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