- #1
timeevaporate
- 2
- 0
Hi All,
I posted this text below in another forum, but didn't get much feedback. I realize I might sound extremely ignorant, but I need directions. Thanks.
"Awhile ago I decided I wanted to learn Relativity comprehensively. I was told that I better brush up on my Differential Geometry if I wanted to delve deeper into Relativity. So I decide to find out what the prerequisites for Diff. Geo were. Some say, Calc 1-3 and Linear Algebra would suffice, others say I should take intro to Multilinear Algebra, whose prereqs are, apparently, Functional Analysis and Topology according to some; yet others claim I must know Linear Algebra and Abstract Algebra as a bridge to Multilinear Algebra and, further into, Diff. Geo. Then, I find out that Functional Analysis has its own prereq like Measure Theory. How do Real Analysis and Complex Analysis, Differential Equations fit into all this? Are there overarching/ more fundamental subjects that treat the above-mentioned subjects as their integral topics?
At this point I don't even care to know what EXACTLY I need for Diff Geo., because I'll, probably, be correctly told to ditch this and pick up that on the road to Diff. Geo, but now that I know these subjects exist I'd rather study them since I find the idea of them very interesting. And if it takes me forever to converge the knowledge of these subjects into a comprehensive intro into Relativity- so be it. I am not even worried about the result here, I want to enjoy the process since math/physics is a little hobby of mine and I am a late- commer to these subjects. I am not out to make a profession out of this, nor do I care to prove anything to anyone else. I feel just because I am a layman doesn't mean I have to limit myself to some very unsatisfying pop-science texts. So far, I am getting ready to teach myself Calc 3 and probably take an intro to Proofs.
That said, could somebody, please, weave these subjects and fit them with each other in a more logical and sequential way with, possibly, some missing subjects as prereqs and stepping stones for me?
By the way, a couple of very stupid questions- Is Analysis arranged in a manner Calculus is typically arranged? That is, Analysis 1, Analysis 2 etc? I mean Calc is self-contained, is Analysis also? If not, what would be the most important Analysis topics/ideas/concepts for people like me? Again, I am not scared of difficulties and I have my whole life to learn all this.
Thanks."
I posted this text below in another forum, but didn't get much feedback. I realize I might sound extremely ignorant, but I need directions. Thanks.
"Awhile ago I decided I wanted to learn Relativity comprehensively. I was told that I better brush up on my Differential Geometry if I wanted to delve deeper into Relativity. So I decide to find out what the prerequisites for Diff. Geo were. Some say, Calc 1-3 and Linear Algebra would suffice, others say I should take intro to Multilinear Algebra, whose prereqs are, apparently, Functional Analysis and Topology according to some; yet others claim I must know Linear Algebra and Abstract Algebra as a bridge to Multilinear Algebra and, further into, Diff. Geo. Then, I find out that Functional Analysis has its own prereq like Measure Theory. How do Real Analysis and Complex Analysis, Differential Equations fit into all this? Are there overarching/ more fundamental subjects that treat the above-mentioned subjects as their integral topics?
At this point I don't even care to know what EXACTLY I need for Diff Geo., because I'll, probably, be correctly told to ditch this and pick up that on the road to Diff. Geo, but now that I know these subjects exist I'd rather study them since I find the idea of them very interesting. And if it takes me forever to converge the knowledge of these subjects into a comprehensive intro into Relativity- so be it. I am not even worried about the result here, I want to enjoy the process since math/physics is a little hobby of mine and I am a late- commer to these subjects. I am not out to make a profession out of this, nor do I care to prove anything to anyone else. I feel just because I am a layman doesn't mean I have to limit myself to some very unsatisfying pop-science texts. So far, I am getting ready to teach myself Calc 3 and probably take an intro to Proofs.
That said, could somebody, please, weave these subjects and fit them with each other in a more logical and sequential way with, possibly, some missing subjects as prereqs and stepping stones for me?
By the way, a couple of very stupid questions- Is Analysis arranged in a manner Calculus is typically arranged? That is, Analysis 1, Analysis 2 etc? I mean Calc is self-contained, is Analysis also? If not, what would be the most important Analysis topics/ideas/concepts for people like me? Again, I am not scared of difficulties and I have my whole life to learn all this.
Thanks."