Learning activities should be considered needs of students and the demands of the curriculum. The mathematics learning objectives and the demands of the current curriculum is to developing student’s higher order thinking skills. In fact the higher order thinking skills of junior high school students are categorized sufficient and still need to be improved. Efforts to improve the quality of st…
This research is motivated by the limited mathematics learning devices that are in accordance with the 2013 Curriculum. This research purposed is to produce mathematics learning devices such as syllabus, lesson plans, and student worksheets by using problem based learning on linear system with two variables material for the eighth grade of junior high school. The development model used in this …
This final project discusses the application of the Varignon’s theorem to the parallelo-hexagon by connecting the midpoints of the two sides which are close to the midpoint of the two sides in front of them so that they form a rectangle in the parallelo-hexagon. Proof is described in three alternatives, using the concept of congruence, geometrical transformation, and using parallelo-hexag…
This final project discusses the reciprocal addition formula of multiplying the m-th and n-th of Fibonacci numbers, where m and n are respectively even and odd integers, using the floor function. The reciprocal addition formula obtained is proven by using the Fibonacci number identities, the properties of the Fibonacci numbers, and algebraic calculations. This final project is a review of …
This nal project discusses the determinant of interval matrices by using arithmetic operations on interval numbers. Next, an analysis of the interval arithmetic is provided, assuming the shortest interval is the best. At the end, using the results of interval arithmetic analysis, the calculation of the determinant of interval matrix is given along with some of its properties. Keywords: In…
This nal project discusses the sequence and series which are constructed from Fibonacci numbers. The sequence and series in question are generated from the length of one of the sides of the triangle and the cross product of two vectors in the dimension space R3 having a numerical element of a Fibonacci number. Furthermore, after the sequence and series have been constructed, it is shown t…
This final discusses the method of sensitivity analysis with changes in objective functions and right hand side of a linear program. The sensitivity analysis method is used to determine the limit of change in the objective function and the right hand side in order to maintain the optimal solution. The results of the linear program on the sensitivity analysis method can be seen in the large …
This final project discusses the premium of healthy insurance of the Rayleigh distribution with m times of payment. Health insurance reserve calculation is solved by determination of the annuity, single premium and annual premium based on the distribution of Rayleigh in advance. By using the cash value of the annuity and premium of health insurance can be determined the calculation of heal…
This final project discusses the iterative method based on minimization techni- ques to solve the system of the absolute value equations. The analysis begins by discussing how to obtain a solution by applying this method. The convergence of the methods discussed shown by looking at the value of the difference of the function values at two consecutive iterations, which is equal to the error …
This article discusses the new SOR-like iterative method for solving the system of absolute value equations introduced by Ke and Ma [Applied Mathematics Letter, 311 (2017) 195-202]. Before proving convergence, the method was driven technically by mimicking the SOR iterative method. The convergence of the discussed method is proved by showing that the norm of error decreases with increasing…
This final project discusses how to solve transshipment problems with mixed constraints using the max-min method. The optimality test for the solution obtained from the max-min method uses the simplex transportation method. From the results of the discussion, it can be seen that the max-min method can be used as an alternative to the Vogel’s method. The procedure of this method is illust…
This final project discusses a nurse scheduling in hospital by using linear pro- gramming to get the optimal solution from the schedule. By using LINGO 11.0 for completing the nurse’s schedule which is found each polyclinic that the num- ber of nurses needed for each polyclinic better than what is available. Based on the discussion, it can be concluded that the hospital nurse scheduling p…
This nal project discusses two concepts of space, that is a fuzzy n-norm space and fuzzy n-inner product space for every natural number n ≥ 1. Then it is shown that for every k from 1 to n−1, it can be constructed a fuzzy (n−k)-norm space from fuzzy n-norm space. Next, for every k from 1 to n − 1 it can also be constructed a fuzzy (n − k)-inner product space from fuzzy n-inner pr…
This final project discusses the solution of fractional order epidemic model by implicit Adam methods. Analysis of the stability is carried out using numerical solutions from fractional order epidemic models. In real life, an implicit numerical scheme is needed using a multistep linear fractional method of the Adam implicit type. Finally , simulation is given with spesific parameters to des…
This final project discusses the analysis of worm propagation models in computer network (SEIS-V ). Analysis of the stability of the equilibrium points is carried out using modified reproduction numbers (R0) that show the worm-free equilibrium points, where the infective compartment is zero. Finally, simulation is given with spesific parameters to describe the behavior of the equilibrium p…
This final project discusses the identities of finite sum of the reciprocal and reciprocal square Fibonacci numbers with two, three or four functions of sums of the Fibonacci numbers. The sum solution is found by using floor function with mn Fibonacci numbers for any value of m and n which are even and odd integers. The sum is proven by using the combination of some propositions of recipro…
This final project discusses Newton type method for solving nonlinear equation systems introduced by Wang and Li [Algorithms, 10 (2017), 1-9]. Through convergence analysis it is shown that this Newton type method has a six-order convergence. By computational cost this method requires one LU decomposition in each iteration, so this method can be said to be efficient in computing. Therefore,…
This final project discusses the average total opportunity cost method to solve transportation problem, with the proposed method is easy since computation works. North west corner method, least cost method and Vogels approximation method used to determine the initial basic feasible solution and to compare of the new method. Then simplex transportation method is used to verifying optimality…
This final project discusses the New Jersey method for adjusted reserve of term life insurance using Makeham’s distribution. In this project, life annuity due and premium for term life insurance are obtained based on Makeham’s law of mortality. By using the value of annuity due and premium insurance it can be determined the adjusted reserve calculation with New Jersey method based on M…
The nal project discusses the modied method of Vogel approximation for solving the balanced transportation problem. This method is used to determine the feasible solution and simplex method to verify the optimal solution. The modied method Vogel's approximaton is more advantageous compared to the method of Vogel approximation. Illustration by example is given to comprehend the advantage…