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Introduction to Differential Geometry

Chapter 1
In this chapter, we will introduce the fundamental concepts of differential geometry and how they relate to the world around us.

Goals

  • Understand the basic concepts of differential geometry

  • Learn how to visualize geometric objects

  • Understand how differential geometry is used in machine learning

Key Concepts

  • Manifolds

  • Curvature

  • Geodesics

What is Differential Geometry?

In this section, we will explore what differential geometry is and why it's important. We will also introduce the concept of a manifold and how it can be used to describe the world around us.

Visualizing Geometric Objects

In this section, we will learn how to visualize geometric objects using Python. We will also introduce the concept of curvature and how it can be used to describe the shape of objects.

Differential Geometry in Machine Learning

In this section, we will explore how differential geometry is used in machine learning. We will introduce the concept of a geodesic and how it can be used to find the shortest path between two points on a manifold.