PERANAN REPRESENTASI BERBANTUAN SOFTWARE MAPLE PADA PEMBELAJARAN MATA KULIAH KALKULUS

Abstract. Computers are essential tools for teaching, learning, and doing mathematics. Computers can visualize or represent mathematical ideas, organize and analyze data, and calculate effectively and accurately. Computers can help students conduct investigations through representations in various fields of mathematics such as geometry, calculus, statistics, algebra, measurements, and numbers. This paper discusses the role of Maple assisted representation in calculus learning. Representation is very supportive in increasing students' understanding of mathematical relations and concepts. There are three main functions of representation, namely complementing, constraining, and constructing. Complementing function is to complete the process and complete the information. The constraining function is to help students experience difficulties in a representation. The constructing function is to support constructing a deeper understanding of a concept. Students can get a deeper understanding if difficulties with only one representation. Maple software is a facility that is very supportive in making representations in learning mathematics as in calculus learning. By using Maple we can do numerical and symbolic calculations and perform graphical representations well. Maple can also effectively determine limits, derivatives, integrals, and a series of other functions and capabilities. With this Maple software capability, we can use it to improve students' understanding of calculus courses.Keywords: Representation, Computers, Maple, Calculu

UPAYA MENINGKATKAN MOTIVASI BELAJAR MATEMATIKA DENGAN MODEL TEAM GAMES TURNAMEN (TGT) MENGGUNAKAN PEMECAHAN SOAL BERKONTEKS CERITA RAKYAT SUMUT DI KELAS V SD

AbstractResearch conducted on the class V students of SD by applying the model Team Games Tournament (TGT) which contextual folklore of North Sumatra in the sub subject of integer operations. This research aims to improve students' motivation to learn mathematics class V Field Elementary School.This research is an action research and the analyzed data are quantitative data and qualitative data. The results showed differences in learning motivation of fifth grade elementary school students using the Team Games Tournament (TGT) model in learning integers from low to high. The results showed an increase in students' mathematics learning activities Keywords: folklore contextual problem solving, Team Games Tournament (TGT) Abstrak. Penelitian dilakukan terhadap siswa kelas V SD dengan menerapkan model Team Games Turnamen (TGT) yang berkonteks cerita rakyat Sumatera Utara pada sub pokok bahasan operasi bilangan bulat. Penelitian ini bertujuan untuk meningkatkan motivasi belajar matematika siswa kelas V SD. Penelitian ini adalah penelitian tindakan dan data yang dianalisa adalah data kuantitatif dan data kualitatif. Hasil penelitian menunjukkan adanya peningkatan motivasi belajar matematika siswa kelas V SD mengunakan model Team Games Turnamen (TGT) dalam pembelajaran bilangan bulat dari tergolong rendah menjadi  tergolong tinggi. Hasil penelitian menunjukkan adanya peningkatan aktivitas belajar matematika siswa.  Kata kunci : Pemecahan soal berkonteks cerita rakyat, Team Games Turnamen (TGT

MINIMASI MAKESPAN PADA PERSOALAN PENJADWALAN ORDERED FLOWSHOP MENGGUNAKAN PSO

The production scheduling problem is in the kind of flowshop with n jobs and m machines, to get the order of the schedule for allocating operations of the jobs to the available machines so as to get the minimum total time for completion of all job or commonly called makespan. This study uses an optimization technique approach with the PSO algorithm to get minimum makespan on the ordered flowhop scheduling problem. The performance of the scheduling algorithm presented is evaluated by testing on a benchmark data set of 240 variations in the combination number of jobs and machines. The minimum measure is obtained as a result of scheduling with PSO, whose process stops at a certain iteration when in the last 10 iterations there is no change in the value of a better makespan. The performance of the PSO algorithm is efficient at regular flow scheduling with the use of the most iterations of 19 iterations and the longest execution time of 28.42 seconds or less than half a minute, namely scheduling instances with the largest number of machines and jobs. In this research, only the analysis of the resulting minimal forward and the time of execution was carried out. Further research can be extended by not only measuring the minimum makespan, such as measuring total flowtime, total tardiness, and others

