I'm a physics major and I typically dislike "pure" mathematics, but I'm loving this group theory stuff. Only problem is, I hate this book. It doesn't even discuss Lie groups, which are the foundations of field theories in physics.
Does /sci/ recommend any good, more advanced texts on group theory and/or other topics in math that are great for contemporary physics?
Lie Groups are more a topic of Differential Geometry than they are Algebra.
They are smooth manifolds which also have the structure of a group.
>>8043173
>I hate this book. It doesn't even discuss Lie groups.
Is this bait? I doubt there's a single introductory algebra book that discusses Lie groups. Not even Dummit and Foote does, IIRC, and that's as encyclopedic as you're going to get.
Pretty much everyone who's inexperienced enough to be reading Artin doesn't have enough background in manifolds to understand that.
That said, I think Knapp has written a book on them. I haven't read it but Knapp's algebra set is top-notch so it's probably worth looking at.
>>8043173
For basic algebra with a view towards category theory (which can be useful in some areas of theoretical physics - mostly toy models such as topological field theories) I would advise Aluffi's "Algebra chapter 0".
For Lie groups, take up e.g. Knapp's "Lie groups: beyond an introduction". You could also try with "Geometry, topology and physics" by Nakahara, where he introduces many notions from mathematics (such as Lie groups) needed in theoretical/mathematical physics. However, it is a bit less detailed.
just gonna use this thread to ask something similar.
i'm a physics major as well and have one more year of undergrad left, but still not confident with einstein summation convention and other notations found in tensor analysis. I want to be at a point where I understand the logic enough to fluidly write out my equations.
Are there any books that thoroughly discuss the logic alone or is this more something I'll develop with practice?
DAE hate Spivak's calculus text? It doesn't even discuss differentiable manifolds, which are the foundations of much of modern physics.
>>8043203
Repeated indicies which switch between covariant and contravariant are summed over.
That is all the logic there is to Einstein Summation.
>>8043173
>im loving this introductory text in algebra
>but I hate that it doesn't cover advanced topics
??????????????????????????????????
don't fucking read something more advanced until you've covered the basics
>>8043203
I have understood the summation convention learning differential geometry (which is of course the good framework for a good part of physics, and especially for gr). But if you don't want to go in depth into this subject, then practice will probably be enough.
>i'm a physics major as well and have one more year of undergrad left, but still not confident with einstein summation convention
wat, there is basically nothing to understand! (?)
It's a simple notation convention
>>8043194
D&F mentions them in passing at two spots. Pretty much this though, no introductory Algebra book is going to talk about Lie groups.
>>8043173
Something like this,
http://www.amazon.com/Principal-Bundles-Classical-Case-Universitext/dp/3319147641/
,is what you want for the use of group theory in physics.
>>8043210
>>8043214
I understand that, I just feel like when I apply it to given problems I don't make the immediate connections, and I take longer than I should to reach a more simplified expression using the convention. Same applies with the levi-civita symbol and so forth. I think I just need to practice more, because as you've said the logic alone is straightforward and simple.
>>8043203
This notes really helped me understand tensor notation, diff geometry and general relativity (they aren't a rigorous book on the subject, but they give a really good overall impression). They are in Spanish though.
http://www.ugr.es/~bjanssen/text/BertJanssen-RelatividadGeneral.pdf
If you just want the tensor algebra, go for chapter 4 (and block II), but it's a 100% recommendable lecture.
Yup should get manifolds under your belt and some differential geometry and differential topology, but after that I recommend Brian hall's book on lie groups, lie algebras, and their representations. It's a good intro book.
Knapp's text assumes an introduction to lie groups at least, and it's more encyclopedic. Get both and use Knapp as a reference.
Hall's focus on matrix lie groups will be more useful to you than a general treatment I imagine
>>8043227
just stick with it
I struggled too, but it is way more convenient in the long run
>>8043203
if youre into lecture series', check out the first few tensor calculus lectures on youtube from the channel maththebeautiful
theyre pretty basic but go into all tensor notation and the covariant derivative and laplacian which are the important things to know about for relativity
http://www.amazon.com/Group-Theory-Nutshell-Physicists-Zee/dp/0691162697
http://www.amazon.com/Symmetry-Standard-Model-Mathematics-Particle/dp/1441982663/
http://www.amazon.com/Introduction-Tensors-Group-Theory-Physicists/dp/3319147935/
