Full Project – Design and implementation of computer aided system that solves algebraic equations

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CHAPTER I

INTRODUCTION

Background of the study

Algebra is a field of mathematics that together with number theory, geometry and analysis, is the study of mathematical symbols and the rules for manipulating those symbols. It is a unifying thread of almost all mathematics. As a result, it includes everything from elementary equations, to the study of abstractions such as groups, rings and fields. Algebra is divided into two main parts; elementary and abstract or modern algebra. Elementary algebra encompasses some of the basic concepts of algebra, and is often used to build one’s understanding of arithmetic (dealing with specified numbers) by introducing quantities without fixed values (called variables). Elementary algebra is mostly concerned with structures within the realm of real and complex numbers. Abstract or modern algebra is the study of algebraic structures such as groups, rings, fields, modules, vector spaces, lattices etc.

Algebraic equations are needed in many aspects of life such as engineering, industry, medicine etc. As a result, we end up solving algebraic equations almost every day as we have to make decisions about specific quantities such as the amount of food to last a week, amount of materials needed for construction of a block in a site, amount of money needed to follow up a project from start to finish etc. As solving algebraic equations manually can be tiring or time-consuming; which is a consequence of the bulky steps one has to pass through that increases as the complexity of the equation increases, this project illustrates the construction of a desktop application that simulates and solves systems of algebraic equations and shows the user the algorithm followed by the computer in solving such equations.

1.1 Statement of the Problem

The following problems are observed in the manual solution of systems of algebraic equations;

Time Conservation: Manually solving an algebraic equation from start to finish can be time consuming especially in cases where the equation is as complex as a quadratic or cubic equation or an exponential equation with long procedures.
Cost: One who wants to solve an algebraic equation prefers manual solution using a calculator, a pen, a piece(s) of paper as well as four-figure tables in order to get his / her facts right. Thus, a project analyst in an industry would need a stand-by calculator, stacks of paper as well as a writing pen, all of which are costly to constantly supply and exhausts space.
Accuracy: Man always has the tendency to make errors as a result of extensive approximation. Example, an average individual tends to solve mathematical problems with values not more than 3-4 decimal places. This can cause significant errors when used in the long-run.

1.2 Aims and Objectives

The aim of this project is to develop a computerized solution for a system of equations, the specific objectives are to;

Reduce the time and energy exhumed in the process of solving algebraic equations manually.
Help students solve algebraic equations on their own without the constant presence of a school teacher or the constant usage of physical textbooks, as well as alleviate the stress of having to carry too many learning materials while going for studies.
Minimize the cost of analytic materials; in a data analyst’s office one workstation or desktop could carry as many mathematical problem solving applications as possible, which reduces the cost of buying, writing and solving materials such as the calculator, papers, pen etc.
Aid teachers and examination bodies in the preparation of questions and the construction of error-free marking schemes.

1.3 Significance of the study

The beneficiaries of this project are;

Science students involved in mathematics
Mathematics teachers

Every science student needs an in-depth understanding of mathematics for any significant goal is to be achieved in his / her study. This project would provide a reliable means of sourcing for help in mathematical problems involving algebraic equations. It would help the student to solve algebraic equations with high degree of accuracy, sighting norms and exceptions, as well as rules to be followed.

Mathematics teachers would benefit widely because they no longer have to rely on the limited examples textbooks offer them, but they can try as many problems as possible to expand their understanding of the algebraic equation to be solved and hence increase their efficiency while teaching.

1.4 Scope of the Project

This project covers three main types of algebraic equations, namely;

Simultaneous Equations which could involve;
- Two Linear equations
- One Linear and one quadratic equation
- One quadratic and one cubic equation
- One Linear and one cubic equation
Quadratic Equations
Cubic Equations

It is limited to real numbers, meaning that complex numbers, trigonometric functions and exponential functions are not considered in this context.

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