What Math to learn for Cosmology?

[freeelectron]

Summary: Roadmap of most useful math to learn to better understand cosmology

I just watched ~20 hours of a serie of videos about cosmology, which stayed at a conceptual level for easier understanding (= minimal math).
I understood about 98% of it and now have a decent understanding of Special/General Relativity, Quantum Mechanics, the Standard Model and some more speculative stuff about Quantum Gravity.

This said, it was frustrating to be quite lost every time the guy was explaining even the most basic math behind it all.

Assuming I'm still quite comfortable with basic algebra (I also studied derivative, integral, etc in high school, but forgot most of it), I'm wondering what parts of math I should have a look at to get at least a better understanding of the math used in astrophyics.

My question is double:
- What would be a natural roadmap from here on (still focusing on astrophysics and cosmology), either in order of usefulness or in order of natural learning
- Any resources (books, videos,...) you recommend for this

Thanks

 

[Arman777]

- What would be a natural roadmap from here on (still focusing on astrophysics and cosmology), either in order of usefulness or in order of natural learning

- Any resources (books, videos,...) you recommend for this

For undergrad level cosmology you need to know calculus and some basic knowledge about differential equations. After learning the math part you can focus on the physics part of the cosmology. Most of the physics/Cosmology textbooks have modern physics / SR/ GR parts so I think the important thing is learning the math behind those things and understand the basic concepts about them.

First, you should start by reading Barbara Ryden- Introduction to Cosmology 2nd Edition. At the same time, you can watch the Leonard Susskind videos on youtube.

I just watched ~20 hours of a series of videos about cosmology, which stayed at a conceptual level for easier understanding (= minimal math).

I bet this was Leonard Susskind videos :p

After finishing Barbara Ryden you should start reading Matts Roos btw if you find the 3rd edition don't try to read it. Notations are kind of complex and he fixes that in 4th edition.

And when you finish Matts Roos then you can move to more advanced books.

I am not sure what to suggest about calculus textbooks but there are many online/books resources so I am sure you can find someone best fits for you.

 

[PeroK]

Summary: Roadmap of most useful math to learn to better understand cosmology

I just watched ~20 hours of a serie of videos about cosmology, which stayed at a conceptual level for easier understanding (= minimal math).
I understood about 98% of it and now have a decent understanding of Special/General Relativity, Quantum Mechanics, the Standard Model and some more speculative stuff about Quantum Gravity.

This said, it was frustrating to be quite lost every time the guy was explaining even the most basic math behind it all.

Your knowledge of these subjects after 20 hours of videos cannot be more than superficial. SR, GR, QM and the standard model of particle physics. All in 20 hours?

You're only kidding yourself.

Students spend years at university to understand the basics of these four subjects.

 

[phinds]

Your knowledge of these subjects after 20 hours of videos cannot be more than superficial. SR, GR, QM and the standard model of particle physics. All in 20 hours?

You're only kidding yourself.

Students spend years at university to understand the basics of these four subjects.

GR and QM in particular. You might get a fair amount of SR but not the rest in such a short amount of time.

 

[kimbyd]

To restate this another way, the reason why you're getting lost in the math is it takes a lot more than 20 hours to get your head around the math. And much of the math is pretty specific to the physics involved. The math basis is calculus, but the notations and ways this math is used in physics really requires lots of work and practice beyond that.

If you really want to get into this, it's going to take a lot of time. If you can work up a basic understanding of calculus, that will be enough to get started. Then you'd just have to slog through physics textbooks to really get a handle on the details. Lecture videos can help guide you, but if you really want understanding it's going to take time.

This is honestly why I chose physics as my major back in the day. I was unsure whether I wanted a computer science major or a physics major, but I'd been teaching myself computer programming for years before I entered college, and I knew I could keep doing that. I didn't think I could ever teach myself physics. So I picked physics, and I've never regretted that decision (even though my career is now in software). The material really is dense enough that it is really really hard to wrap your head around without years of instruction from experts.

 

[DEvens]

Get yourself the book _The First Three Minutes_ by Steven Weinberg.

https://www.amazon.com/dp/B001F0PYX2/?tag=pfamazon01-20

And keep in mind that this is probably the most superficial possible treatment of the barest beginnings of the subject. And it was originally published in 1977, and a lot has happened in cosmology since then.

But get it and treat it as the sign posts at the start of the rows in your garden.

You will see that just large swaths of math and physics contact cosmology. Nuclear physics, high energy physics, and theories of grand unification. Gravity generally and relativity in particular. Topology. Observational astronomy across the full spectrum from radio waves up. And several other things I've not remembered just now.

So that will mean you need calculus, calculus, and more calculus. Differential geometry and tensor algebra and the full machinery of things to do with manifolds. Differential equations aplenty. And some computer classes would not hurt, since some of those equations "shoot back" and require some computer assistance. Quantum mechanics up to quantum field theory.

 

[WWGD]

Ultimately, a good one-stop book for Math training is a good book on' Advanced Calculus'. It will cover a large swath of the 3 calcs, Linear Algebra, some Analysis,Topology, which will take you close to the Math you need and/or give you a good foundation for it. There are a few online ones that are free. It will save or at least cut down on the need of jumping around between books.

 

[DaveE]

calculus, calculus, and more calculus

Yes, an absolutely necessary start. Plus, you can't just study it, you need to really understand it.

 

[TaurusSteve]

For undergrad level cosmology you need to know calculus and some basic knowledge about differential equations. After learning the math part you can focus on the physics part of the cosmology. Most of the physics/Cosmology textbooks have modern physics / SR/ GR parts so I think the important thing is learning the math behind those things and understand the basic concepts about them.

First, you should start by reading Barbara Ryden- Introduction to Cosmology 2nd Edition. At the same time, you can watch the Leonard Susskind videos on youtube.
I bet this was Leonard Susskind videos :p

After finishing Barbara Ryden you should start reading Matts Roos btw if you find the 3rd edition don't try to read it. Notations are kind of complex and he fixes that in 4th edition.

And when you finish Matts Roos then you can move to more advanced books.

I am not sure what to suggest about calculus textbooks but there are many online/books resources so I am sure you can find someone best fits for you.

I've just started watching Leonard Susskin's videos, really great, interesting. I shall watch more when I have more time!

 

[Arman777]

I've just started watching Leonard Susskin's videos, really great, interesting. I shall watch more when I have more time!

That's cool.