Connecting the Dots-A Course on Relations and Functions

Description

Once upon a time, in a beautiful village called Mathville, there lived two best friends Alan and Betty. Alan was a dedicated baker and Betty, an enthusiastic gardener. Each time Alan would bake a delicious pastry, Betty would plant a beautiful flower.

Each pastry that Alan baked corresponded to a particular flower that Betty planted thus establishing a relation. Thus different types of relations such as one to one, onto and many to one could be explained by the relation between the pastries and flowers. The concept of functions was also introduced by associating each pastry with exactly one flower.

The story progresses to explaining domain and range where the domain consisted of all the pastries which Alan could bake and the range comprising all the flowers which Betty could plant. The story continues to unfold by illustrating concepts such as composite functions, invertibility and the identity function.

In short, understanding Relations and functions is a mutual exchange of talents. This course illustrates the beauty of Relations and Functions in our everyday lives..

You have been introduced to Calculus and you realise the importance of Functions in Calculus. That is precisely what this course teaches you.

I am Suman Mathews. I have a double Master's in Mathematics and I have taught and helped students of high school and college for the past three decades.

The course unfolds with the basic concept of Sets and a Relation as a subset of the cross product of two sets. You learn the different types of Relations and a very important concept, namely, what is an equivalence Relation.

Next, you'll be introduced to a function as a type of Relation. You'll understand what is meant by Domain and Range of a function.  As you progress through the course, you'll learn about injective and surjective functions and consequently bijective functions.

You'll learn how to calculate the inverse of a bijective function. You'll glide to Binary Operations, a very important concept used in Group Theory in Higher Mathematics.

You'll receive all the formulas learnt in this course as a gift. There's also a set of Multiple choice questions at the end of the course. This will inspire you to think out of the box.

On a side note, the concepts taught here will also help you to answer SAT and GRE QUANT examinations.

I hope you'll find this course helpful. Encourage your friends and acquaintances to also enrol for the course and learn hassle free at your own pace.

Bonus-Learn how to find the domain and range of Inverse Trigonometric Functions. Also learn simple techniques to find the principal values of Inverse Trigonometric functions.

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