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
-
X-Y plane
-
Cartesian coordinate system
-
X-Y plane
-
Complex plane
-
Polar coordinate system
-
Real plane & complex plane
-
Solved numerical problems
-
-
Groups
-
Categories
-
Groupoid
-
Monoid
-
Semi-Group
-
Group
-
Abelian Group
-
Some solved problems
-
SETS - Names of Sets
SETS - Types of Sets
SETS - Forms of Sets
-
16How many types of sets we have?
-
17Null OR Empty set
-
18Singleton set
-
19Finite set
-
20Infinite set
-
21Equal set
-
22Equivalent set
-
23Subset
-
24Proper subset
-
25Improper subset
-
26Power set
-
27Power set - Learn to derive all the subsets of a set with four elements
-
28Power set - Learn to derive all the subsets of a set with five elements
-
29Universal set
SETS - Some Problems' Solutions
SET OPERATIONS - Types of Set Operations
-
34Problem 1: Write all the given sets in set-builder forms
-
35Problem 2: Write all the given sets in Tabular forms
-
36Problem 3: Write all the given sets in Descriptive forms
-
37Problem 4: Identify the Finite and Infinite sets among all the give sets
-
38Problem 5: Identify the equal and equivalent sets out of the give sets
-
39Problem 6: Write the Proper and Improper subsets of the given sets
-
40Problem 7: Identify and write all the subsets for a power set of the given set
-
41Problem 8: Identify the True and False sets among the give sets
SET OPERATIONS - Properties of Set Operations
-
42Union of sets. What is Union of sets and its notation. Explain it with example
-
43Intersection of sets and its notation. Explain it with example
-
44Disjoint of sets. Explanation of a disjoint set with the relevant example
-
45Overlapping of sets. Explanation of an overlapping set with an example
-
46Difference of sets. What are its notations? Explained with the relevant example
-
47Complement of sets. What are the notations? Explained with the relevant example
SET OPERATIONS - De Morgan's Laws
-
48Property 1: Commutative of Union. Verify it mathematically that LHS = RHS
-
49Property 2: Commutative of Intersection. Verify it mathematically that LHS = RHS
-
50Property 3: Associative of Union. Verify it mathematically that LHS = RHS
-
51Property 4: Associative of Intersection. Verify it mathematically that LHS = RHS
-
52Property 5: Distributive of Union over Intersection. Verify it mathematically
-
53Property 6: Distributive of Intersection over Union. Verify it mathematically
SET OPERATIONS - Venn Diagrams
-
54What are De Morgan's laws? Show the two types of De Morgan's laws
-
55De Morgan's First law. Verify it mathematically and show that the LHS = RHS
-
56De Morgan's 2nd law. Verify it mathematically and show that the LHS = RHS
-
57Prove the De Morgan's First law with an example. Show that the LHS = RHS
-
58Prove the De Morgan's 2nd law with an example. Show that the LHS = RHS
SET OPERATIONS - Venn Diagrams - Problems Solutions
-
59What is Venn Diagram?
-
60Show the Venn Diagram for Union & Intersection of the subset of the sets[A⊂B]
-
61Show the Venn Diagram for Union & Intersection of the subset of the sets[B⊂A]
-
62Show the Venn Diagram for Union & Intersection of the Disjoint sets
-
63Show the Venn Diagram for Union & Intersection of the Overlapping sets
-
64Draw the Venn Diagrams for the Difference of the sets
-
65Show the Venn Diagram for the Complement of the sets
NUMBER SYSTEM - Real Numbers - Addition Laws
NUMBER SYSTEM - Real Numbers - Multiplication Laws
-
67Closure Law of Addition. Give an example and Verify it mathematically
-
68Commutative Law of Addition. Give an example and Verify it mathematically
-
69Associative Law of Addition. Give an example and Verify it mathematically
-
70Additive Identity Law of Addition. Give an example and Verify it mathematically
-
71Additive Inverse Law of Addition. Give an example and Verify it mathematically
NUMBER SYSTEM - Real Numbers - Properties of Inequality
-
72Closure Law of Multiplication. Give an example and Verify it mathematically
-
73Commutative Law of Multiplication. Give an example and Verify it mathematically
-
74Associative Law of Multiplication. Give an example and Verify it mathematically
-
75Multiplicative Identity Law. Give an example and Verify it mathematically
-
76Multiplicative Inverse Law. Give an example and Verify it mathematically
-
77Multiplication - Addition Laws. Give an example and prove it mathematically
NUMBER SYSTEM - Real Numbers - Properties of Equality
-
78Trichotomy Property. Prove it mathematically
-
79Trichotomy Product Property. Prove it mathematically
-
80Transitive Property. Prove it mathematically with the help of an example
-
81Additive Property. Prove it mathematically with the help of an example
-
82Multiplicative Property. Prove it mathematically with the help of an example