So cool that you have all the 4 books of the series! I skimmed through it in the past it and seemed to be rather accessible if you have real analysis! I mean, it's not a wall of formulas, definition, and theorems: it's rather chatty and not too dense. I also looked up and found the solutions online, but don't know the quality since they're not official...
It's an interesting series, although for people like me who were not Princeton students, these will require lots of reading and problems outside these books.
@mathematicaladventures that's what I'll probably do too, using it together with other books! what i meant is that it doesn't seem like a "baby rudin" of Fourier Series, it looks much more accessible! But maybe it's a trap... 😂
You don't have to go through a differential equations book to study the Fourier Analysis book. Everything that is done in solving the Heat, Wave, and Laplace equations are just the applications of things that are given in this book. You have enough background given that you have completed a course worth of material on analysis and topology. The problem sets are on the difficult side. Other than that, concepts are explained very well in these books. Although, I will suggest you to use some other books as a main resource for learning Measure theory and Functional analysis. My suggestions are "Real Analysis" by Gerald Folland or Royden's book by the same name. And "Functional Analysis" by Bachman and Narici. Although, you can find quite a bit of functional analysis in Folland's or Royden's book (depending on whatever you choose).
Agreed. You could probably even get by with less. The heat equation, wave equation and Laplace equation are all presented at the same (semi-rigorous tending towards non-rigorous) level as French or the Feynman Lectures on Physics. Knowing some physics and how to "derive" these equations from scratch is extremely helpful.
A glaring error where "1V" is used as the Roman numeral IV on the spine for Functional Analysis (you don't even have to pull it off the shelf!) does not tell me anything good about the editing standards of this publisher. But I suppose I've read enough textbooks at this level not to get my hopes up about this sort of thing.
my god I thought this comment was originally abvout how Romans preferred IIII as IV could be seen as blasphemy (IVPITER often shortened as IV) but wow it really is one V not IV.
It's not that hard. There are really no prerequisites to learn from these books other than a very strong background in epsilon-delta proofs or calculus done right which is covered in Spivak's fine calculus book. It's probably a good idea to know some linear algebra, abstract algebra, some topological ideas e.g. open sets, compactness, etc. uniform convergence of a sequence of functions but this isn't strictly necessary, it only provides some helpful context. If you did Math Olympiad this shouldn't be overwhelming at all. Why not just do all the first chapter questions? They're mostly things like trig identities and some calculus. If that goes well, you can keep going.
This is true of every book in the series except the Fourth Book. That book will be unreadable unless you master what's in the other three. You could even read the books 1-3 in any order but it does break the narrative. The best part of these books is that it tells a story. This is what Rudin lacks.
As jdbrown said, I like how the three first books weave a story. If and when I get to these, I would attempt to read them whole and attempt most problems. It's my thing.
Absolutely hated Skein and Shakarchi. Impossible book. Only for geniuses. I really don't know why they never simplify real analysis. What's the point of complexifying an already complex topic?
Yeah, baby Rudin says hello about that. Even though Pugh exists, I don't think there is a book out there that does what Rudin does, but in a way that a normal person could understand.
@@mathematicaladventures The most accessible real analysis 1 book that I've seen -- that doesn't sacrifice on rigor -- is the recent "long form" text by Jay Cummings. It's a bit wordy, but it essentially covers chapters 1-7 of baby Rudin in a beginner-friendly way. (I'm toying with writing my own text on real analysis, which I hope will be accessible, rigorous, not overly wordy, and contain lots of counter-examples. At the moment, it's just a bunch of semi-polished lecture notes. The plan is to cover chapters 1-7 and 9-10 of baby Rudin, but with the later chapters closer in spirit to Spivak's calculus on manifolds.) I view Stein and Shakarchi's books more like works of art that should be read for fun, to experience some beautiful mathematics, rather than as textbooks for building solid foundations.
It's not a genius book like Dieudonne's Foundations of Modern Analysis. You just need a solid fluent background in basic real analysis which everyone can acquire one theorem at a time. Spivak's Calculus is excellent for this and studying the main ideas and contemplating them very deeply will take you right to the door step of this book. It would be good to learn some multivariable calculus like the Jacobian matrix and derivatives as a linear transformation which would help you understand volume II. Spivak does some complex variables as well as some series of functions and uniform convergence. When you understand those topics, you are more than read for S&S.
thank you for making these videos !
You bet.
Excellent bibliography
Oh yeah
So cool that you have all the 4 books of the series! I skimmed through it in the past it and seemed to be rather accessible if you have real analysis! I mean, it's not a wall of formulas, definition, and theorems: it's rather chatty and not too dense. I also looked up and found the solutions online, but don't know the quality since they're not official...
