1:07 How to Think About Analysis -- Lara Alcock 4:30 Introductory Real Analysis -- Andrey Kolmogorov 7:00 Fundamentals of Real Analysis -- Sterling Berberian 8:42 From Calculus to Analysis -- Steen Pedersen 10:56 Introduction to Real Analysis -- Bartle and Sherbert 12:14 Measure and Integral -- Richard Wheeden 16:05 Complex Variables and Applications -- Brown and Churchill 17:38 Introduction to Real Analysis -- Robert Brabenec 18:57 Real Analysis -- Stein and Shakarchi 22:27 Real and Complex Analysis -- Papa Rudin :)
That is the two I also got too. I am first reading Tao's, until I catch up with Bartle (since Tao starts off with constructing the reals). So far I do like it, but man am I taking a while. :dogekek:
"Applied Complex Variables" by John W. Dettman (Dover Publishers) is a great read (The Math Sorcerer has a video on it.): the first part covers the geometry/topology of the complex plane from a Mathematician's perspective, and the second part covers application of complex analysis to differential equations and integral transformations, etc. from a Physicist's perspective. I've used Smith Charts (RF/microwave engineering) for years, but learned from Dettman that the "Smith Chart" is an instance of a Möbius Transformation. The Schaum's Outline on "Complex Variables" is a great companion book for more problems/solutions and content.
You were taught by a 'Springer' Author? I envy you my friend! That's almost like having an Erdos Number, what a privilege! Anyways, some minor thoughts /reflections on the titles: *The Princeton Series is a 1st class 4 titles collection *Rudin is tough yes, but considered Gospel *Many 'Introduction to Real Analysis' titles exist BUT, their topics sequence can be of varying degrees of difficulty *Multiple Dover & Springer titles exist BUT, you have to know which Authors are recommended eg. Gilbert Strang, Richard Silverman, Serge Lang, Paul Halmos, etc As a C.A. /Func Analysis wannabe expert I recommend the following for further exploration: *Theory of Functions of a Complex Variable (3 Vols) - Aleksei Ivanovich Markushevich *A Comprehensive Course in Analysis (5 Vols) - Barry Simon *Analysis I&II - Terrence Tao *Introductory functional analysis with applications - Erwin Kreyszig Finally for some humor, a lotta these texts are bound to have the dreaded phrase: 'The proof will be left as an exercise to the Student...' 🤣🤣🤣
I always find it very interesting how people rely more or less on textbooks for learning maths, for example basically everyone in my course never even bought a book in the whole 3 years degree, profs are just expected to develop all the theory during the semester without leaving anything out to do by yourself. I don’t know if this is for better or for worse, but I sure saved some money!
That's how my undergrad was. It was a waste of time. I started learning math after graduating. Right now, the library is my favorite place in the world.
I’m currently taking a graduate level real analysis and the textbook we used is Folland’s book. We also use Royden’s book and Rudin’s book as references.
Are they as dense as his algebra book? I used to like to pull that one out and ask people for help with it when they'd look at me like I was nuts when I'd say my algebra class was kicking my ass. Then they'd see all those commutative diagrams and realize I wasn't talking about the crap they learned in high school lol.
My exposure to Real Analysis was limited to what is covered in "Calculus" (Marsden & Weinstein) and "Vector Calculus" (Marsden & Tromba) as an Undergrad. Since Calculus has such a strong geometric, visual nature, what makes Real Analysis so difficult?
I'll be self--studying real analysis. Can you clarify the difference between undergrad and grad analysis courses, and why/how this book is in between? Thanks.
Here are some books I recommend for self-study: How to think about Analysis - Alcock (for preparation) Introduction to Real Analysis - Bartle and Sherbert (undergrad RA) Intro to Real Analysis - Kolmogorov and Fomin (stepping stone from undergrad to grad) Real Analysis - Stein and Shakarchi (graduate RA) Measure and Integral - Wheeden and Zygmund (post graduate RA) The difference between graduate and undergraduate RA is that undergraduate RA is proof-based calculus (usually functions of a single variable) while graduate RA is all measure theory. It deals with functions that are true monsters that vanilla calculus cannot analyze, so the Lebesgue measure and integral were developed to analyze such functions. I hope this was helpful!
