal untuk ukuran anak sesuai tersebut umumnya hanya bisa bernyanyi dan bermain, tetapi Gauss sudah bisa melakukan hal yang seharusnya hanya orang dewasa yang bisa, dan juga pada usia 10 tahun ia juga sudah bisa menemukan rumus tentang deret aritmatika. Sampai melanjutkan ke pendidikan doktornya, ia masih menciptakan karya-karyanya yang masih digunakan sampai sekarang, antara lain geometri non Euclidis, Teorema Dasar Aljabar, dan juga metode kuadrat terkecil.

Gauss juga tidak hanya berkecimpung di bidang matematika, ia juga seorang ilmuan di bidang fisika dan astronomi. Itu menandakan bahwa Gauss tidak hanya handal di bidang matematika. Karya-karya Gauss yang sampai saat ini yaitu tentang kalkulus dan geometri. 

Book Review : Double-majored in math with English

I.                   The identity book:

Book title                    :  MATHEMATICS 3 for Junior High School 

Author                        : Dr. Marsigit, M.A.

Mathematic editor       : Rahman Dwi Fajarsih

Dewi Noviyanti Sari

Translator                   : Dr. Marsigit, M.A.

English editor              : Mokhamad Irfan

Rina Dwi Indriastuty

Content designer        : Dadi Wiyono

Imam Rohamn

Cover Designer           : M. Nuradi

Publisher                     : Yudhistira

Mold                          : 1, 2009

Thickness                    : viii + 238 pages

ISBN                          : 978-979-019-064-1

Reviewer                     : Dhina Windy Astari

II.                The description of the book:

Mathematics is a subject which is already commonplace taught of us treading elementary school. Mathematics is the basis of all science. Without knowing the math then we'd be hard-pressed to do a thing. The math itself has a variety of things in terms of discussion.

In this book there are various mathematical topics that are very useful, which is acontinuation of the previous book. This book is a book that is intended for the students of junior high school class IX. This book comes with two languages, namely English and Englishso as to facilitate the learning. We can learn two things: Math and English. And this bookhas a 2006 public sukah KTSP we used before.

In the book there are three units, namely geometeri and measurement, statistics and odds, and the number is then divided into five chapters that are packaged in clear. The first chapter is similarity. That has been divided into subchapters  which arethe first two buildings of the datai congruent, the second is a flat wake two congruent, and the third is a pemecahan problem-solving that involves the concept of similarity. The second chapter is up curved side room has sub chapters the first tubes, cones, and spheres. The third chapter is the statistics and opportunities with a sub chapter statistics and oddsanyway. The fourth chapter is the rank and the roots, the subchapters is the same as the rank and the roots. And the last is a sequence and sequence numbers with a subchapter of pattern numbers, line numbers, and a series of numbers. This book is equipped with exercise late in the babnya and also the end of all chapters of the national exam as well as exercises because this book is indeed intended for class IX, who will face the national exam.

III.             Excess books:

In this book the author describes explicitly about his examples, such as a field or image etc.The author also lists an example problem and solution in each end discussion so that makes it easier for readers to understand any of the materials, then the author give latihanuntukwe practice regarding such material. In this book the author in conveying material is also delivered in order and sequence. The given problem is also weighted, ranging from the easiest to the reserved enough humanizing humanity. The language is also easy to understand the various circles and also this book full of color, so make the people who read it are not quickly get bored. This book includes a lightweight book juda if compared toother bilingual books. With two languages will make it easier in a given in the study. We canlearn math and English in one book.

IV.             Weakness of the book:

In this book also has some disadvantages. One such example was a matter of discussion andless berfariasi. As well as for its exercise are also less numerous. In terms of the cover in my opinion less attractive, because it is only showing the old blue color combined with light bluecolour which led to be pale. Because the cover was also very influential towards someone interested in a book. As well as books that's so rare now that re-use ktsp 2006 making many students who come back wearing similar books such as the book.

V.                Conclusion:

Overall, this book has more advantages than disadvantages, so in my opinion this bookincluding a good book. Although this book is intended to show the junior class IX studentsbut this book can also be read or studied by all walks of life.

