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Nugraha K. F. Dethan
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Computer Science & IT Decision Sciences, Operations Research & Management Economics, Econometrics & Finance Education Health Professions Immunology & microbiology Mathematics Public Health

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Journal : Journal of Mathematics Theory and Applications

 1 
Kajian Intgeral Henstock Nugraha K. F. Dethan
Journal of Mathematics Theory and Applications Vol. 1 No. 1 (2022): Edisi Oktober 2022
Publisher : Program Studi Matematika, Universitas Timor

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.32938/j-math.v1i1.3758

Abstract

A study of the properties of Henstock integral has been carried out. Henstock integral is an extension of Riemann integral. This is because the Henstock integral is built on the concept of Riemann integral, using the Riemann sum over the partition on the domain interval of a function. The difference lies in controlling the partition. On Riemann integral the control of a partition is roled by a constant positive number, whereas on Henstock integral the control of a partition is roled by possitive function. In this final project, we will learn how to construct the Henstock integral based on the concept of the Riemann integral, the properties of Henstock integral with its example and its relationship with the Riemann integral. The result of the study shows that every function that Riemann integrable is Henstock integrable, but it does not necessarily apply conversely.
Model Regresi Dummy Indeks Prestasi Akademik Mahasiswa Program Studi Matematika Faperta Unimor Grandianus Seda Mada; Nugraha K. F. Dethan; Faustianus Luan
Journal of Mathematics Theory and Applications Vol. 1 No. 2 (2023): Edisi April 2023
Publisher : Program Studi Matematika, Universitas Timor

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.32938/j-math.v1i2.3759

Abstract

One indicator that can be used as a determinant in the quality of higher education is the academic achievement of students. Grade Point Average (GPA) is a measure of the academic performance. GPA gained students can not be separated from the quality of the incoming student input at the college. This study discusses some of the indicators that can be used as a measure of the quality of student input from the academic side, such as the National Examination (NE), the origin of school (public / private), gender and type of college entrance exam (SNMPTN test, SBMPTN test and independent institution test). Because some of these indicators are qualitative so the data analysis used regression analysis with dummy variables. Research conducted on students of Mathematics Study Program, Faculty of Agriculture, Timor University, class of 2017 to class of 2021. From the data processing, obtained regression model: . From the data analysis, concluded that the female students of Mathematics Study Program, Faculty of Agriculture, Timor University, coming from public schools and type of college entrance exam is SNMPTN have the greatest tendency to obtain high GPA compared with other students. In addition, for the regression equation obtained above was 38.2% means that the independent variable in the model can explain the diversity of the GPA of 38.2%.
KAJIAN TEOREMA BOLZANO-WEIERSTRASS UNTUK MENGKONSTRUKSI BARISAN YANG KONVERGEN DI R^n DAN APLIKASINYA DALAM PEMBUKTIAN TEOREMA EKSISTENSI MAX-MIN Alfonsus Liquria Loin; Nugraha K. F. Dethan; Grandianus Seda Mada
Journal of Mathematics Theory and Applications Vol. 2 No. 1 (2023): Edisi Oktober 2023
Publisher : Program Studi Matematika, Universitas Timor

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.32938/j-math.v2i1.5175

Abstract

A sequence is a function from the set of natural numbers to the set of real numbers . In sequences there is the concept of sequence convergence. Testing the convergence of a sequence can be done using the Bolzano-Weierstrass Theorem. This theorem states that every finite sequence has a convergent sequence. The relationship between convergent sequences and finite sequences is also important to study further. Apart from being used to prove the convergence of sequences, the Bolzano-Weirstrass Theorem can also be applied to prove the Max-Min Existence Theorem. This research was conducted to examine the relationship between convergent sequences and finite sequences, the relationship between convergence and continuous functions and the relationship between continuous functions and max-min values ​​with the aim of constructing a convergent sequence in R^n and its application in proving the Max-Min Existence Theorem. This research is a literature study. This research was conducted through a literature review of books and other literature. From the literature review, the materials are then discussed in depth. The results of the literature study show that a convergent sequence is a finite sequence, but a finite sequence is not necessarily convergent. In determining the convergence of a sequence using the Bolzano-Weierstrass Theorem, it is necessary to first show the limitations of the sequence. Furthermore, to prove the Max-Min Existence Theorem it is necessary to require that the sequence is finite and then this theorem can be proven using the Bolzano-Weierstrass Theorem and Apit Theorem. Keywords: Monotonous Sequence, Finite Sequence, Continuity, Bolzano-Weierstrass Theorem, Max-Min Existence Theorem.
KLASIFIKASI KELAS KONJUGASI GRUP PERMUTASI PADA n UNSUR (S_n) Ana Diana Silvana Bimolo; Nugraha K. F. Dethan; Fitriani
Journal of Mathematics Theory and Applications Vol. 3 No. 1 (2024): Edisi Oktober 2024
Publisher : Program Studi Matematika, Universitas Timor

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.32938/j-math.v3i1.7946

Abstract

Conjugate classes partition the members of a group into mutually exclusive subsets, which can be used to classify the group. For example, conjugate classes can be used to show that two groups are not isomorphic. In this study the author will classify the conjugation class of the permutation group elements . This research uses a literature study method where the author studies the properties, theorems related to conjugation classes and permutation groups. The results obtained from this research are that the conjugation class of a permutation in is determined by its cycle type, namely the partition of with these conjugation classes, namely conjugation classes containing permutations in that have the same cycle type. The number of conjugation classes is equal to the number of cycle types in . Keywords: permutation group, conjugation class.
Co-Authors Alfonsus Liquria Loin Ana Diana Silvana Bimolo Desriyani Yulianita Br. Kolo Teti Faustianus Luan Fitriani Mada, Grandianus Seda Obe, Leonardus Frengky