How can I teach myself advanced mathematics concepts like differential equations and topology without a strong background in algebra and geometry?

I totally understand where you're coming from - I've been there too. The thing is, you don't necessarily need a strong background in algebra and geometry to start learning about differential equations and topology. However, it's true that these subjects do build upon each other, so it's essential to fill in the gaps first. I'd recommend starting with a solid review of algebra and geometry to refresh your memory. Khan Academy is a great resource for this, but you might want to supplement it with other materials, like textbooks or online courses.

For algebra, I'd suggest starting with a textbook like Michael Artin's 'Algebra' or a online course on MIT OpenCourseWare. These resources will give you a comprehensive review of the basics and help you build a strong foundation. As for geometry, you can try Khan Academy's geometry course or MIT's 'Geometry: Points, Lines, and Planes' lecture notes. Once you feel more comfortable with these subjects, you can move on to more advanced topics like differential equations and topology.

For differential equations and topology, I'd recommend checking out 3Blue1Brown's YouTube channel and Khan Academy's differential equations course. Both resources are excellent for visualizing and understanding these complex concepts. Additionally, you can try online courses like Stanford University's 'Differential Equations' or 'Topology' on Coursera. These courses will give you a more structured learning experience and help you apply the concepts to real-world problems.

Lastly, I want to emphasize the importance of practice and patience. Learning advanced math concepts takes time and effort, so don't get discouraged if you struggle at first. Keep practicing, and you'll eventually see progress. Good luck, and have fun exploring the world of mathematics!