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I'm basically looking for a combination of Hoffman Kunze and Artin, I think.

Such a book would ideally take a student who has already seen the basics of matrices and vectors, and the very basics of vector spaces, via Shrifin's Multivariable Mathematics for example, to the point where they could tackle first year graduate / advanced undergraduate courses in differential equations (dynamical systems) / differential geometry (topology).

Hoffman Kunze is close, but doesn't take the algebra far enough, they'd need for example isomorphism theorems for groups and rings. Artin omits dual spaces...

Any ideas?

William Haines
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  • Well I do not know. I would say that is does not really matter which book you take. Also when you describe your goal (differential equations, differential geometry) I would assume some other prerequisites then mainly linear algebra. Besides that Dummit and Foote Abstract Algebra has it all. It is one of my favorite books. It has 1000 pages, you will clearly find everything you need there. The question is, if you want that, as you will find much more and never finish the book... – Cornman Jun 25 '24 at 09:33
  • Other prerequisites of course exist, I'm just more familiar with the with analysis texts at this level. Was hoping to avoid Dummit and Foote for the reason you suggest, as well as its number theoretic bent, and general dryness of the voice. But yes the first three parts of that is an option. – William Haines Jun 25 '24 at 09:44
  • There are in numerous book recommendations for Linear Algebra and Abstract Algebra at this site, e.g., here. You should have a look at the different opinions and suggestions. – Dietrich Burde Jun 25 '24 at 09:54

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