MHB Looking for an online Algebra resource

[topsquark]

As per another thread I have mentioned that I am looking for information on Lie groups (and related Algebras). My personal library has come up dry in my Math texts, and the Physics texts where this comes up are so brief in their Mathematics that I can't really glean any useful (new) information from them.

The other thread suggested I look up Algebraic Topology. I have no extra funds to purchase a new text right now and online resources such as Wikipedia are basically useless to me at this point.

I'm not going to hope for an actual online text, but does anyone know of any kind of resource I might be able to find online? Something to get me started anyway.

Thanks!
-Dan

 

[Euge]

As per another thread I have mentioned that I am looking for information on Lie groups (and related Algebras). My personal library has come up dry in my Math texts, and the Physics texts where this comes up are so brief in their Mathematics that I can't really glean any useful (new) information from them.

The other thread suggested I look up Algebraic Topology. I have no extra funds to purchase a new text right now and online resources such as Wikipedia are basically useless to me at this point.

I'm not going to hope for an actual online text, but does anyone know of any kind of resource I might be able to find online? Something to get me started anyway.

Thanks!
-Dan

Hi Dan,

Here are some links that may refer to for algebraic topology:

1. Course 421 - Algebraic Topology

2. Algebraic Topology Book

3. http://math.ucr.edu/home/baez/algebraic_topology/

Here are ones for Lie groups/Lie algebras:

1. http://www.math.uiuc.edu/~lerman/519/s12/427notes.pdf

2. Lecture Notes | Introduction to Lie Groups | Mathematics | MIT OpenCourseWareThese links all contain online texts that I recommend. I suggest starting with 1. from each topic, and using the other numbers as supplements.

 

[topsquark]

Hi Dan,

Here are some links that may refer to for algebraic topology:

1. Course 421 - Algebraic Topology

2. Algebraic Topology Book

3. Algebraic Topology

Here are ones for Lie groups/Lie algebras:

1. http://www.math.uiuc.edu/~lerman/519/s12/427notes.pdf

2. Lecture Notes | Introduction to Lie Groups | Mathematics | MIT OpenCourseWareThese links all contain online texts that I recommend. I suggest starting with 1. from each topic, and using the other numbers as supplements.

Oh yeah! That'll do me good. Thank you for the links. (I always like multiple sources!)

-Dan

 

[Euge]

Oh yeah! That'll do me good. Thank you for the links. (I always like multiple sources!)

-Dan

I usually give multiple sources since it helps to have different perspectives or ways of understanding concepts. Before you posted this question I was thinking of how I can help you out more with the suggestions I gave you in that other thread. I might add some more comments there if you want extra assistance.

 

[topsquark]

I usually give multiple sources since it helps to have different perspectives or ways of understanding concepts. Before you posted this question I was thinking of how I can help you out more with the suggestions I gave you in that other thread. I might add some more comments there if you want extra assistance.

Please feel free to post, but give me a little while to sink my teeth into it. That's a lot of information to process and even though I'm going to skim it first (to find out just what I need to focus on) it's going to be a couple of weeks, probably, before I can master enough to ask intelligent questions.

-Dan

 

[Euge]

Please feel free to post, but give me a little while to sink my teeth into it. That's a lot of information to process and even though I'm going to skim it first (to find out just what I need to focus on) it's going to be a couple of weeks, probably, before I can master enough to ask intelligent questions.

-Dan

Yes, of course, but if you don't mind me asking, what level of algebra have you studied? Have you done any graduate algebra?

 

[topsquark]

Yes, of course, but if you don't mind me asking, what level of algebra have you studied? Have you done any graduate algebra?

Nothing formal. I have an undergrad text that I've usually been referencing if I need more detail for a Physics question, and I have a 1st year level grad text which pretty much covers the same material but in far more detail. In a general sense I pretty much get the concepts behind rings and can at least follow the development of Algebra from there. But not in much detail. Until now I have not really needed anything formal. In fact most of my Algebra comes from my Physics texts and focuses on Lie Algebras (though they don't call it that.) Needless to say that this doesn't really cover much in terms of the basics.

My current plan is to work on multiple levels. I have a rough idea of what I need to learn for my String Theory text. This pretty much focuses on Lie groups and Lie Algebras, but obviously I need more grounding in the basics of Algebra in general. I am going to peruse the Lie group information you gave me. Then after I have pinpointed my Algebraic deficiencies there I'll head back to the basic Algebra texts that I have. When I am feeling comfortable with this material I'll head to the Algebraic Topology. I may need a more advanced Topology text than the one I currently have.

It's going to take a while to do properly. But I've been studying some 15 years on my own to cover what I need to know to understand String theory already, so a couple more years won't do me any harm.

-Dan