An Interactive Journey Through Linear Algebra

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The team at Immersive Math is thrilled to unveil their debut publication: Immersive Linear Algebra, written by J.

"This represents the world's first linear algebra textbook featuring figures that are fully interactive."

📚 Publication Details

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🌐 Connect With Us

Want to stay updated? You can find more information and follow the project here:

• Twitter: Follow @immersivemath
• Facebook: Check out the Immersive Math page

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📖 Table of Contents

Below is the roadmap for the course. You can track your progress using the checklist:

• Preface: An introductory section providing context and a few words regarding the book's philosophy.
• Chapter 1: Introduction: A guide on how to navigate the interactive elements, a breakdown of the notation used, and a refresher on prerequisite mathematical concepts.
• Chapter 2: Vectors: An exploration of what a vector is, including the mechanics of vector addition and subtraction.
• Chapter 3: The Dot Product: A study of this essential operator that transforms two vectors into a single scalar: $\vec{a} \cdot \vec{b} = \|\vec{a}\| \|\vec{b}\| \cos(\theta)$
• Chapter 4: The Vector Product: Specifically for 3D environments, this tool allows you to derive a new vector from two existing ones.
• Chapter 5: Gaussian Elimination: A systematic methodology for finding solutions to systems of linear equations.
• Chapter 7: Determinants: An analysis of a core property inherent to square matrices.
• Chapter 9: Linear Mappings: Learning how to utilize and master the principles of linearity.
• Chapter 10: Eigenvalues and Eigenvectors: A chapter that—quite literally—has a value in itself.

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🛠️ Technical Implementation

The book utilizes dynamic figures to help students visualize complex transformations. For example, a figure might be rendered using a logic similar to this:

function renderVector(x, y) {
  const canvas = document.getElementById('mathCanvas');
  // Logic to draw an interactive arrow based on user input
  drawArrow(0, 0, x, y);
}

🗺️ Learning Path Logic