Forum Diskusi Materi Topik 13: Teori Bilangan Elementer (Bagian 1)

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Course Content
Topic 11: Tree Part 1 (Topik 11: Pohon Bagian 1)
RootedTrees EN: Welcome to Topic 11 about Tree Part 1. After completing this topic you are expected to know:LO-01: the definition of a tree, forest, and related elementary theorems. LO-02: the definition of rooted tree, tree-related terminology (such as parents, child, degree, level, height, and more advanced terminology such as m-ary tree, regular tree, and balanced tree). LO-03: some basic properties of a rooted tree.ID: Selamat datang di Topik 11 mengenai Pohon Bagian 1. Setelah menyelesaikan topik ini, Anda diharapkan menguasai capaian berikut:LO-01: memahami definisi pohon, hutan, dan teorema-teorema dasar terkait. LO-02: memahami definisi pohon berakar, terminology terkait pohon (contohnya orangtua, anak, derajat, tingkat, dan ketinggian, dan terminology lanjut seperti pohon m-ary, pohon regular, dan pohon seimbang). LO-03: memahami sifat-sifat dasar terkait pohon berarakar.
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11. Tree 1
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11. Pohon 1
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Online Quiz 11: Pohon (Bagian 1)
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Forum Diskusi Materi Topik 11: Pohon (Bagian 1)
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Binary tree data structure
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Youtube video: introduction to tree
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Some theorems pertaining to tree
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CII1G3-30294 – Matematika Diskrit – PB11 – M1 – DEFINISI POHON
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CII1G3-30294 – Matematika Diskrit – PB11 – M2 – DEFINISI HUTAN DAN SIFAT-SIFAT POHON
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CII1G3-30294 – Matematika Diskrit – PB11 – M3 – DEFINISI POHON BERAKAR DAN PEMILIHAN AKAR
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CII1G3-30294 – Matematika Diskrit – PB11 – M4 – TERMINOLOGI DASAR POHON BAGIAN 1
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CII1G3-30294 – Matematika Diskrit – PB11 – M5 – TERMINOLOGI DASAR POHON BAGIAN 2
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CII1G3-30294 – Matematika Diskrit – PB11 – M6 – TERMINOLOGI DASAR POHON BAGIAN 3
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CII1G3-30294 – Matematika Diskrit – PB11 – M7 – POHON M-ARY
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Topic 12: Tree Part 2 (Topik 12: Pohon Bagian 2)
EN: Welcome to Topic 12 about Tree Part 2. After completing this topic you are expected to know:LO-01: the definition of a spanning tree of a graph and minimum spanning tree of a weighted graph. LO-02: procedures to determine the minimum spanning tree of a weighted graph using Prim and Kruskal algorithm. LO-03: the definition of tree traversal and its types, namely preorder traversal, postorder traversal, and inorder traversal (supplementary). LO-04: some tree applications for parse tree and decision tree (supplementary).ID: Selamat datang di Topik 12 mengenai Pohon Bagian 2. Setelah menyelesaikan topik ini, Anda diharapkan menguasai capaian berikut:LO-01: mengetahui definisi pohon perentang (spanning tree) dari suatu graf dan pohon perentang minimum (minimum spanning tree) dari suatu graf berbobot. LO-02: mampu menentukan pohon perentang minimum (minimum spanning tree) dari suatu graf berbobot menggunakan Algoritma Prim dan Kruskal. LO-03: mengetahui definisi traversal pada pohon dan jenis-jenisnya, yaitu traversal preorder, postorder, dan inorder (materi suplemen). LO-04: mengetahui penerapan pohon untuk pohon urai (parse tree) dan pohon keputusan (decision tree) (materi suplemen).
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12. Tree 2
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12. Pohon 2
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Online Quiz 12: Pohon (Bagian 2)
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Forum Diskusi Materi Topik 12: Pohon (Bagian 2)
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Minimum spanning tree (explanation and source code, hackerearth.com, English version)
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Minimum spanning tree (explanation and source code, hackerearth.com, Bahasa Indonesia version)
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Youtube video: Prim’s algorithm
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Youtube video: Kruskal’s algorithm
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Tree traversal (from geeksforgeeks.org)
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CII1G3-30294 – Matematika Diskrit – PB12 – M1 – DEFINISI POHON PERENTANG
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CII1G3-30294 – Matematika Diskrit – PB12 – M2 – ALOGARITMA PRIM
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CII1G3-30294 – Matematika Diskrit – PB12 – M3 – ALOGARITMA KRUSKAL
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CII1G3-30294 – Matematika Diskrit – PB12 – M4 – TRAVERSAL PREORDER
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CII1G3-30294 – Matematika Diskrit – PB12 – M5 – TRAVERSAL POSTORDER
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CII1G3-30294 – Matematika Diskrit – PB12 – M6 – TRAVERSAL INORDER
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CII1G3-30294 – Matematika Diskrit – PB12 – M7 – POHON URAI
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Topic 13: Elementary Number Theory Part 1 (Topik 13: Teori Bilangan Elementer Bagian 1)
