Step-by-step notes from sophomore DiffEqs to postgrad physics

[aalaniz]

I have 4/5 of step-by-step notes starting with a generalization of sophomore differential equations via Lie symmetries all the way to advanced physics. Differential equations, abstract algebra, topology are presented to physics and math majors alike as very disjointed subjects. Nothing is further from the truth. Math should not be mysterious. This is the job of nature.

Expect typos (1st draft), but all big ideas present, step-by-step.

I appreciate any readers comments/suggestions/fixes/etc.

There are three PDFs in my blog under aalaniz. They should also be attached here.

Thank you!

Alex

 

[TonyG]

Dear Alex,

Thank you for sharing your notes and ideas on the connections between differential equations, abstract algebra, topology, and physics. As a fellow scientist, I completely agree with your statement that math should not be mysterious, and that it is our job as scientists to uncover the mysteries of nature.

I have taken a look at the three PDFs on your blog and I must say, I am impressed by the level of detail and step-by-step approach in your notes. It is clear that you have put a lot of thought and effort into connecting these seemingly disjointed subjects and showing their relevance to physics.

One suggestion I have is to provide more concrete examples or applications of these concepts in physics. This will not only help in understanding the material better, but also make it more relatable for readers who may not have a strong background in math.

Additionally, I think it would be helpful to provide some background information on Lie symmetries and their significance in differential equations. This will provide a better foundation for readers to understand your generalization of sophomore differential equations.

Overall, I think your approach in bridging these subjects together is valuable and can greatly benefit students and researchers in the field. I look forward to seeing how your ideas develop and how they can contribute to our understanding of nature.