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:
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Sets
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Introduction
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Names
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Types
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Forms
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Numerical problems
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Set Operations
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Introduction
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Types
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Properties
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Laws of set operation
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De Morgan’s Laws
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De Morgan’s First Law
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De Morgan’s Second Law
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Relevant examples
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Venn Diagrams
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Venn diagrams for subset of sets
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Venn diagrams for disjoint of sets
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Venn diagrams for overlapping of sets
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Venn diagrams for complement of sets
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Venn diagrams for difference of sets.
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Some solved problems
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Binary Operations
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Introduction
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Properties
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Addition Laws with applications
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Multiplication Laws with applications
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Some solved problems
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Numerical System
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Real numbers
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Complex numbers
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Derivations & Verification
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Conjugate of complex numbers
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modulus of complex numbers
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Properties of equality & Inequality
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Addition Laws
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Multiplication Laws
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Solved Problems
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Coordinate System
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Cartesian coordinate system
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X-Y plane
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Cartesian coordinate system
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X-Y plane
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Complex plane
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Polar coordinate system
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Real plane & complex plane
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Solved numerical problems
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Groups
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Categories
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Groupoid
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Monoid
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Semi-Group
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Group
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Abelian Group
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Some solved problems
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2What is set? Introduction to a setVideo lesson
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3Natural NumbersVideo lesson
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4Whole NumbersVideo lesson
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5IntegersVideo lesson
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6Positive IntegersVideo lesson
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7Negative IntegersVideo lesson
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8Even NumbersVideo lesson
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9Odd NumbersVideo lesson
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10Even IntegersVideo lesson
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11Odd IntegersVideo lesson
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12Prime NumbersVideo lesson
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13Rational NumbersVideo lesson
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14Irrational NumbersVideo lesson
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15Real NumbersVideo lesson
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16How many types of sets we have?Video lesson
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17Null OR Empty setVideo lesson
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18Singleton setVideo lesson
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19Finite setVideo lesson
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20Infinite setVideo lesson
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21Equal setVideo lesson
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22Equivalent setVideo lesson
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23SubsetVideo lesson
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24Proper subsetVideo lesson
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25Improper subsetVideo lesson
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26Power setVideo lesson
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27Power set - Learn to derive all the subsets of a set with four elementsVideo lesson
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28Power set - Learn to derive all the subsets of a set with five elementsVideo lesson
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29Universal setVideo lesson
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34Problem 1: Write all the given sets in set-builder formsVideo lesson
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35Problem 2: Write all the given sets in Tabular formsVideo lesson
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36Problem 3: Write all the given sets in Descriptive formsVideo lesson
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37Problem 4: Identify the Finite and Infinite sets among all the give setsVideo lesson
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38Problem 5: Identify the equal and equivalent sets out of the give setsVideo lesson
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39Problem 6: Write the Proper and Improper subsets of the given setsVideo lesson
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40Problem 7: Identify and write all the subsets for a power set of the given setVideo lesson
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41Problem 8: Identify the True and False sets among the give setsVideo lesson
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42Union of sets. What is Union of sets and its notation. Explain it with exampleVideo lesson
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43Intersection of sets and its notation. Explain it with exampleVideo lesson
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44Disjoint of sets. Explanation of a disjoint set with the relevant exampleVideo lesson
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45Overlapping of sets. Explanation of an overlapping set with an exampleVideo lesson
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46Difference of sets. What are its notations? Explained with the relevant exampleVideo lesson
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47Complement of sets. What are the notations? Explained with the relevant exampleVideo lesson
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48Property 1: Commutative of Union. Verify it mathematically that LHS = RHSVideo lesson
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49Property 2: Commutative of Intersection. Verify it mathematically that LHS = RHSVideo lesson
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50Property 3: Associative of Union. Verify it mathematically that LHS = RHSVideo lesson
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51Property 4: Associative of Intersection. Verify it mathematically that LHS = RHSVideo lesson
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52Property 5: Distributive of Union over Intersection. Verify it mathematicallyVideo lesson
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53Property 6: Distributive of Intersection over Union. Verify it mathematicallyVideo lesson
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54What are De Morgan's laws? Show the two types of De Morgan's lawsVideo lesson
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55De Morgan's First law. Verify it mathematically and show that the LHS = RHSVideo lesson
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56De Morgan's 2nd law. Verify it mathematically and show that the LHS = RHSVideo lesson
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57Prove the De Morgan's First law with an example. Show that the LHS = RHSVideo lesson
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58Prove the De Morgan's 2nd law with an example. Show that the LHS = RHSVideo lesson
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59What is Venn Diagram?Video lesson
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60Show the Venn Diagram for Union & Intersection of the subset of the sets[A⊂B]Video lesson
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61Show the Venn Diagram for Union & Intersection of the subset of the sets[B⊂A]Video lesson
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62Show the Venn Diagram for Union & Intersection of the Disjoint setsVideo lesson
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63Show the Venn Diagram for Union & Intersection of the Overlapping setsVideo lesson
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64Draw the Venn Diagrams for the Difference of the setsVideo lesson
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65Show the Venn Diagram for the Complement of the setsVideo lesson
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67Closure Law of Addition. Give an example and Verify it mathematicallyVideo lesson
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68Commutative Law of Addition. Give an example and Verify it mathematicallyVideo lesson
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69Associative Law of Addition. Give an example and Verify it mathematicallyVideo lesson
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70Additive Identity Law of Addition. Give an example and Verify it mathematicallyVideo lesson
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71Additive Inverse Law of Addition. Give an example and Verify it mathematicallyVideo lesson
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72Closure Law of Multiplication. Give an example and Verify it mathematicallyVideo lesson
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73Commutative Law of Multiplication. Give an example and Verify it mathematicallyVideo lesson
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74Associative Law of Multiplication. Give an example and Verify it mathematicallyVideo lesson
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75Multiplicative Identity Law. Give an example and Verify it mathematicallyVideo lesson
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76Multiplicative Inverse Law. Give an example and Verify it mathematicallyVideo lesson
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77Multiplication - Addition Laws. Give an example and prove it mathematicallyVideo lesson
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78Trichotomy Property. Prove it mathematicallyVideo lesson
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79Trichotomy Product Property. Prove it mathematicallyVideo lesson
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80Transitive Property. Prove it mathematically with the help of an exampleVideo lesson
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81Additive Property. Prove it mathematically with the help of an exampleVideo lesson
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82Multiplicative Property. Prove it mathematically with the help of an exampleVideo lesson

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