...CHAPTER ONE 1. INTRODUCTION The study of mathematics as a subject for both primary and post primary level of education and even in tertiary level of education has been made compulsory because the whole o four life is in mathematics, that why study of mathematics is compulsory by the curriculum planners for both primary and post primary level of education. This is so because of it broader application for all subject and learned in schools, particularly science and technology as well as in our daily life activities especially in the modern world. One of the needs of the Nigerian society which must be given priority today is the advancement of science and technology which is not possible without mathematics. Mathematics is a very important subject which is made compulsory from primary to post primary schools level of education. Since mathematics is an important subject our life, what does mathematics mean? The Academic American encyclopedia defined mathematics as the study of numbers, set of points, and various abstract elements, together with the relations between them and operations performed on them. Wikipedia defined mathematics as the abstract study of topics such as quantity (number) structure, space and change. Mathematic is a science subject that deals with the study of numbers, shapes, sizes and other relationships among the quantities. 1.1 BACKGROUND OF THE STUDY: mathematics is one of the most important and compulsory subjects to be taught...
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...The differential equation M ( x, y )dx N ( x, y )dy 0 is called an EXACT EQUATION if there exist a continuos function F ( x, y ) c (c is a constant) such that F F dF dx dy x y Excellent does not an accident, but it comes through a hard work!! Condition for exact equation: M ( x, y )dx N ( x, y )dy 0 is called an EXACT EQUATION if and only if M N y x Excellent does not an accident, but it comes through a hard work!! GOAL By comparing M ( x, y )dx N ( x, y )dy 0 with F F dx dy dF x y F ( x, y) c F M x F N y Test for exactness F M N F yx y x xy 2 2 Excellent does not an accident, but it comes through a hard work!! 1) Write F F M (1) and N (2) x y 4) Compare eqn(4) with eqn(2) to obtain ( y) 2) Integrate eqn(1) w.r.t x, so F x dx M dx ( y) F ( x, y ) M dx ( y ) (3) where ( y ) is a function of y alone. 5) Integrate ( y) w.r.t y to get the unknown ( y ) 6) Substitute ( y) into eqn(3) in order to complete the required solution. 3) Differentiate eqn(3) w.r.t y F Mdx ( y ) (4) y y Let’s Try Excellent does not an accident, but it comes through a hard work!! Solve this differential equation: (e ye ) dx (e xe )dy 0; y x x y y (1) 0 Excellent does not an accident, but it comes through a hard work!!...
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...The characteristics of the samples are made to show the characteristics of the entire population under study. The sample’s statistical results are generally assumed not to represent the characteristics of those who are not part of the population. For example, the $25,111 salary represents the average salary of people chosen for the statistical tests (such as people in Yale alone). However, the $24,111 salary does not represent the people not chosen for the survey, such as the people working in Alaska. The $25,111 average salary is true only for the time period when the statistical tests were undertaken, but it may not be true when the same statistical tests were taken 30 years prior to the current Yale statistical tests. A similar test conducted 20 years after the current statistical tests will generally show a different statistical finding. Interpreting the difference in the findings, the statistical findings should not be taken as occurring in all situations; to do so would be a lie. It is a lie because interpreting the statistical results is all-encompassing would be too twisted, exaggerating, oversimplified, or distorted. Sales people would use the average results of statistical test to convince the prospective buyers to purchase their wares; the sales persons are willing to lie to generate sales. The manager can base one’s expansion policy on the statistical figure stating there is a huge profit. However, the manager must beware of false statistical figures. The statistical...
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...LONDON'S GLOBAL UNIVERSITY Mathematics with Management Studies BSc UCAS code: G1N2 www.ucl.ac.uk/prospectus/maths MATHEMATICS WITH MANAGEMENT STUDIES BSc This BSc combines a broad-based training in mathematics with highly practical courses from UCL’s Department of Management Science and Innovation, which will be of direct use to those seeking a career in management. No previous knowledge of management studies is required. Degree summary • • • • Gain transferable skills such as numeracy, problem-solving and logical thinking, which can lead to a large variety of interesting, diverse and well-paid careers. All of the courses given by UCL's Department of Management Science are validated by external experts from the private, public and charitable sectors. Many of our graduates choose to build their management knowledge and experience by following a further management qualification, such as the MBA (Masters in Business Administration). UCL's internationally renowned Mathematics Department is home to world-leading researchers in a wide range of fields, especially geometry, spectral theory, number theory, fluid dynamics and mathematical modelling. Peer Assisted Learning has been pioneered in the department, with second-year students offering support and advice to first years. Your career We aim to develop your skills in mathematical reasoning, problem-solving and accurate mathematical manipulation. You will also learn to handle abstract concepts and to think critically...
