This thesis discusses some alternatives to determine solution from complex fuzzy linear equation system of the form eC ⊗ez = ~w where eC is complex fuzzy matrix and ew;ez are arbitrary complex fuzzy vectors that are done by using inverse method. There are some cases that include solution of eC ⊗ez = ~w but just 5 cases that are discussed. Finally, some examples are given for applying t…
The concept of direct product of BP-algebra which is constructed by a way similar to direct product of B-algebras. The result are dene direct product of BP-algebra and some of its properties are investigated, such that obtained denition of direct product in BP-algebra is equivalent to direct product in B- algebra. The concept of direct product is a structure, then obtained direct product…
BP-algebra is a non-empty set X with a constant 0 and a binary operation ” ∗ ”, satisfying the certain axioms. An algebra relationship with BP-algebra is a BM-algebra. Their relationship is every BP-algebra 0-commutative is a BM- algebra. The concept of the generalized of derivation in BM-algebra is discussed. In this thesis, the generalized of derivations and the generalized of f-der…
The purpose of this thesis is to introduces alternative proofs for the length of angle bisectors theorem on triangle. In this thesis, the author proves it using the concept of area, law of sines, Pythagoras theorem, and Ptolemy theorem. The result is that the square of length of angle bisector of the triangle is the product between the sides of the triangle on the left and right of the bisector…
This thesis discusses the hypocycloid area starting by determining the auxiliary circle to calculate the hypocycloid area. Furthermore, to determine the hypocycloid area with the auxiliary circle, it is obtained from the reduction of the area of the circle forming the hypocycloid and the area of the auxiliary circle. Base on determining the area of hypocycloid, resulted that the area of hypocyc…
An appropriate constructive planning is the most important key to a successfull production system. This thesis describes problems in production planning using the combination of forecasting method and linear goal programming for decision making. Both methods are used to predict sales of bakery products and determine the best and most efficient product combinations to achieve multi goals. F…
B-algebra is a non-empty set X with a constant 0 and a binary operation ∗ denoted by (X; ∗; 0), satisfying the certain axioms. A specialization of B-algebra is BM-algebra. Moreover, relation of B-algebra and BM-algebra is every BM-algebra is B-algebra, but its converse does not hold in general. In this thesis, discussed derivations and the generalized derivations of BM-algebras and B-a…
The k-Fibonacci sequences have first term is 0, the second term is 1, and the next term depends on a positive integer k. The k-Fibonacci numbers can represented as a k-Fibonacci matrix denoted by Fn(k). Then, the Bernoulli’s number and the Bernoulli polynomial can also be represented as the matrix and denoted by Bn and Bn(x). In this thesis, the new matrices of multiplication of the Bern…
This thesis discusses a develompment of BN1-algebra with addition of companion and homomorphism concepts. An algebra statifies of companion if there is an operation ⊙, then ((x ⊙ y)x) ∗ y = 0 and (z ∗ x) ∗ y = 0 ⇒ z ∗ (x ⊙ y) = 0. In this thesis, we develop the formula definition of companion BN1-algebra. Then a mapping ' : X → Y is said to be a homomorphism, if it statis…
This paper discusses alternative construction methods of a special curve namely lemniscate of Bernoulli using circles, lines and hyperbola. The process of shows the curve obtained is lemniscate of Bernoulli uses simple geometrical concepts such as the Pythagoras Theorem, tangent of circle theorem and secant of circle theorem. In this study there are twelve methods of construction lemniscat…
This research was underlied by the limited Mathematics learning media as the supporting facility of the learning in Curriculum 2013. The purpose of this research is to produce the product in the form of learning media (syllabus, lesson plan, and LKPD) on linear program material of Grade XI Senior High School based on PBL model which fulfills valid and practicality criteria to facilitate student…
This research is motivated by the availability of mathematics teaching materials in schools which are still limited in number. The available teaching materials have not facilitated students 'mathematical problem solving abilities and have not provided contextual problems with students' daily lives. The teaching material is still focused on the delivery of material with questions for understandi…
The results of the preliminary study show that the learning devices used by teachers in schools have not met the rules contained in the 2013 curriculum. This study aims to produce learning tools using the Problem Based Learning model to facilitate mathematical representation skills in the polyhedron material consisting of the syllabus, lesson plan, and student worksheet. In this study, the rese…
The background of this research is student’s abilities are not optimal in Mathematical Problem Solving (MPSA) because they are lack of learning tools that train them about mathematical problem solving skills, especially Student Worksheets (SW). In line with that, the purpose of this study is to develop mathematics learning tools that meet valid and practical requirements to facilitate mathema…
This research was motivated by the low mathematical communication skills of students. To overcome this problem is to improve the learning process, one of which is by applying the 5E learning cycle model. The 5E learning cycle model is a series of activity stages so that students can master the competencies achieved in learning by taking an active role, directed to seek and discover new knowledg…
This research is motivated by the lack of available learning tools that teachers can use in the learning process. Based on the results of observations and analysis of the learning tools used by some high school math teachers in Pekanbaru, it is known that only a small portion of them develop learning tools while others use learning tools obtained from peers, the internet and other sources.…
The development of HOTS questions in this study resulted much of HOTS question bank obtaines used in daily test and last exams. The HOTS problem developed includes three aspects,the analyse aspect (C-4), the evaluation aspect (C-5) and the creative aspect (C-6). The resulting HOTS questions divided into 10 analysis questions, 11 evaluation questions and 9 creative questions. To produce this HOT…
The research that has been done is the effect of the Search, Solve, Create, Share (SSCS) learning model on the mathematical problem-solving abilities (KPMM) and Self Efficacy of the students of SMP Negeri Kampar. The low ability of students' mathematical problem solving and the low self-confidence of students in solving problem solving problems underlie this research. The difficulty of students…