Nice collection! Any books on functional analysis you have? Or are you super concentrated on measure theory and complex analysis for your qualifiers? What I recommend is "Fundamentals of the theory of operator algebras" from Kadison and Ringrose. Or any course on Banach/C* algebras your university offers, when I first learned about them I was amazed.
Your criticism about readability is valid. It's easier to read text that has good formatting and paragraph breaks than a book without these. Also, what book would you recommend for Measure Theory that's readable but advanced?
Would you recommend some problem solving books on real analysis? There are tons of calculus books with plenty of worked examples. It is hard to find books with detailed examples beyond trivial ones on how to tackle measure theory problems!
It is hard to find some books like you mentioned. Most of the time if I don’t know how to do a problem I head to stack exchange. I will keep an eye out :)
I can recommend Russian book "Real analysis in problems" Ulyanov, Bakhvalov. There are collected problems (and all main theorems are formulated as problems) with solutions. Perfect structure for self-study. Apparently it's not translated.
My undergrad analysis sequence did Baby Rudin and man that book was a slog. It had great exercises but the proofs were so slick like they were handed down on stone tablets from god or something. That second chapter on metric space topology was a very hard introduction to upper division math focused on proving results instead of computations, especially with no images in it. I had a good professor but can't imagine many people getting far self-studying the book for their introduction to analysis. Liked Royden way better when we used it for graduate level analysis. When I saw Big Rudin jump immediately to integration without building up the Lesbesgue measure I nope'd out of reading it just like you haha.
Princeton lectures are free available ebook all four parts I use them for reference and problems Edit: Rudin introduces Lebesgue theory in first part goes by name baby rudin. What you have is I think called papa Rudin
It depends on what’s in advanced calculus. I took all my calc then proofs then real variables which is necessary for real analysis. Without undergrad real variables I would have not been able to survive graduate level real analysis.
Currently trying to figure out what real analysis is so I can be doing it when I get into 11th grade, currently teaching myself Calc in 10th for fun, I know derivatives by heart while integrals continue to confuse me
The only book on real analysis I have is Jay Cummings' Real Analysis: A Long-Form Mathematics Textbook, though that's currently sitting on my desk at home over 100 miles away. That book's elementary compared to what you have, but I'm only a hobbyist. Edit: Actually, I lied, I just found Understanding Analysis by Stephen Abbott, Elementary Analysis by Kenneth Ross, and Real Analysis by Miklós Laczkovich and Vera T. Sósas as pdfs on my laptop, downloaded them in 2020, when they were given away for free by Springer.
Many/some grad students” are teaching assistants teaching around a couple of courses per semester. You have been very careful about not saying or having any identifying aspects of your university in your videos. Your “office” would be near the normal sounds of a bustling university such as students seeking your tutoring services, colleagues wondering the hallways etc. Are you a teaching assistant? Do you have an office at the university where you apparently rub elbows with a famous analyst? Your aping of The MATH SORCERER approach is a long way from page view critical mass.
1:07 How to Think About Analysis -- Lara Alcock
4:30 Introductory Real Analysis -- Andrey Kolmogorov
7:00 Fundamentals of Real Analysis -- Sterling Berberian
8:42 From Calculus to Analysis -- Steen Pedersen
10:56 Introduction to Real Analysis -- Bartle and Sherbert
12:14 Measure and Integral -- Richard Wheeden
16:05 Complex Variables and Applications -- Brown and Churchill
17:38 Introduction to Real Analysis -- Robert Brabenec
18:57 Real Analysis -- Stein and Shakarchi
22:27 Real and Complex Analysis -- Papa Rudin :)
these vids are awesome. from a soon-to-be physics phd student, it’s nice to know what other people are learning about
First course of analysis I used 2 books of Tao and Bartle Sherbert and then Rudin.
I think this combination is quite good for learning analysis.
That is the two I also got too. I am first reading Tao's, until I catch up with Bartle (since Tao starts off with constructing the reals). So far I do like it, but man am I taking a while. :dogekek:
bartle and sherbert is so well written. totally agree
"Applied Complex Variables" by John W. Dettman (Dover Publishers) is a great read (The Math Sorcerer has a video on it.): the first part covers the geometry/topology of the complex plane from a Mathematician's perspective, and the second part covers application of complex analysis to differential equations and integral transformations, etc. from a Physicist's perspective. I've used Smith Charts (RF/microwave engineering) for years, but learned from Dettman that the "Smith Chart" is an instance of a Möbius Transformation.
