Application of Newton’s Backward Interpolation Using Wolfram Mathematica

Interpolation is one of the most basic and most useful numerical techniques. It constitutes an irreplaceable tool during work with tabular or graphical functions. The Newton’s backward interpolation is one of most important numerical techniques which have huge application in mathematics, computer science and technical science. This paper provides an analytical description of Newton's backward interpolation and how Wolfram Mathematica software can be used to solve the problems from Newton's backward interpolation

Conditioned Extreme, Determination and Visualization

In mathematics, and especially in the application of mathematics in a number of areas, problems and tasks are encountered in which extremes of function are required, with the variables being bound up with some additional conditions. Extremes of this kind are called conditional extremes. [2]. In this paper, we present the procedure for determining a conditional extremity of a function with two variables, we will present that the point is finding the curve in the space obtained as a cross section on two surfaces and by using free software we will have visualization of the conditional extremum. Key words: Conditioned extreme, function, point, visualization

Social-Economic Advantages Of Weighted C-Centers And M-Centers In North Macedonia

Graph theory has many applications, because with the help of graphs we can model various complex problems, such as the placement of roads and intersections, the placement of electricity networks, computer networks, the placement of facilities of public importance, etc. Starting from the chaos that appears in the Capital, especially in front of the University Clinic or facilities of public importance, we decided to give a mathematical solution to these problems. In the paper, in addition to the theoretical elaboration on the concepts of graph theory, Floyd's Algorithm for minimum distances, concepts for weighted c-centers and m-centers, we will build the graph of the most important roads in North Macedonia, where as vertices we will use cities and crossroads in North Macedonia, then we will find c-centers and m-centers without and with weight in North Macedonia, and we will give some reasoning on the socio-economic advantages of these centers

Using The Simplex Method For Optimizing Some Economic Functions Of The Enterprise "MSA Kompani" Dooel-Skopje

In science, in economics, in practice, problems are often encountered in which it is required to find the largest (smallest) value of a numerical function with real values of the type . More precisely, the elements of the set  are required, where the function  reaches the optimal value. For this reason, such problems are called optimization problems. Optimization problems are also solved by so-called linear programming methods.Linear programming is a mathematical programming that deals with the problem of system optimization within given constraints, it is a method for solving production planning problems.The manufacturer wants to determine how to use the limited quantities of raw materials with maximum profit, the manager how to distribute the assigned work among his employees so that it is done in the shortest possible time, that is, to be as effective as possible. The goal of these problems is optimization, profit maximization or cost minimization [1].Making profit is the main goal of the company, but many companies still need to learn the maximum profit that can be achieved by optimizing their resources, one of which is the company “MSA KOMPANI”. This research focuses on the products of "MSA KOMPANI" DOOEL-SKOPJEdifferent according to the price. The purpose of this paper is to optimize the company's profits and costs. In this paper we will use the simplex linear programming method to solve our problem in "MSA KOMPANI". Modeling a real-life problem as a linear programming problem requires teamwork of experts from several fields.

Using Excel to predict and compare the grade in Mathematics by simplelinear regression model

In this paper was used simple linear regression model to predict and compare the final grade of the students in subject of Mathematics from department of Technical Sciences. Data’s were collected from students of two Universities:University "Mother Teresa" in Skopje and University "Goce Delcev" – Stip. The model was based on the data of students' scores in three tests: 1st periodical exam, 2nd periodical exam and final examination. This analyze was carried out by simple linear regression model. For obtaining our results was used Excel. In this paper also have been given the graphical representations of ours analysis and in the end have been given some conclusions based on the results

Математика за I година средно стручно образование Струки: Геолошко-рударска и металуршка, Градежно-геодетска, Графичка, Економско-правна и трговска, Електротехничка, Лични услуги, Машинска, Сообраќајна, Текстилно-кожарска, Угостителско-туристичка, Хемиско технолошка

Овој учебник е наменет пред сè за учениците од средните стручни училишта во Република Северна Македонија во кои се изучуваат струките: геолошко – рударска и металуршка, градежно – геодетска, графичка, економско – правна и трговска, електротехничка, машинска, сообраќајна, угостителско – туристичка, текстилно – кожарска, хемиско - технолошка и други, како основен учебник по предметот математика, но истата може да послужи како одлична литература за секој што сака да ги изучува модуларните единици опфатени во книгата

The Guideline of MathSTEM Method: Teaching Mathematics in STEM Context for STEM Students

This is a teaching resources which will serve as guidebook for teaching mathematics in STEM context for STEM students. The guidebook also contain appropriate lesson plans

Statistical Data for Modern Communication in Mathematics Subjects at Faculty

This paper specified the applications used for online teaching in the academic year 2019/2020 in both universities Goce Delcev, Stip and Mоther Teresa, Skopje. Then two different questionnaires are listed for students from both universities in order to see their opinion on online teaching for all subject but especially for mathematics subjects. The results of the questionnaires are presented and conclusions from them are drawn. Finally, the opinions of the students from the two universities are compared in order to see if the opinions are the same, similar or different

Importance of Visualization in Math Problems at the Universities

The small desire to learn mathematics among students, difficulties to master the material can be solved if we approach their visual representation. Mathematical books that contain only problems without their visual representation are hardly acceptable by students. So, demonstration and visualization play an important role in the teaching process of the subject mathematics in primary, secondary schools and universities. They make the teaching content interesting and accessible, especially when technical devices are used. This paper is the beginning of the research in which we will have two groups of students, at two Universities: Mother Teresa Skopje and Goce Delchev Stip, which will process mathematical content (algebra, geometry, analysis) in two different ways (some with GeoGebra and on a computer, and others without visualization and GeoGebra) then will be done testing, the results will be compared and a conclusion will be drawn. For this purpose, a student questionnaire was made to see what their thinking about learning mathematics with visualization in both University and the results from questionnaire are given in this paper. Complete results of а whole research will be published additionally. The software we chose to be GeoGebra because it is easy for use and is offered free of charge. It is dynamic mathematics software, supporting science, technology, engineering and mathematics education

Analysing and Comparing the Final Grade in Mathematics by Linear Regression Using Excel and SPSS

In this paper simple and multiple linear regression model is developed to analyze and compare the final grades of students from two Universities, University "Goce Delcev" - Stip, more specifically a group of students who studied in Kavadarci and students from "Mother Teresa" University in Skopje, for the subject of Mathematics. The models were based on the data of students' scores in three tests, 1st periodical exam, 2nd periodical exam and final examination. Statistical significance of the relationship between the variables has been provided. For obtaining our results some solvers like Excel and SPSS were used