EN: Welcome to Topic 13 about Number Theory Part 1. After completing this topic, you are expected to:LO-01: understand division theorem and its application for calculating mod and div. LO-02: know the definition of prime numbers and composite numbers, elementary methods for prime factorization, and elementary algorithm for primality testing. LO-03: know the representation of an integer in specific bases, particularly base 2 (binary), base 8 (octal), and base 16 (hexadecimal).ID: Selamat datang di Topik 13 mengenai Teori Bilangan Bagian 1. Setelah menyelesaikan topik ini, Anda diharapkan menguasai capaian berikut:LO-01: mengetahui teorema keterbagian dan penerapannya untuk menghitung fungsi mod dan div. LO-02: mengetahui definisi bilangan prima, bilangan komposit, faktorisasi prima, dan algoritma untuk memeriksa primalitas bilangan. LO-03: merepresentasikan bilangan bulat dalam basis tertentu, terutama basis 2 (biner), basis 8 (oktal), dan basis 16 (heksadesimal).
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13. Number Theory 1
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13. Teori Bilangan 1
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Online Quiz 13: Teori Bilangan Elementer (Bagian 1)
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Forum Diskusi Materi Topik 13: Teori Bilangan Elementer (Bagian 1)
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Several primality testing algorithm (from brilliant.org)
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Khan academy: sieve of Eratothenes
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Khan academy: introduction to number system
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Youtube video (TedEd): a history of numerical system (by Alessandra King)
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CII1G3-30294 – Matematika Diskrit – PB13 – M1 – DEFINISI KETERBAGIAN
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CII1G3-30294 – Matematika Diskrit – PB13 – M2 – TEOREMA DAN SIFAT SIFAT KETERBAGIAN
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CII1G3-30294 – Matematika Diskrit – PB13 – M3 – TEOREMA PEMBAGIAN
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CII1G3-30294 – Matematika Diskrit – PB13 – M4 – BILANGAN PRIMA DAN ALOGARITMA UJI PRIMALITAS
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CII1G3-30294 – Matematika Diskrit – PB13 – M5 – TEOREMA DASAR ARITMATIKA
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CII1G3-30294 – Matematika Diskrit – PB13 – M6 – KONVERSI BILANGAN BINER OKTAL DAN HEKSADESIMAL KE SISTEM DESIMAL
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CII1G3-30294 – Matematika Diskrit – PB13 – M7 – KONVERSI BILANGAN DESIMAL KE BILANGAN BINER OKTAL DAN HEKSADESIMAL
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Topic 14: Elementary Number Theory Part 2 (Topik 14: Teori Bilangan Elementer Bagian 2)
EN: Welcome to Topic 14 about Number Theory Part 2. After completing this topic, you are expected to know:LO-01: the definition of gcd and lcm as well as their calculation using the prime factorization method. LO-02: how to implement Euclid algorithm to find gcd of several numbers. LO-03: the definition of simple linear congruences. LO-04: the procedure to solve simple linear congruences. LO-05: som applications of number theory, namely problem solving using Chinese Remainder Theorem and mathematical model in Diffie-Hellman Key Exchange (supplementary).ID: Selamat datang di Topik 14 mengenai Teori Bilangan Bagian 2. Setelah menyelesaikan topik ini, Anda diharapkan menguasai capaian berikut:LO-01: mengetahui definisi gcd dan lcm serta kalkulasinya menggunakan faktorisasi prima LO-02: mampu menerapkan algoritma Euclid untuk menghitung gcd dari beberapa bilangan. LO-03: mengetahui definisi kongruensi linier sederhana. LO-04: mampu mencari solusi dari kongruensi linier sederhana. LO-05: mengetahui penerapan teori bilangan, yaitu penyelesaian masalah dengan Chinese Remainder Theorem dan model masalah matematis pada Diffie-Hellman Key Exchange (suplemen).
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14.1. Number Theory 2
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14.1. Teori Bilangan 2
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14.2. Number Theory 3 (Supplementary)
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14.2. Teori Bilangan 3 (Suplemen)
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14.3. Number Theory 4 (Supplementary)
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14.3. Teori Bilangan 4 (Suplemen)
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Online Quiz 14: Teori Bilangan Elementer (Bagian 2)
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Forum Diskusi Materi Topik 14: Teori Bilangan Elementer (Bagian 2)
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Khan academy exercise: greatest common factor and least common multiple word problems
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Euclidean algorithm (basic and extended, with source code)
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Solving linear congruences
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Modular arithmetic (by brilliant.org)
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Chinese remainder theorem (from brilliant.org)
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CII1G3-30294 – Matematika Diskrit – PB14 – M1 – gcd (FAKTOR PERSEKUTUAN TERBESAR, FPB)
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CII1G3-30294 – Matematika Diskrit – PB14 – M2 – lcm (KELIPATAN PERSEKUTUAN TERKECIL, KPK)
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CII1G3-30294 – Matematika Diskrit – PB14 – M3 – ALGORITMA EUCLID
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CII1G3-30294 – Matematika Diskrit – PB14 – M4 – gcd SEBAGAI KOMBINASI LINIER
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CII1G3-30294 – Matematika Diskrit – PB14 – M5 – ARITMETIKA MODULAR DAN TING Zm
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CII1G3-30294 – Matematika Diskrit – PB14 – M6 – KONGRUENSI LINIER
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CII1G3-30294 – Matematika Diskrit – PB14 – M7 – PENCARIAN INVERS MENGGUNAKAN ALGORITMA EUCLID
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Menjelajahi Matematika Diskrit: Dari Pohon hingga Teori Bilangan Elementer dalam Dua Bagian
Discussion Forum for Topic 13: Elementary Number Theory (Part 1). You can ask for any material relating to topic 13 here.

 

 

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