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This is the complete lecture note for ECO 103 INTRODUCTORY MATHEMATICS. You can read it online below, open it in the full viewer, or download the PDF for offline study. It pairs with the course's video lectures, so you can read and watch together.
LA-NET | ONLINE LEARNING VIDEO PLATFORM FOR POST-SECONDARY & HIGHER INSTITUTION STUDENTS
LA-NET | ONLINE LEARNING VIDEO PLATFORM FOR POST-SECONDARY & HIGHER INSTITUTION STUDENTS Course code: ECO 103 Course title: INTRODUCTORY MATHEMATICS Course credit load: 2 unit Series 1: Mathematical Concepts in the Social Sciences Series 2: Set Theory, Factors, Exponents, and Logarithms Series 3: Equations, Functions, and Progressions Series 4: Co-ordinate Geometry and Inequalities Series 5: Matrix Algebra, Trigonometric Functions, and Differentiation Series 1: Mathematics in the Social Sciences Part 1 Roles of Mathematics in Social Sciences • Importance of mathematics in economics • Applications of mathematics in other social sciences (political science, sociology, geography) • Limitations of mathematics in social science analysis Part 2 Basic Mathematical Concepts and Modern Mathematics • Fundamental mathematical ideas (numbers, operations, symbols) • Relationship between basic mathematics and modern mathematics (set theory, algebra, trigonometry) • Relevance of these concepts to economic investigation Introduction Mathematics plays a vital role in the study of the social sciences, particularly in economics. It provides the language and tools that allow us to describe, analyse, and interpret complex relationships in a clear and precise manner. For example, economists use mathematical models to explain how markets function, how resources are allocated, and how individuals and organisations make decisions. In political science, sociology, and geography, mathematics is equally important for measuring trends, comparing data, and predicting outcomes. The aim of this Series is to help you appreciate the relevance of mathematics in the social sciences and to introduce you to some of the basic concepts that underpin modern mathematics. By the end of this Series, you should be able to explain the roles of mathematics in economics and other social sciences, and to connect fundamental mathematical ideas with advanced concepts such as set theory, algebra, and trigonometry.
LA-NET | ONLINE LEARNING VIDEO PLATFORM FOR POST-SECONDARY & HIGHER INSTITUTION STUDENTS We shall begin by examining the roles of mathematics in social sciences, with particular emphasis on economics. Next, we will explore basic mathematical concepts and show how they form the foundation for modern mathematics. This sequential approach will ensure that you build a strong understanding of why mathematics is indispensable in the study of social sciences, and how it prepares you for more advanced topics later in the course. Series learning outcomes By the end of Series 1: Mathematics in the Social Sciences, you should be able to: • Define the role of mathematics in economics and other social sciences. • Explain how mathematics provides tools for analysing and interpreting social science problems. • Analyse the connections between basic mathematical concepts and modern mathematical approaches such as set theory, algebra, and trigonometry. • Evaluate the usefulness and limitations of mathematics in investigating social science issues. 1.1 Roles of Mathematics in Social Sciences Mathematics is often described as the language of science, meaning it provides a precise and logical way of expressing ideas. In the social sciences, mathematics is used to measure, analyse, and interpret human behaviour and social phenomena. By applying mathematical tools, economists and other social scientists can build models that explain relationships, predict outcomes, and guide decision-making. Fill in the blank: In the social sciences, mathematics is often referred to as the ______ of science. 1.1.1 Importance of mathematics in economics Economics relies heavily on mathematics to explain how individuals, firms, and governments make decisions. Concepts such as demand function (a mathematical expression showing the relationship between the quantity demanded of a good and its price) and supply function (a mathematical expression showing how producers respond to changes in price) are central to economic analysis. Mathematics also helps economists to calculate costs, revenues, and profits, and to evaluate how changes in one variable affect another. For example, when the price of a product increases, the demand may decrease, and this relationship can be expressed clearly using equations and graphs.
LA-NET | ONLINE LEARNING VIDEO PLATFORM FOR POST-SECONDARY & HIGHER INSTITUTION STUDENTS Fill in the blank: The mathematical expression that shows the relationship between price and quantity demanded is called the ______ function. 1.1.2 Applications in other social sciences Mathematics is not limited to economics. In political science, it is used to study voting behaviour and decision-making processes. In sociology, mathematics helps in analysing demographic data such as birth rates, migration, and population growth. In geography, mathematical tools are applied to measure distances, population densities, and spatial distributions.
LA-NET | ONLINE LEARNING VIDEO PLATFORM FOR POST-SECONDARY & HIGHER INSTITUTION STUDENTS Fill in the blank: In sociology, mathematics is often used to analyse ______ data. 1.1.3 Limitations of mathematics in social sciences Although mathematics is powerful, it has limitations. Human behaviour is complex and influenced by qualitative factors such as culture, values, and emotions, which cannot always be captured in equations. For this reason, mathematics should be seen as a tool that complements other methods of analysis rather than replacing them.
LA-NET | ONLINE LEARNING VIDEO PLATFORM FOR POST-SECONDARY & HIGHER INSTITUTION STUDENTS Fill in the blank: Human behaviour is complex and influenced by ______ factors that cannot always be captured mathematically. Pilot questions 1.1 1. Mathematics is often described as the ______ of science. 2. Which function shows the relationship between quantity demanded and price? 3. Name one social science other than economics where mathematics is applied. 4. What is one limitation of using mathematics in social sciences? 5. Fill in the blank: Geography uses mathematical tools to measure ______ distributions. 1.2 Basic Mathematical Concepts and Modern Mathematics Mathematics is built upon a set of fundamental ideas that form the foundation for more advanced concepts. These basic ideas include numbers, operations, and symbols, which are used to represent and manipulate relationships. In the social sciences, these concepts are not studied in isolation, but rather as tools for analysing real-world problems.
LA-NET | ONLINE LEARNING VIDEO PLATFORM FOR POST-SECONDARY & HIGHER INSTITUTION STUDENTS When we speak of basic mathematical concepts, we refer to elements such as addition, subtraction, multiplication, division, and the use of symbols to represent unknowns. These are the building blocks that allow us to progress to modern mathematics, which includes areas such as set theory, algebra, and trigonometry. Fill in the blank: The basic mathematical operation used to combine two numbers into a larger total is ______. 1.2.1 Fundamental mathematical ideas Numbers are symbols used to represent quantities. They allow us to count, measure, and compare. Operations are processes such as addition, subtraction, multiplication, and division, which enable us to manipulate numbers. Symbols such as x or y are used to represent unknown quantities, making it possible to generalise problems and solve them systematically. Fill in the blank: Symbols such as x or y are used to represent ______ quantities. 1.2.2 Relationship between basic and modern mathematics
LA-NET | ONLINE LEARNING VIDEO PLATFORM FOR POST-SECONDARY & HIGHER INSTITUTION STUDENTS Modern mathematics builds upon these fundamentals. For example, set theory is the study of collections of objects, often represented using symbols and logic. Algebra extends basic operations to include variables and equations, allowing us to solve problems involving unknowns. Trigonometry applies ratios and functions to study angles and shapes, which can be used to model cycles and patterns. Fill in the blank: Algebra extends basic operations to include ______ and equations. 1.2.3 Relevance to economic investigation Economists often use these mathematical tools to investigate issues such as production, consumption, and distribution. For instance, logarithms are applied in measuring growth rates, while trigonometric functions may be used in modelling cycles or waves in economic activity. These applications show how basic concepts evolve into powerful tools for social science analysis.
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