BEING A GOOD MASTER OF CEREMONY

          Until we should consider some points. First about preparation,  preparation is very-very important. Before we do everything not only for being master of ceremony, but for doing everything, so preparation is everything. He even say that preparation is everything. Why ? Because it is such kind of “kodrat, takdir, or sunatullah”. Being a human life, that life is something moving a process and circeling moving from the past, present, and future. So, the past is a preparation for present and the present time is a preparation for the future. So, in order that, we are able to perform the best in the present or also we do the best preparation in the past in order that we do able to perform the best in the future. We should do the best preparation in the present. So preparation is very important. What should we do to prepare a preparation in there are many aspect. First our psychology, our emotion, and then our personality and our attitude and behaviour, thats very important. In order we have good attitude, good behaviour, personality, so we should be aware of everything related to aim, the purpose that we will do and we order should to understand about the knowledge, understand about the people, understand about even, understand about the program. And we have contextually experience involving in the activity, because our involvment in the activity will make us good understanding and then will make us to feel confident. Our confident is very important. So we also should understand about the relationship among the peolpe, position of the people, and the assignment from the people, and the structure of the community, the structure of institution the time and the program. It is about preparation. The next step in a preparation is doing simulation to simulate a commonly people said as “gladi resik”. “Gladi kotor and gladi resik” doing simulation can be conducted by individual people or by a group of people or by a whole community. We our self as a master of ceremony and conduct a simulation in our room but is whole all member of community can conduct together in the same time, in the same place to simulate what will happen next day or tomorrow when the even start to begin. Simulation is very important. And then the next thing is getting skill and experience. After you try to prepare to simulatated and then we try to get our skill. Skill in influencing peoples, skill in introducing something, skill in sharing information etc. So to get our skill and our competence we need a basic competence. Basic competence a cover for example pronounciation, good pronounciation, loud but not too loud, soft but not too soft so. Experience, doing experience , so in order to get experience you need to get a skill and we need to get a understanding. We can learn from everywhere anytime, whatever of resource, now we can browse internet to look for, to find out, the reference related to our plan activity. As we here all this morning that some of us have similar resources, no problem. But, because language need skill, need to repeat and repeat again. So, sometimes we just need to copy, to copy other people in talking, in presenting, in posting something in front of audience. I think that’s all about the first part that’s all about being master of ceremony because in the next here probably we will involve in such kind of event because our departement, our faculty sometimes conducting national seminar and international seminar of mathematics and mathematics education. In which involving many students as commitee, possibly some of we choosen as a master of ceremony. Secondly, in here he would like to remind we and to remember we about continue our reading my posting by making a comment again, please write our english in standard english. The longer the better, the longer our sentences is better, to get more experiences in writing english and for somebody for we that we feel  not good achievement in here, we should work hard to collect our point. Collecting number of comment. Shouldly, he wish to talk about developing english for mathematics. He also would like to remember we that, please read his junior text book for grade 1,2,and 3. Because he will take some material from the text book to be final examination. So, if we can learn from the meeting between us and him, there are some remark here. The first, he assume that we are an adult people, the characteristic of adult people is that we can take we own responsibility, we learn. Number two, his philosophy of teaching for him to teach is to facilitate we all in order that we are able to learn english individually and colaborativly. Number three, his philosophy of learning. Learning is constructing, we can learn something if we learn the concept of A. So, really for him we try to construct the concept of A, so learning is to construct. In general learning is to construct  our  life, learning is to construct our english. So, he like we to have a different achievement of english. So, the kind and the type of english depend on our activity.So, as the adult learner we have a responsibility to actively construct our own english. Constructing our own english by reading, by writing, by speaking, by translating, by discussing, etc. Number four, the philosophy of learing resources. The learning resources, he developes is that we can learn from everything that lives in surrounding us can be use as learning resources. So, we can learn english from the books, television, newspaper, internet, or direct communication with native speaker. The next is about examination or evaluation. How can he evaluate we or how can he evaluate our competence and our english? So, he use portofolio, he use documentation contain our achievement. So, at the end of this semester i will close my blog, maybe we can still open my blog, but we can’t access and we can’t give a comment. Possibly we can give a comment, but our comment cannot deliver to my email at the end of this month. So please use the time effectively to improve our comment. And then he will combine the result and the comment also, but speaking here is a highly score and also the comment also has a high score.  And a examination only small portion. Expecially in a spesific translation about mathematics and written mathematics in english, he thinks it is very easy because most of mathematics written in symbolic language. So, if we have experiences in communication in general he think we can also have experiences, a good competents in explaining elaborating mathematics in english. 

