EN: Discrete Mathematics provides rigorous exposure concerning discrete structures and their relevant properties for computer science. This course supports the discrete structure materials used in data structure and other relevant foundations in algorithms. There are four main topics in this course, which correspond to four course learning outcomes. The first topic discusses relation, function, and simple homogenous recurrence relation. The students will learn the definition of relation and function as well as their representation and mathematical characteristics. In addition, the students will learn the recurrence relations that will be used in algorithm analysis. The second topic is pertaining to combinatorial mathematics. The student will study the basic counting principle, pigeonhole principle, permutations and combinations, as well as their generalization. The third topic is about graphs and trees. In this topic, the students will be exposed to the formal definition of graphs, some properties of graphs, and some elementary graph algorithms (algorithm for solving vertex coloring problem, shortest path problem, and minimum spanning tree problem). Finally, in the last topic, the students will learn elementary number theory, which contains the discussion about divisibility, greatest common divisor, least common multiple, and their applications, and elementary modular arithmetic as well as their related algorithms.


ID: Matematika Diskrit memberikan paparan yang rinci terkait struktur diskrit dan sifat-sifatnya yang relevan untuk ilmu komputer. Kuliah ini mendukung materi struktur diskrit yang digunakan pada struktur data dan fondari relevan lain dalam algoritma. Ada empat topik utama dalam kuliah ini yang berkaitan dengan empat capaian pembelajaran (course learning outcome). Topik pertama membahas relasi, fungsi, dan relasi rekurensi homogen sederhana. Mahasiswa mempelajari definisi relasi dan fungsi beserta representasi dan karakteristik matematisnya. Selain itu mahasiswa juga mempelajari relasi rekurensi yang akan digunakan selanjutnya dalam analisis algoritma. Topik kedua terkait matematika kombinatorika. Mahasiswa mempelajari dasar teknik berhitung, prinsip sarang merpati, serta permutasi dan kombinasi beserta perumumannya. Topik ketiga terkait graf dan pohon. Pada topik ini mahasiswa akan mengkaji definisi formal graf, sifat-sifat graf, dan beberapa algoritma graf elementer (pewarnaan simpul, pencarian lintasan terpendek, dan konstruksi pohon perentang minimum). Terakhir, pada topik ke empat mahasiswa mengkaji teori bilangan elementer, yang meliputi keterbagian, faktor persekutuan terbesar dan kelipatan persekutuan terkecil beserta aplikasinya, dan aritmetika modular elementer, serta algoritma yang terkait dengan hal-hal tersebut.