Analisis Real Course

The real analysis course I aims to study the real number system (algebra of real numbers and their properties, rational and irrational numbers, sequence of real numbers and their properties, absolute value, point vicinity, supremum and infimum of a set and their properties, intervals and its properties, the surroundings of a point), topology on the real line (special points of a set and their properties, open sets and closed sets and their properties), sequences of real numbers (limits of sequences, properties of sequence limits, tails of sequences , monotone sequence, partial sequence, divergent sequence, Cauchy‘s criterion, contractive sequence). Learning is carried out by applying a combination of expository, discussion and question and answer approaches. Assessment is carried out during the learning process with active interactive participation, presentations, assignments and mid-semester exams, as well as final semester exams with proportional weighting.

• PLO-3
  Mengembangkan pemikiran logis, kritis, sistematis, dan kreatif dalam melakukan pekerjaan yang spesifik di bidang keahliannya serta sesuai dengan standar kompetensi kerja bidang yang bersangkutan
• PLO-5
  Menerapkan prinsip-prinsip dasar matematika untuk memecahkan masalah matematika sederhana
• PLO-9
  Mendemonstrasikan pengetahuan dan wawasan matematika

PO-1
Mengembangkan pemikiran matematis yang diawali dari pemahaman sistem bilangan real, nilai mutlak, persekitaran titik, himpunan terbuka dan tertutup, barisan, limit barisan dan sifat - sifatnya, barisan monoton, sub barisan, teorema Bolzano-Weierstrass, kriteria Cauchy, barisan divergen.

PO-2
Mengkaji pengertian himpunan terbatas, supremum dan infimum dan teorema yang terkait serta sifat kelengkapan pada R yang melibatkan keterampilan berpikir logis dan sistematis

PO-3
Menyelesaikan masalah terkait sifat aljabar pada R, nilai mutlak, persekitaran titik, himpunan terbatas dan supremum infimum yang melibatkan keterampilan berpikir kreatif