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...Running Head: MATHEMATICS and VISUALITY Mathematics and Visuality By: Monica McCarty Jackson State University Mathematics is one of the most useful and fascinating divisions of human knowledge. It includes many topics of study. For this reason, the term mathematics is difficult to define. It comes from a Greek word meaning “inclined to learn.” Most of the basic math taught in school involves the study of number, quantity, form, and relations. Arithmetic, for example, concerns problems with numbers. Algebra involves solving equations in which letters represent unknown quantities. Geometry concerns the properties and relationships of figures in space. The most important skills in mathematics are careful analysis and clear reasoning. These skills can help us solve some of the deepest puzzles we must face. Mathematics is based upon logic. Starting from, widely accepted statements, Mathematicians use logic to draw conclusions and develop mathematical systems. The work of mathematicians may be divided into pure mathematics and applied mathematics. Pure mathematics seeks to advance mathematical knowledge for its own sake rather than for any immediate practical use. Applied mathematics seek to develop mathematical techniques for use in science and other fields. In everyday life we use mathematics for simple tasks as telling time from a clock or counting change after making a purchase...
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...EFFICIENCY LEVEL IN SOLVING POLYNOMIAL EQUATIONS AND THEIR PERFORMANCE IN MATHEMATICS OF GRADE 9 STUDENTS A Thesis Presented to the Faculty of the Teacher Education Program Ramon Magsaysay Memorial Colleges General Santos City In Partial Fulfillment of the Requirement for the Degree Bachelor of Secondary Education Major in Mathematics Armando V. Delino Jr. October 2015 TABLE OF CONTENTS Contents Page Title Page i Table of contents ii CHAPTER I THE PROBLEM AND ITS SETTING 1 Introduction 1 Theoretical Framework Conceptual Framework Statement of the problem Hypothesis Significance of the study Scope of the study Definition of terms CHAPTER II REVIEW OF RELATED LITERATURE CHAPTER III METHODOLOGY Research Design Research Locale Sampling Technique Research Instrument Statistical Treatment CHAPTER 1 PROBLEM AND ITS SETTING Introduction In Mathematics, a polynomial is an expression consisting of variables (or indeterminates) and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents. Polynomials appear in a wide variety of areas of Mathematics and Science. For example, they are used to form polynomial equations, which encode a wide range of problems, from elementary word problems to complicated problems in the Sciences; they are used to define polynomial functions, which appear in...
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...MATHEMATICS has played a significant role in the development of Indian culture for millennia. Mathematical ideas that originated in the Indian subcontinent have had a profound impact on the world. Swami Vivekananda said: ‘you know how many sciences had their origin in India. Mathematics began there. You are even today counting 1, 2, 3, etc. to zero, after Sanskrit figures, and you all know that algebra also originated in India.’ It is also a fitting time to review the contributions of Indian mathematicians from ancient times to the present, as in 2010, India will be hosting the International Congress of Mathematicians. This quadrennial meeting brings together mathematicians from around the world to discuss the most significant developments in the subject over the past four years and to get a sense of where the subject is heading in the next four. The idea of holding such a congress at regular intervals actually started at The Columbian Exhibition in Chicago in 1893. This exhibition had sessions to highlight the advancement of knowledge in different fields. One of these was a session on mathematics. Another, perhaps more familiar to readers of Prabuddha Bharata, was the famous Parliament of Religions in which Swami Vivekananda first made his public appearance in the West. Following the Chicago meeting, the first International Congress of Mathematicians took place in Zurich in 1897. It was at the next meeting at Paris in 1900 that Hilbert...