Simple Reality Of Mathematic

The majority of people must know mathematics, ranging from children to the elderly who don’t know letter of the alphabet  may still be familiar with the mathematics that is identical with counting. But most of the people that only understand mathematics globally only, and don’t know how the concept of mathematics itself. As with the simple counting  like this, when people are asked whether 4x6 and 6x4 are the same, they will surely answer that question is the same, but it is wrong. If 4x6 is translated "four times six" which means that 4x 6 or 6 + 6 + 6 + 6 = 24, and as much as 6x 6x4 which is 4 or 4 + 4 + 4 + 4 + 4 + 4 = 24. Although the final answer is equal, but the way in finding answers are worth 24 was different. 

Most people just want to think practically in mathematics. As the above example would not think to bother just to find the answer. As long as that is true then most people will use a practical way. Most people will only look at it in terms of size, value, shape, contents etc. But for someone interested in mathematics, they will seek to know and prove the truth of this fact. From there we can know that the person is a different way of thinking. Why does the way of thinking of different people? What's wrong with our brains? Let's see...

1.      The first is from our system. Each person will definitely develop a system in the brain lives in each of which will determine what will be created as a way of thinking.

2.      The second is the icon, it will make a person's perspective is different, because every person has the Qibla icon that will be followed in accordance with common sense.

3.   The third is of symbolic meaning or the other of our level. This is very important because it determines the level of a person's ability to think. 

As we let the level of a person is a volcano, we call it volcano mountain, from the volcano can be divided into 4 levels.

1.      Low level is a basic or initial of us that pre-school education, there we only excercise about basic ability just simply according to ability level with this because it is the stage where the gold is still contaminated by the burdensome thoughts, and at this stage it is not taught by any complex the math.

2.  The second level is the primary here began to be trained in basic math tingkatanya above pre-school, this is the key level with someone can go to the next level.

3.      That is junior high school, math has narrowed here and start a little complicated, but it is not level with nothing further than the level of senior high school. This mathematics stage has begun to lead to college.

4.      Last ditingkatan filled by the university level, where a person has been directed specifically to the only mathematics course for mathematics majors who take good fit with this discussion. 

In addition, it requires a perception of mathematics, concepts, understanding, implementing decisions in order to deepen mathematics not only superficially but also to keakar-roots. Memory, comprehension, application, analysis consisting of the will, knowledge, attitudes, abilities, and translation, as well as a standard in the evaluation steeped in pure mathematics and in accordance reality.

The Bright Diamond Motivation

Motivation is very important for us, its can make our spirit up. I have a lecture in my university who makes my spirit is up and he has many inspiration story. In here, i want to share his great experiences. When he was in Junior High School, he didn’t really has a lot of language and artistry talent, but he has a tremendous interest in the subject of Mathematics in the High School.When he was in Senior High School, he was included to the student community who has the best track record.

However one of his expectation, he want to be able to speak in English. The distance from home to school is 20 kilometers and the lack of Internet access in the time is not a barrier for him who are eager to speak English. In his spare time, he liked to cycle to his grandfather’s house. He also liked to shop a lot of books in the Shoping Center first because so many people were selling in that area. Start of books published by Hong Kong, Rainbow magazine that tells about the environment and animals and so forth. In essence, he was  motivated to continue read  interested things.

In the story, in high school, he successed to win both general and intends to continue his studies in FKIE Yogyakarta State University (Mathematics Education IKIP Yogyarta). One of the most memorable experiences and he ever got result B in the Statistics lesson. Imagine, only two people at that time, which totaled completed in the course. Finally, he was appointed to be an assistant professor and kept his expectation be able to speak English, because he wished to college and then he would be a master in foreign. TOEFL minimum requirement when it should reach 500, then in the end he was financed by the University to get an English Language course scholarship  in the IKIP Malang for 6 months. It is very unfortunate, one of the bitter struggle which had been done was obtaining a TOEFL score which only 449. Apparently, it's based on some mistakes and he was not aware.

After  6 months course at the IKIP Malang, he got a good result on TOEFL test. The result is 550. In 1996, he got a scholarship from the World Bank to continue his college in England. He was able to complete his college for 1.5 years. Finally, he decided to spent his time to complete his S3. So many stories that he got in the England. Starting from a very formal English language to the unformal language. I think, he was very brave man, because everytime he always around in English by himself.  His routine activity was jogging around the Hospital University of London and heard conversation of
“bule”.

In 2000, he had traveled to many countries. He had been visited in Thailand up to six times, in Japan up to ten times, four times visited to Australia and he also visited in Kamboja. He always told to every audiences that "If we always speak with correct grammar, we don’t be worry with our pronouncation.”  He has many times in the presentation of an international seminar on Mathematics Education.

I think, one conclution based on his great experience is “from zero to hero”. It means we must struggle to get our dreams come true.