**QC051 Math Prerequisites for Quantum Computing**

English | MP4 | AVC 1280×720 | AAC 44KHz 2ch | 4h 12m | 367 MB

eLearning | Skill level: All Levels

Review basic math prerequisites for quantum computing and quantum physics

This is a refresher course in Mathematics for students who studied Math and Physics through 12th grade at high school but have now forgotten many of the details. In fewer than 4 hours, this course reviews the Math you will need to understand quantum computing concepts.

The focus is on getting you up-to-speed as quickly as possible. This covers only what you need to know: probability, statistics, Boolean logic, complex numbers, and linear algebra. You will not waste time on topics you do not need for quantum computing.

To get the most out of this course, you need to have already studied Math at a 12th-grade level in high school. This is merely a review course to help you refresh your memory. If you have not studied these topics in high school, then this 4-hour course is no substitute for 2 years of high school Math classes.

This course reviews basic high-school Math. It doesn’t go into any details about quantum physics or quantum computing.

Learn

- A Math foundation for learning about quantum computing: probability, statistics, Boolean logic, complex numbers, and linear algebra.

**+ Table of Contents**

**Boolean Algebra**

1 Introduction

2 Boolean Algebra

3 Boolean Variables & Operators

4 Truth Tables

5 Logic Gates

6 Logic Circuits

7 AND Gate

8 OR Gate

9 NOT Gate

10 Multiple Input Gates

11 Equivalent Circuits 1

12 Equivalent Circuits 2

13 Universal Gate – NAND

14 Exclusive-OR

15 XOR for Assignment

16 XOR of Bit Sequences 1

17 XOR of Bit Sequences 2

**Cryptography**

18 Introduction to Cryptography

19 Cryptography with XOR

20 Shared Secret

21 Importance of Randomness

22 Breaking the Code

**Probability**

23 Introduction to Probability

24 Probability of a Boolean Expression

25 Mutually Exclusive Events

26 Independent Events

27 Manipulating Probabilities with Algebra

28 P (Mutually Exclusive Events )

29 P (Independent Events )

30 Complete Set of Mutually Exclusive Events

31 P (A OR B )

32 Examples

33 Examples

34 P (Bit Values )

35 Analysis with Venn Diagrams

36 Venn Diagram P (A AND B )

37 Venn Diagram P (A OR B )

38 Venn Diagram P (NOT A )

39 Examples

40 Examples

41 Conditional Probability

42 Examples

**Statistics**

43 Introduction to Statistics

44 Random Variables

45 Mapping Random Variables

46 Mean, Average, Expected Value …

47 Example

48 Example

49 Beyond Mean

50 Standard Deviation

51 Examples

52 Combinations of Random Variables

53 Correlation

54 Analysis of Correlation

**Complex Numbers**

55 Introduction to Complex Numbers

56 Imaginary i

57 Addition

58 Subtraction

59 Multiplication by a Real

60 Division by a Real

61 Complex Multiplication

62 Examples

63 Complex Conjugates

64 Squared Magnitude

65 Complex Division

66 Examples

67 Euler’s Formula

68 Polar Form

69 Examples

70 Fractional Powers

71 Complex Cube Roots of 1

72 Square Root of i

73 D Coordinates

**Linear Algebra & Matrices**

74 Matrices

75 Matrix Dimensions

76 Matrix Addition

77 Subtraction

78 Scalar Multiplication

79 Matrix Multiplication

80 Examples

81 Examples

82 x3 Example

83 Exercises

84 More Multiplications

85 When is Multiplication Possible

86 Example

87 Not Commutative

88 Associative & Distributive

89 Dimension of Result

90 Odd Shaped Matrices

91 Examples

92 Outer Product

93 Exercise

94 Inner Product

95 Exercises

96 Identity Matrix

97 Matrix Inverse

98 Transpose

99 Transpose Examples

100 Transpose of Product

101 Complex Conjugate of Matrices

102 Adjoint

103 Unitary

104 Hermitian

105 Hermitian & Unitary

106 Why Hermitian or Unitary

107 Vectors & Transformations

108 Rotation in 2D

109 Special Directions

110 Eigen Vectors & Eigen Values

111 More Eigen Vectors

112 Conclusion

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