WEB-BASED LESSON: CONES

In our daily life, we are certainly familiar with these following things:

Rice Cone

Hat

Ice Cream

Trumpet

Farmer Hat

If we look at the objects carefully, we will find that those things have the same shape. Yes, the objects are equally formed one of solid figures with curved surfaces, one of learning materials which have been learned in Elementary School. As we have been learned, solid figures with curved surfaces consists of three types namely cylinder, cone and sphere. What about the things above, are they cylinders, cones or spheres? Look at the objects around us and find the other objects which have the same shape with the objects above!

 

WEB-BASED LESSON: KERUCUT

Dalam kehidupan sehari-hari, kita pasti tidak asing dengan benda-benda berikut ini:

Tumpeng

Caping

Topi

Es Krim

Terompet

Jika kita perhatikan benda-benda di atas dengan seksama, akan kita temukan bahwa benda-benda tersebut memiliki kesamaan bentuk. Ya, benda-benda tersebut sama-sama membentuk salah satu bangun ruang dan sisi lengkung, sebuah materi geometri yang sudah dipelajari di Sekolah Dasar. Sebagaimana telah dipelajari, bangun ruang dan sisi lengkung terdiri atas tiga jenis yaitu tabung, kerucut dan bola. Bagaimana dengan benda-benda di atas, berbentuk tabung, kerucut atau bola? Perhatikan sekitar kita dan temukan benda-benda lain yang memiliki kesamaan bentuk dengan benda-benda di atas!

 

Penukaran Uang di Koperasi Sekolah

Oleh:

Nikmatul Husna (nikmatulhusna13@gmail.com)

Sri Rejeki (srirejeki345@rocketmail.com)

Uang adalah salah satu benda yang tidak dapat dipisahkan dalam kehidupan kita. Uang merupakan alat yang digunnakan untuk melakukan transaksi jual beli. Oleh karena itu,  hendaknya setiap orang dapat memahami dengan baik nilai mata uang.

Materi mengenai uang mulai dipelajari siswa di kelas III Sekolah Dasar. Siswa akan mempelajari mengenai nilai-nilai mata uang dan kesetaraan dari nilai mata uang. Dalam mempelajari materi ini, kita dapat mengaitkannya dengan situasi yang sering dijumpai siswa. Hal ini sesuai dengan yang diungkapkan oleh Freudenthal  tentang didactical phenomenolgy. Didaktikal fenomenologis adalah menggunakan analisis dari kejadian di dunia nyata sebagai sumber dari matematika. Hal yang penting dalam didaktikal fenomenologis adalah fenomena-fenomena nyata yang terjadi dapat memberikan kontribusi dalam matematika, bagaimana siswa dapat menghubungkan fenomena-fenomena tersebut dan bagaimana konsep-konsep muncul kepada siswa. (Freudenthal,2002:12)

 

Fibonacci and Kelinci

Bilangan Fibonacci ditemukan oleh seorang matematikawan Italia Leonardo Fibonacci (kira-kira tahun 1175 – 1250) ketika mempelajari angka kelahiran kelinci. Andaikan sepasang kelinci terlalu muda untuk bereproduksi di bulan pertama, tapi pada bulan kedua dan seterusnya memproduksi sepasang bayi kelinci setiap bulannya. Aturan ini berlaku pada setiap pasang kelinci. Pasangan kelinci pada lima bulan pertama ditunjukkan pada gambar di atas. Banyaknya pasangan kelinci untuk lima bulan pertama merupakan bilangan Fibonacci 1, 1, 2, 3, 5. Jika pola kelahiran ini dilanjutkan, banyaknya pasangan kelinci pada bulan-bulan berikutnya akan membentuk bilangan Fibonacci. Kenyataan  bahwa bilangan Fibonacci dapat diaplikasikan pada tanaman dan pepohonan terjadi beberapa ratus tahun setelah penemuan dari barisan bilangan ini.

