Lecture Note Mat Diskrit S1

# Lecture Note Mat Diskrit S1 - LECTURE NOTES MATEMATIKA...

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LECTURE NOTES MATEMATIKA DISKRIT Disusun Oleh : Dra. D. L. CRISPINA PARDEDE, DEA. JURUSAN TEKNIK INFORMATIKA UNIVERSITAS GUNADARMA PONDOK CINA, MARET 2004 0

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DAFTAR ISI DAFTAR ISI .............................................................................................................................. 1 BAB I STRUKTUR ALJABAR ......................................................................................... 2 1.1. OPERASI BINER ............................................................................................................ 2 1.2. SIFAT OPERASI BINER ................................................................................................. 3 1.3. SISTEM ALJABAR SATU OPERASI ............................................................................ 5 1.3.1. SEMIGROUP ........................................................................................................... 5 1.3.2. MONOID .................................................................................................................. 5 1.3.3. GROUP ..................................................................................................................... 6 1.3.4. SUBGROUP ............................................................................................................. 7 1.3.5. SUBGROUP SIKLIK ................................................................................................ 7 1.3.6. SUBGROUP NORMAL ............................................................................................ 8 1.4. SISTEM ALJABAR DUA OPERASI ........................................................................... 10 1.4.1. RING ....................................................................................................................... 10 1.4.2. FIELD ..................................................................................................................... 11 1.4.3. SUBRING ............................................................................................................... 12 BAB II KOMBINATORIK ................................................................................................... 13 2.1. PERMUTASI DAN KOMBINASI ................................................................................ 13 2.2. KOMBINASI PADA HIMPUNAN DENGAN PENGULANGAN .............................. 15 BAB III PRINSIP INKLUSI DAN EKSKLUSI ................................................................. 17 BAB IV FUNGSI DISKRIT NUMERIK ............................................................................ 23 4.1. FUNGSI NUMERIK ..................................................................................................... 23 4.2. MANIPULASI FUNGSI NUMERIK ............................................................................ 24 BAB V RELASI REKURENSI LINIER BERKOEFISIEN KONSTAN ........................ 27 5.1. SOLUSI DARI RELASI REKURENSI ........................................................................ 28 5.2. SOLUSI HOMOGEN DARI RELASI REKURENSI ................................................... 30 5.3. SOLUSI KHUSUS DARI RELASI REKURENSI ....................................................... 33 BAB VI FUNGSI PEMBANGKIT ..................................................................................... 35 DAFTAR PUSTAKA .............................................................................................................. 38 1

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1.2. SIFAT OPERASI BINER Sifat-sifat yang dimiliki oleh sebuah sistem aljabar nantinya ditentukan oleh sifat-sifat yang dimiliki oleh setiap operasi di dalam sistem aljabar tersebut. Berikut akan diuraikan sifat-sifat yang dapat dimiliki oleh sebuah operasi biner. Misalkan dan adalah operasi biner. Operasi dikatakan : -. KOMUTATIF , jika a b = b a, untuk setiap a, b. -. ASOSIATIF, jika (a b) c = a (b c), untuk setiap a, b, c.
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• Spring '16
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