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Kumaresan Ramanathan

Purchase this course if you want only the math lessons without the rest of QC101.

The contents of this course have been added to the section on Math Foundation in QC101.

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.

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Purchase this course if you want only the math lessons without the rest of QC101.

The contents of this course have been added to the section on Math Foundation in QC101.

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.

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What's inside

Learning objective

Math prerequisites for quantum computing and quantum physics

Syllabus

Boolean Algebra
AND Gate
Introduction
Boolean Variables & Operators
Read more
Reviewing Your Experience
Truth Tables
Logic Gates
Logic Circuits
OR Gate
NOT Gate
Multiple Input Gates
Equivalent Circuits 1
Equivalent Circuits 2
Universal Gate: NAND
Exclusive-OR
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 )
P( Bit Values )
Analysis with Venn Diagrams
Venn Diagram P( A AND B )
Venn Diagram P( A OR B )
Venn Diagram P( NOT A )
Conditional Probability
Statistics
Introduction to Statistics
Random Variables
Mapping Random Variables
Mean, Average, Expected Value ...
Example
Beyond Mean
Standard Deviation
Examples
Combinations of Random Variables
Correlation
Analysis of Correlation
Test to Determine if Real-World Random Variables are Correlated
Complex Numbers
Introduction to Complex Numbers
Imaginary i
Addition
Subtraction
Multiplication by a Real
Division by a Real
Complex Multiplication
Complex Conjugates
Squared Magnitude
Complex Division
Euler's Formula
Polar Form
Fractional Powers
Complex Cube Roots of 1
Square Root of i
2D Coordinates
Linear Algebra & Matrices
Matrices
Matrix Dimensions
Matrix Addition
Scalar Multiplication
Matrix Multiplication
3x3 Example
Exercises
More Multiplications
When is Multiplication Possible?
Not Commutative
Associative & Distributive
Dimension of Result
Odd Shaped Matrices
Outer Product

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Provides an in-depth treatment of Boolean functions and equations, including topics such as satisfiability, optimization, and counting. It is suitable for researchers and advanced students in computer science and mathematics.
Provides a comprehensive and rigorous treatment of Boolean algebras, including both the algebraic and order-theoretic aspects. It is suitable for researchers and advanced students in mathematics.
Provides a clear and concise introduction to Boolean algebras, suitable for students and professionals with a basic understanding of mathematics. It covers the basic concepts, operations, and applications of Boolean algebra.
Provides an introduction to Boolean algebra in Spanish. It is suitable for students and professionals in mathematics and computer science.
Provides an introduction to Boolean algebra in Portuguese. It is suitable for students and professionals in mathematics and computer science.
Provides a comprehensive introduction to probability theory, covering both the theoretical foundations and practical applications. It is well-suited for students with a strong mathematical background who want to learn the fundamentals of probability.
Is designed for students in engineering and science who need a strong foundation in probability and statistics. It covers a wide range of topics, including probability distributions, statistical inference, and regression analysis.
Provides an introduction to stochastic processes, which are random processes that evolve over time. It is suitable for advanced undergraduate students and graduate students who have a strong mathematical background.
Provides an introduction to Bayesian data analysis, which statistical approach that uses probability to represent uncertainty. It is suitable for advanced undergraduate students and graduate students who have a strong mathematical background.
Provides an introduction to machine learning from a probabilistic perspective. It covers a wide range of topics, including supervised learning, unsupervised learning, and reinforcement learning.
Provides an introduction to information theory, which branch of mathematics that deals with the measurement and transmission of information. It is suitable for advanced undergraduate students and graduate students who have a strong mathematical background.
Provides an introduction to probability theory and random processes for electrical engineering students. It covers a wide range of topics, including probability distributions, statistical inference, and random signals.
Provides an introduction to stochastic processes for computer science students. It covers a wide range of topics, including Markov chains, queuing theory, and random walks.
Provides a comprehensive overview of basic statistical concepts, including data collection, analysis, and interpretation. It is written in a clear and concise style, making it accessible to readers of all levels.
Comprehensive introduction to statistics, covering topics such as data collection, analysis, and interpretation. It is well-written and provides plenty of examples and exercises.
Concise introduction to statistical inference, covering topics such as point estimation, hypothesis testing, and confidence intervals. It good choice for students who want to learn the basics of statistical inference.
Comprehensive introduction to Bayesian data analysis, covering topics such as Bayesian probability, Bayesian inference, and Bayesian modeling. It good choice for students who want to learn the basics of Bayesian statistics.
Comprehensive introduction to machine learning, covering topics such as supervised learning, unsupervised learning, and reinforcement learning. It good choice for students who want to learn the basics of machine learning.
Provides a comprehensive overview of Boolean algebra, covering both the theoretical foundations and practical applications. It is suitable for students and professionals in computer science, mathematics, and engineering.

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