Fundamentals of Mathematics
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Learn the Fundamental of Mathematics through animation. This course includes videos explanation starting right from introduction and basics, then takes graphical and numerical phase with formulas, verification and proofs. At the end it carries plenty of solved numerical problems with the relevant examples. The lectures’ videos are appealing, attractive, fancy (with some nice graphic designing), fast and take less time to walk you through the whole lecture. It’s a prefect choice for students who feel boredom watching long lectures and wants things to finish them quickly with the maximum knowledge gain. So join me here and do it in a quick and easy way. This course covers the below list of topics:

Sets

Introduction

Names

Types

Forms

Numerical problems


Set Operations

Introduction

Types

Properties

Laws of set operation


De Morgan’s Laws

De Morgan’s First Law

De Morgan’s Second Law

Relevant examples


Venn Diagrams

Venn diagrams for subset of sets

Venn diagrams for disjoint of sets

Venn diagrams for overlapping of sets

Venn diagrams for complement of sets

Venn diagrams for difference of sets.

Some solved problems


Binary Operations

Introduction

Properties

Addition Laws with applications

Multiplication Laws with applications

Some solved problems


Numerical System

Real numbers

Complex numbers

Derivations & Verification

Conjugate of complex numbers

modulus of complex numbers

Properties of equality & Inequality

Addition Laws

Multiplication Laws

Solved Problems


Coordinate System

Cartesian coordinate system

XY plane

Cartesian coordinate system

XY plane

Complex plane

Polar coordinate system

Real plane & complex plane

Solved numerical problems


Groups

Categories

Groupoid

Monoid

SemiGroup

Group

Abelian Group

Some solved problems


2What is set? Introduction to a setVideo lesson

3Natural NumbersVideo lesson

4Whole NumbersVideo lesson

5IntegersVideo lesson

6Positive IntegersVideo lesson

7Negative IntegersVideo lesson

8Even NumbersVideo lesson

9Odd NumbersVideo lesson

10Even IntegersVideo lesson

11Odd IntegersVideo lesson

12Prime NumbersVideo lesson

13Rational NumbersVideo lesson

14Irrational NumbersVideo lesson

15Real NumbersVideo lesson

16How many types of sets we have?Video lesson

17Null OR Empty setVideo lesson

18Singleton setVideo lesson

19Finite setVideo lesson

20Infinite setVideo lesson

21Equal setVideo lesson

22Equivalent setVideo lesson

23SubsetVideo lesson

24Proper subsetVideo lesson

25Improper subsetVideo lesson

26Power setVideo lesson

27Power set  Learn to derive all the subsets of a set with four elementsVideo lesson

28Power set  Learn to derive all the subsets of a set with five elementsVideo lesson

29Universal setVideo lesson

34Problem 1: Write all the given sets in setbuilder formsVideo lesson

35Problem 2: Write all the given sets in Tabular formsVideo lesson

36Problem 3: Write all the given sets in Descriptive formsVideo lesson

37Problem 4: Identify the Finite and Infinite sets among all the give setsVideo lesson

38Problem 5: Identify the equal and equivalent sets out of the give setsVideo lesson

39Problem 6: Write the Proper and Improper subsets of the given setsVideo lesson

40Problem 7: Identify and write all the subsets for a power set of the given setVideo lesson

41Problem 8: Identify the True and False sets among the give setsVideo lesson

42Union of sets. What is Union of sets and its notation. Explain it with exampleVideo lesson

43Intersection of sets and its notation. Explain it with exampleVideo lesson

44Disjoint of sets. Explanation of a disjoint set with the relevant exampleVideo lesson

45Overlapping of sets. Explanation of an overlapping set with an exampleVideo lesson

46Difference of sets. What are its notations? Explained with the relevant exampleVideo lesson

47Complement of sets. What are the notations? Explained with the relevant exampleVideo lesson

48Property 1: Commutative of Union. Verify it mathematically that LHS = RHSVideo lesson

49Property 2: Commutative of Intersection. Verify it mathematically that LHS = RHSVideo lesson

50Property 3: Associative of Union. Verify it mathematically that LHS = RHSVideo lesson

51Property 4: Associative of Intersection. Verify it mathematically that LHS = RHSVideo lesson

52Property 5: Distributive of Union over Intersection. Verify it mathematicallyVideo lesson

53Property 6: Distributive of Intersection over Union. Verify it mathematicallyVideo lesson

54What are De Morgan's laws? Show the two types of De Morgan's lawsVideo lesson

55De Morgan's First law. Verify it mathematically and show that the LHS = RHSVideo lesson

56De Morgan's 2nd law. Verify it mathematically and show that the LHS = RHSVideo lesson

57Prove the De Morgan's First law with an example. Show that the LHS = RHSVideo lesson

58Prove the De Morgan's 2nd law with an example. Show that the LHS = RHSVideo lesson

59What is Venn Diagram?Video lesson

60Show the Venn Diagram for Union & Intersection of the subset of the sets[A⊂B]Video lesson

61Show the Venn Diagram for Union & Intersection of the subset of the sets[B⊂A]Video lesson

62Show the Venn Diagram for Union & Intersection of the Disjoint setsVideo lesson

63Show the Venn Diagram for Union & Intersection of the Overlapping setsVideo lesson

64Draw the Venn Diagrams for the Difference of the setsVideo lesson

65Show the Venn Diagram for the Complement of the setsVideo lesson

67Closure Law of Addition. Give an example and Verify it mathematicallyVideo lesson

68Commutative Law of Addition. Give an example and Verify it mathematicallyVideo lesson

69Associative Law of Addition. Give an example and Verify it mathematicallyVideo lesson

70Additive Identity Law of Addition. Give an example and Verify it mathematicallyVideo lesson

71Additive Inverse Law of Addition. Give an example and Verify it mathematicallyVideo lesson

72Closure Law of Multiplication. Give an example and Verify it mathematicallyVideo lesson

73Commutative Law of Multiplication. Give an example and Verify it mathematicallyVideo lesson

74Associative Law of Multiplication. Give an example and Verify it mathematicallyVideo lesson

75Multiplicative Identity Law. Give an example and Verify it mathematicallyVideo lesson

76Multiplicative Inverse Law. Give an example and Verify it mathematicallyVideo lesson

77Multiplication  Addition Laws. Give an example and prove it mathematicallyVideo lesson

78Trichotomy Property. Prove it mathematicallyVideo lesson

79Trichotomy Product Property. Prove it mathematicallyVideo lesson

80Transitive Property. Prove it mathematically with the help of an exampleVideo lesson

81Additive Property. Prove it mathematically with the help of an exampleVideo lesson

82Multiplicative Property. Prove it mathematically with the help of an exampleVideo lesson
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