ABSTRACT
Traditionally, the concept of teaching mathematics has always been a teacher – student relationship; in which the teacher explains the concept of the topic to the student and illustrates it with some examples. The student is then left to understand the topic on his or her own using the tools given by the teacher. A problem often results when the student needs a guide while practicing and the teacher is not available. In that case, learning becomes slow and hindered. As we are in a digital age, where computers have been built to emulate most services usually offered by a human, it is believed that the computer can also stand in the gap for the teacher in his / her absence. With respect to algebra, the objective of this project is the design and implementation of a computer aided system that algebraic equations with limitations to simultaneous equations, quadratic equations and cubic equations (involving real numbers only). The system is designed using Java, CSS (Cascading Style Sheet) and MathTex as the programming languages. The methodology used is the Object-Oriented Analysis and Design method. It is expected that this software would be able to stand in the gap in the absence of the teacher and help students solve algebraic equations on their own, using their own examples and at their own pace and also help teachers in getting versatile knowledge of a algebraic equations by testing them with their own variables. It could also help teachers understand the most optimal methods for solving an algebraic equation to avoid errors in the process of teaching and learning.
TABLE OF CONTENTS
Title page i
Certification ii
Approval Page iii
Dedication iv
Acknowledgement v
Abstract vi
Table of contents vii
List of Figures ix
List of Tables x
CHAPTER ONE: INTRODUCTION
- Background of the study 1
- Statement of the problem 2
- Objective of the study 3
- Significance of the study 3
1.4 Scope of the study 4
CHAPTER TWO: REVIEW OF RELATED LITERATURE
2.0 Introduction 5
2.1 Theoretical Background 7
2.2 Review of Related Literature 9
2.3 Summary 24
CHAPTER THREE: SYSTEM ANALYSIS AND DESIGN
- Introduction 26
- Analysis of Existing System 28
- Design of the Proposed System 29
3.2.1 Input Design 31
3.2.2 Output Design 31
- Database Design 32
3.2.4 System Architecture 33
CHAPTER FOUR: SYSTEM IMPLEMENTATION
4.0 Introduction 35
4.1 Choice of Programming Environment 35
4.2 Implementation Architecture 37
4.3 Software Testing 37
4.4 Documentation 40
4.4.1 User Manual 40
4.4.2 Source Code listing 41
CHAPTER FIVE: SUMMARY AND RECOMMENDATION
5.0 Summary 42
5.1 Recommendation 43
REFERENCES 44
APPENDIX 46
List of Figures
Fig 1: Graph of Quadratic Equation showing Real and Distinct roots 17
Fig 2: Graph of Quadratic Equations showing Imaginary roots 18
Fig 3: Graph of a Cubic Equation 24
Fig 4: Software Design Methodology using Object Oriented Analysis and Design 28
Fig 5: Use Case Diagram showing the design of the proposed system 30
Fig 6: Input Design sample using Quadratic Equations 31
Fig 7: Output Design sample using Quadratic Equations 32
Fig 8: System Architecture 34
Fig 9: Eclipse Integrated Development Environment Interface 36
Fig 10: Implementation Architecture 37
Fig 11: Screenshot showing the Homepage 38
Fig 12: Screenshot showing Insertion of Variables 39
Fig 13: Screenshot showing Choice Method 39
Fig 14: Screenshot showing Output 40
List of Tables
Table 1: Database Structure for Simultaneous Equations Design 33
CHAPTER
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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