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 high school, but have now forgotten many of the details. In less than 4 hours I review the Math you will need to understand quantum computing concepts.

The focus is on getting you up to speed as quickly as possible. I cover 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 cannot 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**. Those topics will be discussed in subsequent courses of this series.

1

Introduction

2

Boolean Algebra

3

Boolean Variables & Operators

4

Reviewing Your Experience

5

Truth Tables

6

Logic Gates

7

Logic Circuits

8

AND Gate

9

OR Gate

10

NOT Gate

11

Multiple Input Gates

12

Equivalent Circuits 1

13

Equivalent Circuits 2

14

Universal Gate: NAND

15

Exclusive-OR

16

XOR for Assignment

17

XOR of Bit Sequences 1

18

XOR of Bit Sequences 2

1

Introduction to Cryptography

2

Cryptography with XOR

3

Shared Secret

4

Importance of Randomness

5

Breaking the Code

1

Introduction to Probability

2

Probability of a Boolean Expression

3

Mutually Exclusive Events

4

Independent Events

5

Manipulating Probabilities with Algebra

6

P( Mutually Exclusive Events )

7

P( Independent Events )

8

Complete Set of Mutually Exclusive Events

9

P( A OR B )

10

Examples

11

Examples

12

P( Bit Values )

13

Analysis with Venn Diagrams

14

Venn Diagram P( A AND B )

15

Venn Diagram P( A OR B )

16

Venn Diagram P( NOT A )

17

Examples

18

Examples

19

Conditional Probability

20

Examples

1

Introduction to Statistics

2

Random Variables

3

Mapping Random Variables

4

Mean, Average, Expected Value ...

5

Example

6

Example

7

Beyond Mean

8

Standard Deviation

9

Examples

10

Combinations of Random Variables

11

Correlation

12

Analysis of Correlation

13

Test to Determine if Real-World Random Variables are Correlated

1

Introduction to Complex Numbers

2

Imaginary i

3

Addition

4

Subtraction

5

Multiplication by a Real

6

Division by a Real

7

Complex Multiplication

8

Examples

9

Complex Conjugates

10

Squared Magnitude

11

Complex Division

12

Examples

13

Euler's Formula

14

Polar Form

15

Examples

16

Fractional Powers

17

Complex Cube Roots of 1

18

Square Root of i

19

2D Coordinates

1

Matrices

2

Matrix Dimensions

3

Matrix Addition

4

Subtraction

5

Scalar Multiplication

6

Matrix Multiplication

7

Examples

8

Examples

9

3x3 Example

10

Exercises

11

More Multiplications

12

When is Multiplication Possible?

13

Example

14

Not Commutative

15

Associative & Distributive

16

Dimension of Result

17

Odd Shaped Matrices

18

Examples

19

Outer Product

You can view and review the lecture materials indefinitely, like an on-demand channel.

Definitely! If you have an internet connection, courses on Udemy are available on any device at any time. If you don't have an internet connection, some instructors also let their students download course lectures. That's up to the instructor though, so make sure you get on their good side!

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