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...Discrete mathematics is the study of mathematical structures that are fundamentally discrete rather than continuous. In contrast to real numbers that have the property of varying "smoothly", the objects studied in discrete mathematics – such as integers, graphs, and statements in logic[1] – do not vary smoothly in this way, but have distinct, separated values.[2] Discrete mathematics therefore excludes topics in "continuous mathematics" such as calculus and analysis. Discrete objects can often be enumerated by integers. More formally, discrete mathematics has been characterized as the branch of mathematics dealing with countable sets[3] (sets that have the same cardinality as subsets of the natural numbers, including rational numbers but not real numbers). However, there is no exact definition of the term "discrete mathematics."[4] Indeed, discrete mathematics is described less by what is included than by what is excluded: continuously varying quantities and related notions. The set of objects studied in discrete mathematics can be finite or infinite. The term finite mathematics is sometimes applied to parts of the field of discrete mathematics that deals with finite sets, particularly those areas relevant to business. Research in discrete mathematics increased in the latter half of the twentieth century partly due to the development of digital computers which operate in discrete steps and store data in discrete bits. Concepts and notations from discrete mathematics are useful...
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...Introduction In this chapter, research from multiple authors will provide supporting answers for my research question, how do games and manipulatives impact students' interest in Mathematics?, how do games and manipulatives impact students' performances in Mathematics?, and what are the benefits of using games and manipulatives when teaching fractions? Based on research thus far manipulative and games improve students’ interest and performance, while some researchers don’t see a significance difference in manipulatives increasing students interest in mathematics. (Kontaş) (2016).I found that manipulatives were proven to assist in helping students in building conceptual understanding, and eliminate misconception in mathematics. DeGeorge and...
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...Pascal and developed a revolutionary math learning material for children as young as 3 years old. Her mathematical materials allow the children to begin their mathematical journey from a concrete concept to abstract idea”. With reference to the above statement please discuss how these children utilize their mathematical mind as part of their natural progression, to reason, to calculate and estimate with these Montessori mathematical materials in conjunction with their aims and presentations? The child doesn’t learn mathematics only through Montessori, but he learns it from the day he was born or even before that. It is a known fact that an embryo can hear its mother. When a mother says ‘the baby kicked me 4 times’, the baby can understand this in her womb. After the baby is born people often tell him what day he was born or how many siblings he has, etc. The child’s day-to-day life and environment is connected with math. The child is born into a mathematic world where he has to adapt to it. The child needs math to sort and group objects within their environment. When the child enters the Montessori environment, he can already count without knowing the real meaning of the numbers (rote-counting). He counts with understanding of numbers and gradually learns arithmetic’s, geometry and algebra in the Montessori classroom. ‘The Mathematical Mind’ refers to the unique tendencies of the human mind. The French philosopher B. Pascal said that ‘every human being is born with a mathematical...
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...are using drugs and alcohol and every one out of ten schoolgirl are pregnant. We encounter many discipline problems and not all the teachers are capable to deal with this learners. Our learner total are 920 and the teachers are 26 . The school have a teacher and classroom shortage . There are many social problems at the school and they are struggling mostly with Mathematics . Our feeder school is the local primary school and the total of the gr. 8 learners are near 300 every year. These Gr. 8 learners are very weak in Mathematics and the class sizes are 50 and more. The Gr 9 classes are also very big and most of them pass not Mathematics at the end of the year , but been condened to Gr. 10 . Usually there are only one gr. 10, 11 and Gr.12 class for Mathematics. The passrate for Mathematics in Gr. 9 are so poor that only 10 % of the learners can do pure Mathematics , The rest of the learners should do Mathematical Literacy. The Maths learners are not commited and only a few pass at the end of Gr. 10 . JUSTIFICATION When the grade 8 learners came to our school they usually struggle with Mathematics .The can`t do the basic fractions , do not even know how to use the factors and multiples . in grade 8 the learners are suppose to do know how to get the LCM and the bigests factor . When we do this in class the learners are able to do it but in a test they could not do it. Then in gr. 9 they also can do it but the same problem occurs in a test they get it wrong...