The Schaum's Outline on "Complex Variables" is a great companion book for more problems/solutions and content.
You were taught by a 'Springer' Author?
I envy you my friend!
That's almost like having an Erdos Number, what a privilege!
Anyways, some minor thoughts /reflections on the titles:
*The Princeton Series is a 1st class 4 titles collection
*Rudin is tough yes, but considered Gospel
*Many 'Introduction to Real Analysis' titles exist BUT, their topics sequence can be of varying degrees of difficulty
*Multiple Dover & Springer titles exist BUT, you have to know which Authors are recommended eg. Gilbert Strang, Richard Silverman, Serge Lang, Paul Halmos, etc
As a C.A. /Func Analysis wannabe expert I recommend the following for further exploration:
*Theory of Functions of a Complex Variable (3 Vols) - Aleksei Ivanovich Markushevich
*A Comprehensive Course in Analysis (5 Vols) - Barry Simon
*Analysis I&II - Terrence Tao
*Introductory functional analysis with applications - Erwin Kreyszig
Finally for some humor, a lotta these texts are bound to have the dreaded phrase:
'The proof will be left as an exercise to the Student...' 🤣🤣🤣
this is a really cool video. theres 100% a market in nerdy book reviews and hindsight galore.
I always find it very interesting how people rely more or less on textbooks for learning maths, for example basically everyone in my course never even bought a book in the whole 3 years degree, profs are just expected to develop all the theory during the semester without leaving anything out to do by yourself. I don’t know if this is for better or for worse, but I sure saved some money!
That's how my undergrad was. It was a waste of time. I started learning math after graduating. Right now, the library is my favorite place in the world.
I've used the Bartle Sherbert book in my first year of stuyding math. Quite good to be fair, and really well explained
I’m currently taking a graduate level real analysis and the textbook we used is Folland’s book. We also use Royden’s book and Rudin’s book as references.
Ever looked at Serge Lang's Analysis books? Those are my favorite. They force me to really think and focus HARD.
Are they as dense as his algebra book? I used to like to pull that one out and ask people for help with it when they'd look at me like I was nuts when I'd say my algebra class was kicking my ass. Then they'd see all those commutative diagrams and realize I wasn't talking about the crap they learned in high school lol.
Bartle and Sherbert is used in undergraduate Maths in Delhi University. By far the best book that I've come across for real analysis.
I'm currently working through D J H Garlings analysis textbooks, certainly the most dense textbooks I've seen on analysis.
Please do more book reviews
My exposure to Real Analysis was limited to what is covered in "Calculus" (Marsden & Weinstein) and "Vector Calculus" (Marsden & Tromba) as an Undergrad.
Since Calculus has such a strong geometric, visual nature, what makes Real Analysis so difficult?
This is great!! I've been looking around for good analysis books, your insight is dope
The way you were talking about splitting up the metric spaces and measure theory classes is how my PhD program is structured
I'm using Introduction to Analysis by Bartle and using Real Analysis by Jay Cummings!
I simply love bartle's book!
I want the Measure Theory book but it is still quite expensive! It must be used currently and a lot.
I'll be self--studying real analysis. Can you clarify the difference between undergrad and grad analysis courses, and why/how this book is in between? Thanks.
Here are some books I recommend for self-study:
How to think about Analysis - Alcock (for preparation)
Introduction to Real Analysis - Bartle and Sherbert (undergrad RA)
Intro to Real Analysis - Kolmogorov and Fomin (stepping stone from undergrad to grad)
Real Analysis - Stein and Shakarchi (graduate RA)
Measure and Integral - Wheeden and Zygmund (post graduate RA)
The difference between graduate and undergraduate RA is that undergraduate RA is proof-based calculus (usually functions of a single variable) while graduate RA is all measure theory. It deals with functions that are true monsters that vanilla calculus cannot analyze, so the Lebesgue measure and integral were developed to analyze such functions. I hope this was helpful!
@@PhDVlog777"Vanilla Calculus". That's a fresh one for me. And thanks for the answer and book list.
glad i found such a channel on mathematics...its quite motivating😎
Nice collection! Any books on functional analysis you have? Or are you super concentrated on measure theory and complex analysis for your qualifiers? What I recommend is "Fundamentals of the theory of operator algebras" from Kadison and Ringrose. Or any course on Banach/C* algebras your university offers, when I first learned about them I was amazed.