 

Abstract Algebra – Exercises 2.4

2.4 The Principle of Mathematical Induction

In the world of mathematics, the well-ordering principle (WOP) is often taken as an axiom. In this section, we derive a theorem based on the WOP called the principle of mathematical induction (PMI). In high school, you might have done what is called proofs by induction, where you built an argument that was analagous to knocking down an infinite row of dominoes. First, you showed figuratively that you can knock the first domino down. Then you showed that if the nth domino falls, then so does the (n + 1)st. This very, very important proof technique is useful when the theorem you’re trying to prove has a form like one of these:

1 + 2 + 3 + ··· + n = (n(n + 1))/2

or perhaps

A ∪ (B1 ∩ B2 ∩ ··· ∩ Bn ) = (A ∪ B1 ) ∩ (A ∪ B2 ) ∩ ··· ∩ (A ∪ Bn )

where the theorem makes a statement about a finite but unspecified n number of things, and you want to prove that the claim is true for any n ∈ N.

In this section, my friend (Ahmad Wachidul Kohar) and I try to make a resume and solve the exercises which can be downloaded in this following link: 2.4 The Principle of Mathematical Induction

 

Abstract Algebra – Exercises 2.3

2.3 Algebraic and Ordering Properties of R

Assumptions A1-A18 will be used to derive basic and familiar algebraic and ordering properties of the real numbers. The theorems and examples that follow are designed to do two things. First, they will give a feel for how to write proofs of this sort. Second, they will serve as assumptions for the exercises and theorems from later sections.

These are the (A1 – A18):

(A1)         Properties of equality;

(A2)         Addition is well defined;

(A3)         Closure property of addition;

(A4)         Associative property of addition;

(A5)         Commutative property of addition;

 

Abstract Algebra – Exercises 2.1 and 2.2

2.1 Proof Involving Sets

This is the first section of the second chapter in Mathematical Thinking and Writing book. It is time to begin applying the language and logic of chapter 1 to prove writing. A  a good place to do this is with sets. In this section, we address two things. First, we return to the set terminology from chapter 0, and we use to practice some of the concepts we’ve learned so far. second, we get our feet wet by beginning  to write proofs. Right of the bat, we’ll see three useful techniques  for writing proofs: direct proofs, proofs by contrapositive and proofs by contradiction.

2.2 Indexed Families of Sets

If we’re working with a few sets at a time, it’s probably sufficient to use A, B , and C to represent them. Yet, if we have many sets, for instance, 10 sets (generally called a family or collection of sets instead of a set of sets), it might be more sensible to put them into a family and address them as A1 , A2 , …, A10 . In a case like this, we would say that the set {1, 2, 3,…, 10} indexes the family of sets.

My friend (Ahmad Wachidul Kohar) and I try to make a resume and solve the exercises in those two sections which can be downloaded in this following link: 2.1 Proof Involving Sets and 2.2 Indexed Families of Sets

 

Oulu International Master’s Scholarship Programme

Deadline: 31 Jan 2013 (annual)
Study in: Finland
Course starts September 2013

Brief description:

The University of Oulu International Master’s Scholarships provide scholarships in architecture, business, economics, education, engineering, and sciences to academically talented international students who wants to study a Master’s Programme in Finland.

 

Scholarship 2013 at University of Groningen in Netherlands

Deadline: around Feb 2013
Study in:  Netherlands
Course starts September 2013

Brief description:

The Erik Bleumink Fund Scholarships are usually awarded for a maximum of 2 years for a Master’s degree programme, and a maximum of 4 years for a PhD. For PhD, part of the research should be conducted in the home country and part in Groningen .

 

Erasmus Mundus Scholarship (12 November 2012 hingga 31 Januari 2013)

Ayo, Masih Bisa Daftar Beasiswa Erasmus Mundus!

JAKARTA – Komisi Eropa melalui Erasmus Mundus, menyediakan beasiswa bagi mahasiswa-mahasiswi S-1. Bagi lulusan S-1 yang memenuhi syarat dari negara-negara di luar Uni Eropa, bisa  mengikuti program-program magister Erasmus Mundus tertentu di Eropa dalam jangka waktu satu sampai dua tahun.

Erasmus Mundus adalah sebuah program kerjasama dan mobilitas dalam bidang pendidikan tinggi yang bertujuan untuk mempromosikan Uni Eropa sebagai pusat keunggulan ilmu di dunia. Program Erasmus Mundus dibiayai oleh Uni Eropa dan terdiri atas Kegiatan satu sampai dengan tiga.