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Course Description
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.
Program Objectives (PO)
- 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.
- Mengkaji pengertian himpunan terbatas, supremum dan infimum dan teorema yang terkait serta sifat kelengkapan pada R yang melibatkan keterampilan berpikir logis dan sistematis
- Menyelesaikan masalah terkait sifat aljabar pada R, nilai mutlak, persekitaran titik, himpunan terbatas dan supremum infimum yang melibatkan keterampilan berpikir kreatif
Aktifitas Pembelajaran
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Pertemuan 1 Sifat aljabar pada R dan teorema yang terkait dengan operasi penjumlahan dan perkalian -
Pertemuan 2 Pengertian bilangan rasional, irasional dan sifat-sifatnya -
Pertemuan 3 Kembali definisi bilangan real positif, non negatif, negatif dan non positif -
Pertemuan 4 Harga mutlak -
Pertemuan 5 Pengertian persekitaran titik -
Pertemuan 6 Himpunan terbatas, supremum dan infimum -
Pertemuan 7 Masalah terkait sifat aljabar pada R, nilai mutlak, persekitaran titik, himpunan terbatas dan supremum infimum yang melibatkan keterampilan berpikir kreatif -
Pertemuan 8 -
Pertemuan 9 Konsep interval, interval bersarang, titik-titik khusus pada suatu himpunan -
Pertemuan 10 Konsep dan karakteristik himpunan terbuka dan tertutup -
Pertemuan 11 Konsep dan karakteristik himpunan terbuka dan tertutup -
Pertemuan 12 Konsep barisan dan limitnya -
Pertemuan 13 Konsep barisan dan limitnya -
Pertemuan 14 Konsep barisan dan limitnya -
Pertemuan 15 Konsep barisan dan limitnya -
Pertemuan 16
Lecturer
Difficult Things About Education.
$75$10
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