My Analysis textbook collection!

[nicholashayek]

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 :)

[sona]

these vids are awesome. from a soon-to-be physics phd student, it’s nice to know what other people are learning about

[BB-mrvy]

bartle and sherbert is so well written. totally agree

[AnuvabSpeaks]

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.

[padraighill]

this is a really cool video. theres 100% a market in nerdy book reviews and hindsight galore.

[dragonchato]

I've used the Bartle Sherbert book in my first year of stuyding math. Quite good to be fair, and really well explained

[enrico]

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!

[MadScientyst]

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...' 🤣🤣🤣

[namesake]

This is great!! I've been looking around for good analysis books, your insight is dope

[AhmadKhan-dnyh]

I'm using Introduction to Analysis by Bartle and using Real Analysis by Jay Cummings!

[paullopez]

11:00 this was the book used in my intro to analysis class.

[hyz]

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.

[cvdevol]

Ever looked at Serge Lang's Analysis books? Those are my favorite. They force me to really think and focus HARD.

[arijitgogoi]

Bartle and Sherbert is used in undergraduate Maths in Delhi University. By far the best book that I've come across for real analysis.

[plutothetutor]

I'm currently working through D J H Garlings analysis textbooks, certainly the most dense textbooks I've seen on analysis.

[douglasstrother]

"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.

[RizwanAli-ibmg]

glad i found such a channel on mathematics...its quite motivating😎

[jacobmanning]

The way you were talking about splitting up the metric spaces and measure theory classes is how my PhD program is structured

[lewessays]

Introductory level analysis books I would say like very introductory...meaning i don't think you could go below that level 😂 are the Jay Cummings and Stephen Abbott's(springer) books.
For higher level though I haven't personaly looked through deeply that I have seen recommended are analysis by Terrance Tao and Amann and Escher(German translation).

[jarrodanderson]

I want the Measure Theory book but it is still quite expensive! It must be used currently and a lot.