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...Discrete Mathematics Lecture Notes, Yale University, Spring 1999 L. Lov´sz and K. Vesztergombi a Parts of these lecture notes are based on ´ ´ L. Lovasz – J. Pelikan – K. Vesztergombi: Kombinatorika (Tank¨nyvkiad´, Budapest, 1972); o o Chapter 14 is based on a section in ´ L. Lovasz – M.D. Plummer: Matching theory (Elsevier, Amsterdam, 1979) 1 2 Contents 1 Introduction 2 Let 2.1 2.2 2.3 2.4 2.5 us count! A party . . . . . . . . Sets and the like . . . The number of subsets Sequences . . . . . . . Permutations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 7 7 9 12 16 17 21 21 23 24 27 27 28 29 30 32 33 35 35 38 45 45 46 47 51 51 52 53 55 55 56 58 59 63 64 69 3 Induction 3.1 The sum of odd numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Subset counting revisited . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3 Counting regions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Counting subsets 4.1 The number of ordered subsets . . . . 4.2 The number of subsets of a given size 4.3 The Binomial Theorem . . . . . . . . 4.4 Distributing presents . . . . . . . . . . 4.5 Anagrams . . . . . . . . . . . . . . . . 4.6 Distributing money . . . . . . . . . . ...
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...Mathematics: An Integral Discipline Mathematics is one of the most foundational and elemental principles and disciplines to any educational institution. With the basic components of all mathematical disciplines and areas of studies being equal, there appears to be an inherent, social need to master this study of a seemingly complex nature, particularly since this subject is ingrained into so many important and relevant aspects of the world economy. Without the understanding and overall comprehension of at least some basic, elementary mathematical principles, it would go without saying that countless workforce employees and job seekers would fail to find the most meager of professions. It is also an unfortunate prospect to understand that mathematical principles and the study of such major applications is no longer a popular social trend. On the other hand of the social and professional spectrum, the vast majority of college students seeking future majors are leaning towards other convenient modes of study, including those in the healthcare industry and other related sciences and studies. Now understanding how modern culture had become so predisposed to ascertaining studies unrelated to heavy mathematical analytics, despite the obvious need to otherwise acquire, it will be important to frame this expose’s subject matter around the need to further explain and analyze how different regions of scholastic establishments have come to define mathematical disciplines in completely different...
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...Mathematics is used all over the world in a person’s everyday career. Criminal Justice careers use mathematics in a variety of different ways to complete a day’s work. Most Criminal Justice degree programs emphasis particularly on statistics as a core measureable expertise for students in this specific program. The Mathematical Association of America stresses that students in social science majors require a strong foundation in mathematical literacy. The degree I am studying for at Westwood College is an associate’s degree in applied science. So, by me taking mathematics serious and working hard it would benefit me in the long run. Programs predominantly want people studying Criminal Justice to be competent in statistics in order to succeed in a data compelled career field. The specific career I want to perform when I receive my degree is becoming a police officer. Police officers use mathematics in the field everyday. Police are usually the first to the scene when an accident transpires. Police measure impact angles after car accidents, measure skid marks, build statistical models of crime patterns to put patrol officers where thy need to be and a whole lot more. Math is generally used to prevent crime because without mathematics crime would not be as detectable. All police officers use mathematics while patrolling the field. For instance, say someone is pulled over for a DUI, the police use Breathalyzer’s to measure the blood alcohol content of the person they suspect of...
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...Today the use of applied mathematics to solve challenging problems in science and engineering or related fields by using numerical computation have reached to a new level. Computation is today considered as a very important tool needed for the advancement of scientific knowledge and engineering practice along with theory and experiment. In the modern world all sorts of calculations are done by sophisticated computer systems. Every company and research farms from small-scale to large-scale are getting more and more reliant on mathematical principles these days. Numerical simulation has enabled the study of complex systems and natural phenomena that would be too expensive or sometimes impossible, to study directly by experimentation. As a matter of fact, engineers and scientists now require solid knowledge of computer science and applied mathematics in order to get optimized output from a system. To make things easier in this matter, Scientific Computing is a discipline that conglomerates Mathematics, Computer Science and Engineering in a single degree program and utilizes mathematical models in computer simulations to solve complex problems for not only in science laboratories but also in business and engineering firms. I have always been fascinated by the application of mathematics and computer science in the real world problems. That is why...
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