# Master Discrete Mathematics-Set Theory, Relations & More

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- By the end of this course, you will be able to define a set and represent the same in different forms;
- define different types of sets such as, finite and infinite sets, empty set, singleton set, equivalent sets, equal sets, sub sets, proper subsets, supersets, give examples of each kind of set, and solve problems based on them;
- define union and intersection of two sets, and solve problems based on them;
- define universal set, complement of a set, difference between two sets, and solve problems based on them;
- define Cartesian product of two sets, and solve problems based on them;
- represent union and intersection of two sets, universal sets, complement of a set, difference between two sets by Venn Diagram;
- solve problems based on Venn Diagram;
- define relation and quote examples of relations;
- find the domain and range of a relation;
- represent relations diagrammatically;
- define different types of relations such as, empty relation, universal relation, identity relation, inverse relation, reflexive relation, symmetric relation, transitive relation, equivalence relation, and solve problems based on them;
- define function and give examples of functions;
- find the domain, codomain and range of a function;
- define the different types of functions such as injective function (one-to-one function), surjective function (onto function), bijective function, give examples of each kind of function, and solve problems based on them.
- define and give examples of even and odd functions;
- figure out if any given function is even, odd, or neither from graphs as well as equations;
- define composition of two functions;
- find the composition of functions;
- define the inverse of a function;
- find the inverse of any given function;
- find the domain and range of the inverse function;
- Understand the concept of Mathematical Induction and the logic behind it;
- Learn to prove statements using Mathematical Induction;
- Learn to apply Mathematical Induction in a Brain Teasing Real World Problem;
- Understand the application of Mathematical Induction in Computer Program/Algorithm Correctness Proofs;
- Learn to apply Mathematical Induction for proving a Result from Geometry;
- Learn to apply Mathematical Induction for proving the Divisibilities;
- Learn to apply Mathematical Induction for proving the sum of Arithmetic Progressions;
- Learn to apply Mathematical Induction for proving the the Sum of squares of first n natural numbers;
- Learn to apply Mathematical Induction for proving the Inequalities;
- Learn to apply Mathematical Induction for proving the sum of Geometric Progressions.

- There are no pre-requisites for this course.

Welcome to this course on Discrete Math.** **In this course you will learn *Set Theory, Relations, Functions *and *Mathematical Induction*.

Discrete Math is the real world mathematics. It is the mathematics of computing. The mathematics of modern computer science is built almost entirely on Discrete Math. This means that in order to learn the fundamental algorithms used by computer programmers, students must have a solid background in Discrete Math. At most of the universities, a undergraduate-level course in discrete mathematics is a required part of pursuing a computer science degree.

**"Set Theory, Relations and Functions"** form an integral part of Discrete Math. They are the fundamental building blocks of Discrete Math and are highly significant in today's world. Nearly all areas of research be it Mathematics, Computer Science, Actuarial Science, Data Science, or even Engineering use Set Theory in one way or the other. Set Theory is now-a-days considered to be the base from where all the other branches of mathematics are derived.

**"Mathematical Induction"**, on the other hand, is very important for the Computer Program/Algorithm Correctness Proofs used in Computer Science. Correctness Proofs are very important for Computer Science**. **Usually coders have to write a program code and then a correctness proof to prove the validity that the program will run fine for all cases, and Mathematical Induction plays a important role there. Mathematical Induction is also an indispensable tool for Mathematicians. Mathematicians use induction to conclude the truthfulness of infinitely many Mathematical Statements and Algorithms.

**This course is a perfect course to understand Set Theory, Relations, Functions and Mathematical Induction and learn to solve problems based on them. After completing this discrete math course, you will be able to:**

*define a**SET**(Set Theory)**define different types of sets such as, finite and infinite sets, empty set, singleton set, equivalent sets, equal sets, sub sets, proper subsets, supersets, give examples of each kind of set, and solve problems based on them;**(Set Theory)**define union and intersection of two sets, and solve problems based on them;**(Set Theory)**define universal set, complement of a set, difference between two sets, and solve problems based on them;**(Set Theory)**define Cartesian product of two sets, and solve problems based on them;**(Set Theory)**represent union and intersection of two sets, universal sets, complement of a set, difference between two sets by Venn Diagram;**(Set Theory)**solve problems based on Venn Diagram;**(Set Theory)**define**RELATION**and quote examples of relations;**(Relations)**find the domain and range of a relation;**(Relations)**represent relations diagrammatically;**(Relations)**define different types of relations such as, empty relation, universal relation, identity relation, inverse relation, reflexive relation, symmetric relation, transitive relation, equivalence relation, and solve problems based on them;**(Relations)**define**FUNCTION**(Functions)**find the domain, codomain and range of a function;**(Functions)**define the different types of functions such as injective function (one-to-one function), surjective function (onto function), bijective function, give examples of each kind of function, and solve problems based on them;**(Functions)**define and give examples of even and odd functions;**(Functions)**figure out if any given function is even, odd, or neither from graphs as well as equations;**(Functions)**define composition of two functions;**(Functions)**find the composition of functions;**(Functions)**define the inverse of a function;**(Functions)**find the inverse of any given function;**(Functions)**find the domain and range of the inverse function;**(Functions)**define The Principle of**DISCRETE MATHEMATICAL INDUCTION**and use it for Proving Mathematical Statements;**(Mathematical Induction)**Mathematical Induction for "Proving the Sum of an Arithmetic Progression";**(Mathematical Induction)**Mathematical Induction for "Proving the Sum of squares of first n natural numbers";**(Mathematical Induction)**Mathematical Induction in "Proving the Divisibility";**(Mathematical Induction)**Mathematical Induction in "Proving the Inequality";**(Mathematical Induction)**Mathematical Induction for "Proving the Sum of a Geometric Progression";**(Mathematical Induction)**Mathematical Induction in a "Brain Teasing Real World Problem";**(Mathematical Induction)**Mathematical Induction for "Proving a result from Geometry";**(Mathematical Induction)**Mathematical Induction in "The Towers of Hanoi";**(Mathematical Induction)**and**Learn to use Mathematical Induction to do Computer Program/Algorithm Correctness proofs.**(Mathematical Induction)*

**We recommend this course to you if you are Math or Computer Science student, or are a working IT professional. **After completing this discrete math course, you will find yourself more confident on Set Theory, Relations, Functions and Mathematical Induction, and will be clear with various terms and concepts associated with them.

- Math Students.
- Computer Programmers/Computer Science Students.
- Engineering Majors.
- Working Professionals.
- Anybody who learnt Discrete Math long time and want to refresh his/her knowledge.