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RPS) PROGRAM STUDI : S1 MATEMATIKA FAKULTAS /Pps: MATEMATIKA DAN ILMU PENGETAHUAN ALAM UNIVERSITAS ANDALAS RENCANA PEMBELAJARAN SEMESTER (RPS) PROGRAM STUDI : S1 MATEMATIKA FAKULTAS /PPs: MATEMATIKA DAN ILMU PENGETAHUAN ALAM UNIVERSITAS ANDALAS MATA KULIAH KODE Rumpun MK BOBOT (sks) SEMESTER Tgl Penyusunan Pengantar Matematika PAM 453 Matematika Dasar 4 1 15-2-2017 Dosen Pengembang RPS Koordinator Rumpun MK Ka Program Studi Dr. Susila Bahri Dr. Susila Bahri Dr. Ferra Yanuar Dr. Haripamyu Radhiatul Husna, MSi Capaian Pembelajaran (CP) CPL Program Studi S9 Menunjukkan sikap bertanggungjawab atas pekerjaan di bidang keahliannya secara mandiri P1 Menguasai konsep teoretis matematika meliputi logika matematika, matematika diskret, aljabar, analisis dan geometri, serta teori peluang dan statistika; KU1 Mampu mengembangkan pemikiran matematis, yang diawali dari pemahaman prosedural / komputasi hingga Catatan : pemahaman yang luas meliputi eksplorasi, penalaran logis, generalisasi , abstraksi , dan bukti formal; S : Sikap KU2 Mampu mengamati, mengenali, merumuskan dan memecahkan masalah melalui pendekatan matematis dengan atau P : Pengetahuan tanpa bantuan piranti lunak; KU : Keterampilan Umum KK1 Mampu menerapkan pemikiran logis, kritis, sistematis, dan inovatif dalam konteks pengembangan atau KK : Keterampilan Khusus implementasi ilmu pengetahuan dan teknologi yang memperhatikan dan menerapkan nilai humaniora yang sesuai dengan bidang keahliannya KK2 Mampu menunjukkan kinerja mandiri, bermutu, dan terukur CP Mata Kuliah 1 Memiliki kemampuan memahami permasalahan matematika sederhana, menyelesaikan, melakukan konjektur, dan menarik kesimpulan. (S9, P1) 2 Mahasiswa mampu mengembangkan pemikiran matematis yang diawali dari pemahaman procedural hingga penalaran logis dan bukti formal. (KU1) 2 Memiliki kemampuan penalaran matematika yang melibatkan argumentasi satu langkah atau lebih. (KU1, KK1) 3 Menguasai berbagai strategi pembuktian teorema.(KK1) 4 Memiliki keterampilan menuliskan permikiran matematika dengan baik dan benar. (KK2) Deskripsi Singkat Dalam mata kuliah ini dijelaskan beberapa konsep dasar dalam matematika, yaitu konsep logika, himpunan, fungsi serta cara- Mata Kuliah cara pembuktian sederhana.. Bahan Kajian 1. Logika 2. Logika Proposisi 3. Himpunan 4. Fungsi Pustaka Utama : D.W. Morris and J. Morris, Proofs and Concepts: The Fundamental of Abstract Mathematics, University of Lethbridge, 2009 Pendukung : E. D. Bloch, Proofs and Fundamentals: A First Course in Abstract Mathematics, Birkhauser, Boston, 2000 Media Pembelajaran Perangkat lunak : Perangkat keras : LCD & Projector Team Teaching Dr. Susila Bahri Dr. Lyra Yulianti Dr. Haripamyu Assessment NO KOMPONEN PENILAIAN BOBOT (%) Penilaian Hasil 1 Ujian Tengah Semester 30 % 2 Ujian Akhir Semester 30 % Penilaian Proses 1 Keaktifan 20 % 2 Tugas 5 % 3 Kuis 15% TOTAL 100 % Norma Akademik a. Mengikuti Peraturan Akademik Program Sarjana Universitas Andalas. b. Toleransi keterlambatan adalah 10 menit (berlaku juga untuk dosen). c. Pengumpulan tugas dilakukan sebelum deadline yang ditetapkan. Bagi yang telat menyerahkan tugas, nilai tugasnya dikurangi (10 x n hari keterlambatan)%. d. Yang berhalangan hadir karena sakit harus disertai dengan keterangan sakit/surat pemberitahuan sakit dan diserahkan paling lambat pada saat ybs masuk kuliah kembali. e. Tugas yang merupakan plagiat diberi nilai nol. f. Mahasiswa yang berlaku curang dalam ujian, ujiannya diberi nilai nol. g. Mahasiswa yang melakukan ‘titip absen’ (baik yang ‘menitip’ maupun yang ‘dititip’), selain ‘kehadiran’-nya tersebut tidak dihitung, skor nilai akhir (NA)-nya juga dikurangi sebesar 5 x n kali ‘titip absen’. h. Hal-hal lain yang tidak tercantum dalam norma akademik ini akan ditetapkan kemudian. Matakuliah Syarat - BOBOT MINGGU KRITERIA DAN BENTUK METODE SUB-CP-MK INDIKATOR MATERI PEMBELAJARAN PENILAIAN KE PENILAIAN PEMBELAJARAN (%) 1 Mampu memahami Aturan Kedisiplinan dalam Presentasi dosen Aturan Penilaian, RPS, Silabus, Penilaian, RPS, Silabus serta melaksanakan Kontrak Kuliah Kontrak Kuliah kontrak kuliah Proposisi dan deduksi, Mampu memahami dan Ketepatan validitas deduksi, nilai menggunakan beberapa konsep memahami materi kebenaran, kebenaran logis, logika sederhana terkait ekivalensi logika 2 Mampu memahami logika Ketepatan Keaktifan Brainstorming Simbolisasi proposisi, negasi, 2 proposisi memahami materi Presentasi dosen konjungsi, disjungsi, Mampu mengaitkan dengan terkait implikasi, biimplikasi keadaan nyata. 