It's an interesting series, although for people like me who were not Princeton students, these will require lots of reading and problems outside these books.
@mathematicaladventures that's what I'll probably do too, using it together with other books! what i meant is that it doesn't seem like a "baby rudin" of Fourier Series, it looks much more accessible! But maybe it's a trap... 😂
I don't think it's a trap, just a book that requires complementing books.
MRI and putting the future into perspective with quantum computing is funny
Do you mean how quantum computing can improve MRIs?
You don't have to go through a differential equations book to study the Fourier Analysis book. Everything that is done in solving the Heat, Wave, and Laplace equations are just the applications of things that are given in this book. You have enough background given that you have completed a course worth of material on analysis and topology. The problem sets are on the difficult side. Other than that, concepts are explained very well in these books.
Although, I will suggest you to use some other books as a main resource for learning Measure theory and Functional analysis. My suggestions are "Real Analysis" by Gerald Folland or Royden's book by the same name. And "Functional Analysis" by Bachman and Narici. Although, you can find quite a bit of functional analysis in Folland's or Royden's book (depending on whatever you choose).
Thanks for the references. I have Royden's book.
@mathematicaladventures Great!
Agreed. You could probably even get by with less. The heat equation, wave equation and Laplace equation are all presented at the same (semi-rigorous tending towards non-rigorous) level as French or the Feynman Lectures on Physics. Knowing some physics and how to "derive" these equations from scratch is extremely helpful.
ODEs wont really help much. Real analysis is probably the pre req with maybe a little bit of complex analysis and PDEs.
Thanks for that.
A glaring error where "1V" is used as the Roman numeral IV on the spine for Functional Analysis (you don't even have to pull it off the shelf!) does not tell me anything good about the editing standards of this publisher. But I suppose I've read enough textbooks at this level not to get my hopes up about this sort of thing.
Yeah, this is common for small market books. There probably was just one person over the whole 'look and feel' aspect.
my god I thought this comment was originally abvout how Romans preferred IIII as IV could be seen as blasphemy (IVPITER often shortened as IV) but wow it really is one V not IV.
Interesting Roman angle.
It's not that hard. There are really no prerequisites to learn from these books other than a very strong background in epsilon-delta proofs or calculus done right which is covered in Spivak's fine calculus book. It's probably a good idea to know some linear algebra, abstract algebra, some topological ideas e.g. open sets, compactness, etc. uniform convergence of a sequence of functions but this isn't strictly necessary, it only provides some helpful context. If you did Math Olympiad this shouldn't be overwhelming at all. Why not just do all the first chapter questions? They're mostly things like trig identities and some calculus. If that goes well, you can keep going.
This is true of every book in the series except the Fourth Book. That book will be unreadable unless you master what's in the other three. You could even read the books 1-3 in any order but it does break the narrative. The best part of these books is that it tells a story. This is what Rudin lacks.
As jdbrown said, I like how the three first books weave a story. If and when I get to these, I would attempt to read them whole and attempt most problems. It's my thing.
Absolutely hated Skein and Shakarchi. Impossible book. Only for geniuses.
I really don't know why they never simplify real analysis. What's the point of complexifying an already complex topic?
Yeah, baby Rudin says hello about that. Even though Pugh exists, I don't think there is a book out there that does what Rudin does, but in a way that a normal person could understand.
Yeah it is very high level.. I ended up selling my copy of Real Analysis by S&S. I've got Papa Rudin and Analysis II by Tao anyway
@@mathematicaladventures The most accessible real analysis 1 book that I've seen -- that doesn't sacrifice on rigor -- is the recent "long form" text by Jay Cummings. It's a bit wordy, but it essentially covers chapters 1-7 of baby Rudin in a beginner-friendly way.
(I'm toying with writing my own text on real analysis, which I hope will be accessible, rigorous, not overly wordy, and contain lots of counter-examples. At the moment, it's just a bunch of semi-polished lecture notes. The plan is to cover chapters 1-7 and 9-10 of baby Rudin, but with the later chapters closer in spirit to Spivak's calculus on manifolds.)
I view Stein and Shakarchi's books more like works of art that should be read for fun, to experience some beautiful mathematics, rather than as textbooks for building solid foundations.
I should check that book out. I have his proofs book.
It's not a genius book like Dieudonne's Foundations of Modern Analysis. You just need a solid fluent background in basic real analysis which everyone can acquire one theorem at a time. Spivak's Calculus is excellent for this and studying the main ideas and contemplating them very deeply will take you right to the door step of this book. It would be good to learn some multivariable calculus like the Jacobian matrix and derivatives as a linear transformation which would help you understand volume II. Spivak does some complex variables as well as some series of functions and uniform convergence. When you understand those topics, you are more than read for S&S.