I need help with Javier's historical...

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I need help with Javier's historical route to algebraic geometry 2016-02-07 20:50:10 Post No. 7841439

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I need help with Javier's historical route to algebraic geometry 2016-02-07 20:50:10 Post No. 7841439

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I need help with Javier's historical route to algebraic geometry
Anonymous
2016-02-07 20:50:10
Post No. 7841439
[Report]

https://math.stackexchange.com/questions/285201/path-to-basics-in-algebraic-geometry-from-hs-algebra-and-calculus

OK, so I have started my path toward algebraic geometry; however, I have trouble understanding this Javier's English, perhaps you could help me?

Question 0: It would be easier if someone could make a reading order from Javier's text, I'm having trouble with it. Can anyone please help me with this? I would like a definitive list (without any choices between texts that I have to make) from Javier's text.

Question 1: When he says:

>Geometry by Its History by A. Ostermann and Geometry by R. Fenn, or Elementary Euclidean Geometry: An Undergraduate Introduction by C.G. Gibson

Does he meant both Ostermann's and Fenn's book or just Gibson's or does he mean Ostermann and Fenn's or Ostermann and Gibson?

Question 2: I'm guessing based on the comma that he means Ostermann and Fenn or just Gibson but I can't tell based on some of his other grammar mistakes. Which one should I choose?

Question 3: When he says:

>Here you will need formal linear algebra like Jänich, or like Hausner, or like Banchoff/Wermer

Does he mean before Geometry by M. Audin or after Geometry vol. I and vol. II by M. Berger?

Question 4: Should I go with Jänich, Hausner, or Banchoff/Wermer?

Question 5: When he says:

>For this you will also need multivariable calculus and vector analysis: Advanced Calculus: A Geometric View by J.J. Callahan

Does he mean I need it before Geometries by A. B. Sossinsky?

Question 6:

>The most important thing at first is to get what is all about, i.e. how loci defined by solutions to systems of polynomial equations generalize to abstract algebraic varieties and their regular and rational morphisms

What does he mean here?

(cont.)

>>

Question 7:

>You may get first a good introduction by starting with just algebraic curves: Elementary Geometry of Algebraic Curves: An Undergraduate Introduction by C.G. Gibson and Complex Algebraic Curves by F.C. Kirwan.

Does he mean that this is an alternative to An Invitation to Algebraic Geometry by K. E. Smith et al. and Undergraduate Algebraic Geometry by M. Reid?

Question 8: When he says:

For the latter, and anyway, you will need an understanding of complex numbers and complex analysis, heuristically explained and pictured by Needham's book.

Does he mean that you need Needham's before Complex Algebraic Curves or both Complex Algebraic Curves and Elementary Geometry of Algebraic Curves?

Question 9: Which one should I choose?

>Algebraic Geometry: An Introduction by D. Perrin, or a more complex-analytic thorough introduction Algebraic Geometry over the Complex Numbers by D. Arapura

Question 10: Which one should I choose?

>Algebra: Chapter 0 by P. Aluffi or Advanced Modern Algebra by J.J. Rotman

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>>7841439

>most important thing at first: get what it's all about

>first what it's all about

>all of it

>first

tru kek my man

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>>7841507

You see what I mean. I think he might have a good guide here but I'm having trouble discerning some of it.

>>

1

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>>7841442

Dunno about the other books, but the introduction by D.Perrin (question 9) is very nice. I struggled for a long time with harder algebraic geometry texts, but after reading his book I finally got what it was all about.

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>>7841857

Have you tried Arapura's?

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>>7841439

Honestly this kind of way of studying mathematics is a bit misguided.

You aren't anywhere near the level of understanding what algebraic geometry even is, or how it's done, or why anyone would want to study it. How can you decide you want to do it?

Focus on what's right in front of your face. Learn the logical next steps and stop planning your graduate studies; learn your basic algebra and your multivariable calculus.

Then when you actually have something resembling the needed background, you can make an informed decision on whether you actually want to do algebraic geometry or not.

I see this all the time on /sci/ and it baffles me. Why do people plan out their studies years in advance when they have no idea what's even in the books they say they'll read?

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>>7841996

You assume a lot about me. I've already taken calculus 1-3, differential equations, and linear algebra. I want to expand into algebraic geometry. I've skimmed through Kerr's and Gathmann's lecture notes on algebraic geometry, so I think I know some basics of what algebraic geometry is about. Part of the reason I'm interested in AG is the connection to my interest in cryptography, in Frameproof Codes to be specific. I'm also interested in robotics, especially where AG is used. I know some basic principles of Bezout's theory, the work of Grothendieck, etc.

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>>7842129

>I've already taken calculus 1-3, differential equations, and linear algebra

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>>7842152

What?

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>>7842157

you're still fucking baby-tier

next reasonable step is real/complex analysis, don't kid yourself

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>>7842195

Did you read the post? It doesn't start with AG.

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>>7842157

Nigger you haven't even taken courses in basic proofs and abstract algebra. You also should have experience with commutative algebra.

You want to learn an advance graduate level topic but you are basically are at the sophomore level of math. Your going to need a at least a year of studying before you ready.

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>>7842256

Did you read the post? Both abstract algebra and commutative algebra are included. Though, proofs texts aren't listed by Javier, I have a couple proofs books in my possession.

>>

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>>7842129

I highly recommend pic/link related.

http://math.lssu.edu/bsnyder/PCMI/MathFest/compilemeforamsbook.pdf

Also:

>I'm also interested in robotics

You might know already, but "Ideas, Varieties and Algorithms" has a whole chapter on robotics (kinematics)

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>>7842460

Thanks, yes, I was aware of that book.

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Questions 3, 5, and 8 are the most I need help answered.

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>>7843786

I have Audin's book with me and I can say with confidence that you need some linear algebraic background.

For the 8, I guess you don't *need* to have read Needham's book (I'm sure many competent complex geometers haven't) but it definitely won't hurt to have a visual understanding the complex plane and projective transformations of the CP^1 if you then want to work on Riemann surfaces and all that

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>>7843786

Buddy if you're so fucking helpless/retarded/lazy you can't figure out for yourself if you're capable of reading a book or not you're never going to make it anywhere near algebraic geometry.

Stop begging for us to spoonfeed you a complete path with no choices or thought on your part from year 1.5 of university to graduate level mathematics and do some of your own research.

>>

>no mention of Topology in the OP

I can tell you right now that book is not worth shit.

>>

>>7843803

I know I'm not capable yet, I just like to plan out my entire life.

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