Where to learn differential geometry online?

In summary, differential geometry is a branch of mathematics that uses techniques from calculus and linear algebra to study the properties of geometric objects. Learning it online offers flexibility and convenience, and reputable courses can be found on platforms like Coursera and edX. Prerequisites include a strong foundation in calculus, linear algebra, and geometry, and it has real-world applications in fields such as physics and engineering.
  • #1
Superposed_Cat
388
5
Hi all, I was wondering where I could learn differential geometry online. Preferably via videos. If anyone could post any links to free sites it would be much appreciated. Thanks in advance.
 
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  • #2
Looking at your posts, you should probably hold off on differential geometry and finish learning linear algebra and calculus properly.
 

1. What is differential geometry?

Differential geometry is a branch of mathematics that studies the properties of curves, surfaces, and other geometric objects using techniques from calculus and linear algebra. It is used to describe and analyze the curvature and shape of objects in multi-dimensional space.

2. Why should I learn differential geometry online?

Learning differential geometry online allows for flexibility and convenience. You can access materials and lectures at any time, and often at a lower cost than traditional in-person classes. It also allows for self-paced learning, which can be beneficial for those with busy schedules.

3. Where can I find reputable online courses for learning differential geometry?

There are many reputable online platforms that offer courses in differential geometry, such as Coursera, edX, and Khan Academy. You can also check with universities or colleges that offer online courses in mathematics.

4. What are some prerequisites for learning differential geometry?

A strong foundation in calculus, linear algebra, and geometry is necessary for understanding differential geometry. Familiarity with vector calculus and partial derivatives is also helpful.

5. How can I apply differential geometry in real-world contexts?

Differential geometry has various applications in fields such as physics, engineering, computer graphics, and economics. It is used to model and analyze real-world phenomena such as the motion of objects, the shape of surfaces, and the behavior of systems in space.

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