QC051 Math Prerequisites for Quantum Computing [Video]
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Boolean Algebra
 Introduction
 Boolean Algebra
 Boolean Variables & Operators
 Truth Tables
 Logic Gates
 Logic Circuits
 AND Gate
 OR Gate
 NOT Gate
 Multiple Input Gates
 Equivalent Circuits 1
 Equivalent Circuits 2
 Universal Gate: NAND
 ExclusiveOR
 XOR for Assignment
 XOR of Bit Sequences 1
 XOR of Bit Sequences 2

Cryptography
 Introduction to Cryptography
 Cryptography with XOR
 Shared Secret
 Importance of Randomness
 Breaking the Code

Probability
 Introduction to Probability
 Probability of a Boolean Expression
 Mutually Exclusive Events
 Independent Events
 Manipulating Probabilities with Algebra
 P (Mutually Exclusive Events )
 P (Independent Events )
 Complete Set of Mutually Exclusive Events
 P (A OR B )
 Examples
 Examples
 P (Bit Values )
 Analysis with Venn Diagrams
 Venn Diagram P (A AND B )
 Venn Diagram P (A OR B )
 Venn Diagram P (NOT A )
 Examples
 Examples
 Conditional Probability
 Examples

Statistics
 Introduction to Statistics
 Random Variables
 Mapping Random Variables
 Mean, Average, Expected Value ...
 Example
 Example
 Beyond Mean
 Standard Deviation
 Examples
 Combinations of Random Variables
 Correlation
 Analysis of Correlation

Complex Numbers
 Introduction to Complex Numbers
 Imaginary i
 Addition
 Subtraction
 Multiplication by a Real
 Division by a Real
 Complex Multiplication
 Examples
 Complex Conjugates
 Squared Magnitude
 Complex Division
 Examples
 Euler's Formula
 Polar Form
 Examples
 Fractional Powers
 Complex Cube Roots of 1
 Square Root of i
 2D Coordinates

Linear Algebra & Matrices
 Matrices
 Matrix Dimensions
 Matrix Addition
 Subtraction
 Scalar Multiplication
 Matrix Multiplication
 Examples
 Examples
 3x3 Example
 Exercises
 More Multiplications
 When is Multiplication Possible?
 Example
 Not Commutative
 Associative & Distributive
 Dimension of Result
 Odd Shaped Matrices
 Examples
 Outer Product
 Exercise
 Inner Product
 Exercises
 Identity Matrix
 Matrix Inverse
 Transpose
 Transpose Examples
 Transpose of Product
 Complex Conjugate of Matrices
 Adjoint
 Unitary
 Hermitian
 Hermitian & Unitary
 Why Hermitian or Unitary?
 Vectors & Transformations
 Rotation in 2D
 Special Directions
 Eigen Vectors & Eigen Values
 More Eigen Vectors
 Conclusion