I have a pdf of Kreyszigs book which I like. I might get a hard back if it in the near future. Definitely prioritizing qualifiers.
@@PhDVlog777 That's a nice book. I had to learn some of its chapters for my qualifiers last summer.
11:00 this was the book used in my intro to analysis class.
Good suggestions. I own Lay and Gaughan (both undergrad) and wasn't really happy with either.
Your criticism about readability is valid. It's easier to read text that has good formatting and paragraph breaks than a book without these. Also, what book would you recommend for Measure Theory that's readable but advanced?
Would you recommend some problem solving books on real analysis? There are tons of calculus books with plenty of worked examples. It is hard to find books with detailed examples beyond trivial ones on how to tackle measure theory problems!
It is hard to find some books like you mentioned. Most of the time if I don’t know how to do a problem I head to stack exchange. I will keep an eye out :)
I recommend problems in real and functional by torchinski
And exercises in analysis part 1 by gasinski
@@nicolasoyarce9734 Thanks a lot.
I can recommend Russian book "Real analysis in problems" Ulyanov, Bakhvalov. There are collected problems (and all main theorems are formulated as problems) with solutions. Perfect structure for self-study. Apparently it's not translated.
I think we should teach pure math earlier than we do.
Whats best way to learn real analysis historically .
Or in the usual textbook logical way
Just curious, why no love for Dieudonne or Sternberg?
I was towards the end of the vid and was about to comment, "Hey, check out Royden". lol
My undergrad analysis sequence did Baby Rudin and man that book was a slog. It had great exercises but the proofs were so slick like they were handed down on stone tablets from god or something. That second chapter on metric space topology was a very hard introduction to upper division math focused on proving results instead of computations, especially with no images in it. I had a good professor but can't imagine many people getting far self-studying the book for their introduction to analysis. Liked Royden way better when we used it for graduate level analysis. When I saw Big Rudin jump immediately to integration without building up the Lesbesgue measure I nope'd out of reading it just like you haha.
Princeton lectures are free available ebook all four parts I use them for reference and problems
Edit: Rudin introduces Lebesgue theory in first part goes by name baby rudin. What you have is I think called papa Rudin
there is nothing that can surpass math , and i love it
We used Bartle when I did Real Analysis at Tulane in the early '80's...still have the book in my collection of old college textbooks!
Is necessary study “advanced calculus” for study real analysis, or we can “jump” from normal calculus to real analysis?
It depends on what’s in advanced calculus. I took all my calc then proofs then real variables which is necessary for real analysis. Without undergrad real variables I would have not been able to survive graduate level real analysis.
Kolmogorov is a giant in fluid turbulence.
Currently trying to figure out what real analysis is so I can be doing it when I get into 11th grade, currently teaching myself Calc in 10th for fun, I know derivatives by heart while integrals continue to confuse me
Take it easy bud, you’ll get there when you get there (in college)
Do you know Sheldon Axler’s recent graduate book?
could you share that free pdf copy of the Royden book you mentioned? (is it legally free?)
It comes up on google if you search Royden Fitzpatrick real analysis. Although it is not complete, there are pages missing :(
Ah, yes. Papa Rudin at the end. I'm currently reading that one. Spectacular modern approach.
I just realized, we go to the same University.
math sorcerer?
The Math Sorcerer's Apprentice!
The only book on real analysis I have is Jay Cummings' Real Analysis: A Long-Form Mathematics Textbook, though that's currently sitting on my desk at home over 100 miles away. That book's elementary compared to what you have, but I'm only a hobbyist.
Edit: Actually, I lied, I just found Understanding Analysis by Stephen Abbott, Elementary Analysis by Kenneth Ross, and Real Analysis by Miklós Laczkovich and Vera T. Sósas as pdfs on my laptop, downloaded them in 2020, when they were given away for free by Springer.
cana boy get a list
Review real analysis book by sk mapa
Many/some grad students” are teaching assistants teaching around a couple of courses per semester.
You have been very careful about not saying or having any identifying aspects of your university in your videos.
Your “office” would be near the normal sounds of a bustling university such as students seeking your tutoring services, colleagues wondering the hallways etc.
Are you a teaching assistant? Do you have an office at the university where you apparently rub elbows with a famous analyst?
Your aping of The MATH SORCERER approach is a long way from page view critical mass.
._.
books have become 💩 too many errors... a missing math operator and your lost in the sauce ... create a learning playlist...