Abstract:
This course is for a diverse set of learners in business, economics and other social sciences including (a) those who may lack a strong enough math and statistics background from high school, (b) learners seeking to refresh their math and statistics knowledge in preparation for upper years in university and college, (c) learners wishing to re-skill or up-skill by switching majors or adding a minor and lacking the necessary math and statistics tools.
The course has two parts: pre-calculus and calculus.
Part 1 covers precalculus algebra. These topics are necessary for performing mathematical calculations and higher-level mathematics. It can be useful to think of algebra as a language with its own definitions and rules. Topics are introduced assuming the learner has forgotten all their high school math. We begin by relating algebraic expressions to real world examples from the social sciences. These examples demonstrate the utility of mathematics to motivate the learner as more technical topics are introduced. Sets and real numbers are explored, followed by exponents, factors, and fractions. These mathematical concepts are illustrated using two-dimensional graphs, and their applications are demonstrated with real-world examples whenever possible. Functions and summation notation are important tools for relating real-world phenomena to mathematics in a way that is useful for analysis and simplifies communication.
Part 2 introduces differential calculus which is perhaps the most commonly used mathematical concept in business and the social sciences. We begin by introducing the concept of limits: the value of a function as the input variable moves closer and closer to some particular number. Limits help understand the concept of differentiation which is in turn used to calculate rates of change for expressions more complicated than a straight line. We develop the important idea that on a graph, differentiation equates to the slope of a curve. We then explore three useful applications of differential calculus: implicit differentiation, linear approximation, and optimization.
Each module relies on at least some of the topics covered in a previous module, so we suggest that the learner work through each module in sequence. A learner who has not mastered the content in part 1 is likely to be challenged to develop even a basic understanding of the content in part 2.
