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QC051 : Math Prerequisites for Quantum Computing
Boolean Algebra
Introduction (4:18)
Boolean Algebra (4:43)
Boolean Variables and Operators (7:09)
Truth Tables (3:17)
Logic Gates (1:22)
Logic Circuits (0:52)
AND (0:58)
OR (0:51)
NOT (1:03)
Multiple Input Gates (1:35)
Equivalent Circuits 1 (1:59)
Equivalent Circuits 2 (0:59)
Universal Gate : NAND (2:56)
Exclusive-OR (2:17)
XOR for Assignment (2:03)
XOR of Bit Sequences 1 (2:40)
XOR of Bit Sequences 2 (4:21)
Cryptography
Introduction to Cryptography (1:50)
Cryptography with XOR (2:34)
Shared Secret (2:35)
Importance of Randomness (1:25)
Breaking the Code (5:34)
Probability
Introduction to Probability (5:08)
Probability of a Boolean Expression (1:42)
Mutually Exclusive Events (3:01)
Independent Events (1:16)
Manipulating Probabilities with Algebra (2:24)
P ( Mutually Exclusive Events ) (0:53)
P ( Independent Events ) (1:17)
Complete Set of Mutually Exclusive Events (2:00)
P ( A OR B ) (1:35)
Examples (0:51)
Examples (7:53)
P ( Bit Values ) (3:56)
Analysis with Venn Diagrams (1:27)
Venn Diagram P ( A AND B ) (0:53)
Venn Diagram P ( A OR B ) (1:09)
Venn Diagram P ( NOT A ) (0:34)
Examples (2:42)
Examples (2:35)
Conditional Probability (2:06)
Examples (1:28)
Statistics
Introduction to Statistics (1:21)
Random Variables (1:33)
Mapping Random Variables (4:20)
Mean, Average, Expected Value ... (1:49)
Example (2:23)
Example (1:37)
Beyond Mean (1:46)
Standard Deviation (3:50)
Examples (4:15)
Combinations of Random Variables (2:53)
Correlation (2:36)
Analysis of Correlation (6:19)
Complex Numbers
Introduction to Complex Numbers (5:07)
Imaginary i (4:55)
Addition (1:54)
Subtraction (1:08)
Multiplication by a Real (0:55)
Division by a Real (0:41)
Complex Multiplication (2:30)
Examples (1:26)
Complex Conjugates (1:37)
Squared Magnitude (2:12)
Complex Division (3:01)
Examples (1:12)
Euler's Formula (2:15)
Polar Form (2:44)
Examples (2:43)
Fractional Powers (3:24)
Complex Cube Roots of 1 (1:30)
Square Root of i (1:29)
2D Coordinates (3:00)
Linear Algebra & Matrices
Matrices (1:36)
Matrix Dimensions (2:13)
Matrix Addition (1:42)
Matrix Subtraction (1:12)
Scalar Multiplication (1:12)
Matrix Multiplication (7:40)
Examples (0:59)
Examples (0:41)
3x3 Example (0:59)
Exercises (0:33)
More Multiplications (0:57)
When is Multiplication Possible ? (2:06)
Example (1:23)
Not Commutative (1:52)
Associative & Distributive (1:25)
Dimension of Result (2:22)
Odd Shaped Matrices (1:03)
Examples (1:01)
Outer Product (1:46)
Exercises (0:21)
Inner Product (1:43)
Exercises (0:41)
Identity Matrix (2:15)
Matrix Inverse (2:46)
Transpose (1:21)
Transpose Examples (1:00)
Transpose of Product (1:16)
Complex Conjugate of Matrices (1:19)
Adjoint (1:07)
Unitary (1:45)
Hermitian (1:08)
Hermitian & Unitary (1:37)
Why Hermitian or Unitary ? (0:57)
Vectors & Transformations (4:50)
Rotation in 2D (1:51)
Special Directions (3:59)
Eigen Vectors & Eigen Values (4:35)
More Eigen Vectors (2:58)
Conclusion (0:51)
XOR of Bit Sequences 1
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