3 Mampu memahami Ketepatan Brainstorming,Presen Menentukan nilai kebenaran 5 beberapa teorema dalam menjelaskan dan Keaktifan tasi dosen suatu proposisi logika proposisi memahami materi Tugas Tautology-kontradiksi- terkait kontingensi, ekivalensi logika 4 Mampu memahami Ketepatan Brainstorming Konvers, invers, kontraposisi, 2 beberapa teorema dalam menjelaskan dan Keaktifan Presentasi Dosen Deduksi valid, contoh logika proposisi memahami materi Kuis penyangkal terkait 5 Mampu memahami Ketepatan Tugas Brainstorming Himpunan dan anggotanya, 5 beberapa konsep dalam teori menjelaskan dan Keaktifan Presentasi Dosen subhimpunan himpunan memahami materi Predikat, menggunakan terkait predikat dalam menyatakan subhimpunan 6 Mampu memahami dan Ketepatan Brainstorming Gabungan dan irisan, selisih 2 menggunakan konsep menjelaskan dan Presentasi Dosen dan komplemen operasi dalam himpunan memahami materi Keaktifan Hasilkali himpunan saling terkait lepas, himpunan kuasa Ketepatan dalam menjawab soal tugas Kerapihan pengerjaan tugas Orisinalitas hasil tugas 7 Review materi Ketepatan Presentasi Dosen Kompilasi 2 memahami materi Tugas Review materi terkait Pembahasan contoh-contoh soal 8 UJIAN TENGAH SEMESTER 30 9 Mampu memahami konsep Ketepatan Keaktifan Brainstorming Kuantor, menyatakan 2 logika orde satu memahami materi Presentasi Dosen proposisi dalam logika orde terkait satu, Kuantor berganda, negasi, kesamaan, kebenaran hampa Ketunggalan, variable terikat Contoh penyangkal pada logika orde pertama 10 Mampu memahami konsep Ketepatan Brainstorming Definisi fungsi 2 fungsi menjelaskan dan Keaktifan Presentasi Dosen Daerah hasil dan daerah hasil memahami materi invers terkait 11 Kemampuan memahami Ketepatan Brainstorming Fungsi injektif, surjektif, 5 konsep fungsi menjelaskan dan Keaktifan Presentasi Dosen bijektif, komposisi fungsi dan memahami materi Kuis fungsi invers terkait 12 Kemampuan memahami dan Ketepatan Brainstorming Strategi pembuktian, 2 menggunakan beberapa menjelaskan dan Keaktifan Presentasi Dosen Bukti langsung, bukti dengan strategi pembuktian memahami materi Tugas kontraposisi dan kontradiksi, terkait bukti perkasus, bukti jika dan hanya jika 13 Kemampuan memahami dan Ketepatan Brainstorming Bukti yang melibatkan 2 menggunakan beberapa menjelaskan dan Keaktifan Presentasi Dosen kalimat kuantor strategi pembuktian memahami materi terkait Ketepatan dalam menjawab soal tugas Kerapihan pengerjaan tugas • Orisinalitas hasil tugas 14 Kemampuan memahami dan Ketepatan Brainstorming Bukti dengan induksi 5 menggunakan beberapa menjelaskan dan Keaktifan Presentasi Dosen strategi pembuktian memahami materi terkait Ketepatan dalam menjawab soal tugas Kerapihan pengerjaan tugas • Orisinalitas hasil tugas 15 Review materi Ketepatan Presentasi Dosen Review materi 2 menjelaskan dan Tugas memahami materi terkait Ketepatan dalam menjawab soal tugas Kerapihan pengerjaan tugas 16 UJIAN AKHIR SEMESTER 30 Proofs and Concepts the fundamentals of abstract mathematics by Dave Witte Morris and Joy Morris University of Lethbridge incorporating material by P. D. Magnus University at Albany, State University of New York Preliminary Version 0.78 of May 2009 This book is offered under the Creative Commons license. (Attribution-NonCommercial-ShareAlike 2.0) The presentation of logic in this textbook is adapted from forallx An Introduction to Formal Logic P. D. Magnus University at Albany, State University of New York The most recent version of forallx is available on-line at http://www.fecundity.com/logic We thank Professor Magnus for making forallx freely available, and for authorizing derivative works such as this one. He was not involved in the preparation of this manuscript, so he is not responsible for any errors or other shortcomings. Please send comments and corrections to: [email protected] or [email protected] c 2006–2009 by Dave Witte Morris and Joy Morris. Some rights reserved. Portions c 2005–2006 by P. D. Magnus. Some rights reserved. Brief excerpts are quoted (with attribution) from copyrighted works of various authors. You are free to copy this book, to distribute it, to display it, and to make derivative works, under the following conditions: (1) Attribution. You must give the original author credit. (2) Noncommercial. You may not use this work for commercial purposes. (3) Share Alike. If you alter, transform, or build upon this work, you may distribute the resulting work only under a license identical to this one. — For any reuse or distribution, you must make clear to others the license terms of this work. Any of these conditions can be waived if you get permission from the copyright holder. Your fair use and other rights are in no way affected by the above. — This is a human-readable summary of the full license, which is available on-line at http://creativecommons.org/licenses/by-nc-sa/2.0/legalcode to Harmony Contents Part I. Introduction to Logic and Proofs Chapter 1. What is Logic? 3 §1A. Assertions and deductions .................................................... 3 §1B. Two ways that deductions can go wrong - - - - -
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