PENGEMBANGAN KEMAMPUAN BERPIKIR MATEMATIK DENGAN METODE MOORE TERMODIFIKASI

The ability to think mathematically is an ability that every student and teacher of mathematics needs to be able to understand mathematics better. Various studies have been conducted to apply appropriate approaches and learning methods to develop this mathematical thinking ability. This paper is a theoretical study, which will briefly describe one alternative learning method, which is expected to develop this ability. The alternative method that will be described is the Modified Moore method, which provides opportunities for students to be actively involved in learning, with little direction or guidance from the teacher

Kombinasi Vigenère dan Beaufort Cipher Konsep Simulasi Three-pass Protocol pada Data Penerbangan

Computer security is very important in data exchange, especially flight data. The data sent is confidential data. This data should not be known by irresponsible people. Data theft is a risk that can occur which can result in large losses. This data must be encrypted so that it is safe when sending. Good delivery does not need to exchange keys so that the key is not given to the recipient who will decrypt the data. Security needs to be improved by using the Three-pass Protocol scheme where this scheme will maintain that there is no exchange of keys between the sender and the recipient of the data. Each party will carry out the encryption and decryption process using their respective keys. This key does not need to be given to other parties. The concept of the Three-pass protocol uses the Vigenère and Beaufort Cipher algorithms. The sender will carry out the encryption and decryption process using the Vigenère Cipher algorithm while the recipient will carry out the encryption and decryption process using the BeaufortCipher algorithm. The encrypted data will automatically maintain the authenticity of the data when the data is decrypted again. The combination of the two algorithms with multiple keys makes the encryption results more difficult to decrypt by unauthorized parties. The result of the combination of these two methods is that the encryption quality is better than the Beaufort or Vigenère methods alone. By utilizing the Three-pass Protocol scheme, flight data will be kept confidential.   Keywords—Beaufort; Vigenère; Three-pass; Protocol   Keamanan komputer sangat penting diterapkan dalam pertukaran data, terutama data penerbangan. Data-data yang dikirim adalah data yang bersifat rahasia. Data ini tidak boleh diketahui oleh orang yang tidak bertanggung jawab. Pencurian data adalah resiko yang dapat terjadi sehingga dapat mengakibatkan kerugian besar. Data-data ini harus dienkripsi sehingga aman pada saat melakukanpengiriman. Pengiriman yang baik tidak perlu melakukan pertukaran kunci sehingga kunci tersebut tidak diberikan kepada penerima yang akan melakukan dekripsi data tersebut. Pengamanan perlu ditingkatkan dengan menggunakan skema Three-pass Protocol dimana skema ini akan mempertahankan agar tidak terjadi pertukaran kunci antara pengirim dan penerima data. Masing-masing pihak akan melakukan proses enkripsi dan dekripsi menggunakan kunci masing-masing. Kunci ini tidak perlu diberikan kepada pihaklain. Konsep Three-pass protocolmenggunakan algoritma Vigenère dan BeaufortCipher. Pengirim akan melakukan proses enkripsi dan dekripsi dengan menggunakan algoritma Vigenère Cipher sementara penerima akan melakukan proses enkripsi dan dekripsi menggunakan algoritma BeaufortCipher.Data yang terenkripsi secara otomatis akan menjaga keaslian data tersebut pada saat data tersebut kembali didekripsi. Kombinasi kedua algoritma dengan kunci ganda agar hasil enkripsi semakin sulit untuk didekripsi oleh pihak yang tidak berwenang. Hasil dari kombinasi kedua metode ini didapatkan kualitas enkripsi yang lebih baik dibandingkan dengan satu metode Beaufort atau Vigenère saja.Dengan memanfaatkanskema Three-pass Protocol dihasikan data penerbangan akan terjaga kerahasiaannya.   Kata Kunci—Beaufort; Vigenère; Tiga lintasan; Protoko