How to visualize quaternions, a 4d number system, in our 3d world

Euler's formula, e^{pi i} = -1, is one of the most famous expressions in math, but why on earth is this true? A few perspectives from the field of group theory can make this formula a bit more intuitive.

How to visualize quaternions, a 4d number system, in our 3d world

How to think about this 4d number system in our 3d space.

Euler's formula, e^{pi i} = -1, is one of the most famous expressions in math, but why on earth is this true? A few perspectives from the field of group theory can make this formula a bit more intuitive.

An algorithm for solving continuous 2d equations using winding numbers.

An algorithm for numerically solving certain 2d equations. Even though we described how winding numbers can be used to solve 2d equations at a high level, it's worth pointing out that there are a few details missing for if you wanted to...

What exactly is a topological space?

An algorithm for solving continuous 2d equations using winding numbers.

By the end of this learning object, the student will be able to: Use two ways to get the number of small cubes to put these cubes in the cuboid.4584

The student will be able to use the ratio and its properties to solve real life problems.3455

This video will give you a clear and concise overview of the different types of numbers you'll encounter in mathematics. We focus on the different types of numbers within the Real Number category, including natural, whole, integers,...

This video explains the purpose of neural networks.
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This clip is from the chapter "Artificial Neural Networks" of the series "Fundamentals in Neural Networks".This section explains artificial neural networks where you will...

This video explains logistic regression and specifically if the target here is discrete or binary.
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This clip is from the chapter "Artificial Neural Networks" of the series "Fundamentals in Neural Networks".This section...

This video explains statistical machine learning, where you will start with the linear regression model.
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This clip is from the chapter "Artificial Neural Networks" of the series "Fundamentals in Neural Networks".This section...

In this video, we will explore our data for Sigmoid Neuron.<br<br/>/>

This clip is from the chapter "Sigmoid Neuron" of the series "Deep Learning - Crash Course 2023".In this section, we will begin our journey with Sigmoid Neuron.

In this video, we will be introduced to Sigmoid Neuron.<br<br/>/>

This clip is from the chapter "Sigmoid Neuron" of the series "Deep Learning - Crash Course 2023".In this section, we will begin our journey with Sigmoid Neuron.

This video explores the intriguing world of equations, showcasing how they can lead to straightforward solutions or unexpected contradictions. Viewers are guided through solving equations with no solution, equations with one solution,...

This video will review how to interpret the different features of linear, quadratic, and exponential functions.

Use two ways to get the number of small cubes to put these cubes in the cuboid.

The ratio and its properties to solve real life problems.

This video discusses the limitations of using zeros to graph a quadratic function and introduces the concept of functions with no zeros or real roots. It explains that if a quadratic function has no real number values that make it equal...

In this lesson, students will learn how to multiply complex numbers that have just one term. The lesson covers the definition of "i" as the square root of negative 1, and the algebraic procedures for multiplying one-term expressions....

In this lesson, you will learn how to determine whether the solutions of a quadratic equation with no linear term are real or imaginary. By isolating the quadratic term and considering the square roots involved, you can determine if the...