The Best Math Textbook for Everyone

I discuss one of my favorite math textbooks, Fourier Analysis: An Introduction by Elias Stein and Rami Shakarchi. I recommend this book to everyone in a STEM field who knows multivariable calculus and has some familiarity with ODE and linear algebra.

This book is excellent for initiating students into analysis. Students need not wait until after a semester of real analysis to learn from this book.

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Let me know what you think of this book in the comments, or if you have a different preference for treatment of Fourier analysis.

[robertforster]

I used this book along with baby Rudin and My teacher’s (Patrick Gallagher) hand written notes in my analysis class. My teacher actually took courses with Lars Ahlfors in the early ‘50s using Ahlfors own Complex Analysis book. His Phd advisor grandfather was G.H. Hardy. I was lucky to have known and done my senior thesis under him.

[chefrich]

Stein and Shakarachi's Book on Measure Theory; particularly chapter 1 is *chef's kiss*. No abstract sigma-algebras, just a intuitive explanation of the Lesbesgue measure and a development of integration theory. Then and only then do you tackle more general measures.

[leodu]

As a current Johns Hopkins student who also went through dozens of pure math books by now (and also suffered in grades in high school because I was way too into pure math), I am very very moved by your story. I bought the Princeton four part lecture series for a bargain before I came to USA. I didn't finish those but for the parts I did read, they were amazing. These are some of my prized books in my now quite large math books collection.

[indianatlarge]

this is sheer nostalgia.. i am going to buy this book again and read all over again,

[nini_kys]

17 is insane, you must be very talented. Thanks for the great vid. I'm in my second sem of analysis as a third year undergrad studying CS and math. This vid is really insightful to me as I get to pick a textbook to read with graduate students and I wanted to pick either this one or Grafakos as they recommend that for students who've already have taken analysis.

[anthonyymm]

Took a course based on this book a semester before I took measure theory and functional analysis. Glad I did it that way and not the other way around.

[felixchengtk]

I have to check this book out from the library! My favorite Fourier Analysis book is G Folland's Fourier Analysis and It's Applications.

[julianwilson]

Goes well with Bressoud's A Radical Approach to Real Analysis. Bressoud starts with Fourier to motivate the development of real analysis.

[atharvmishraiiit-k]

you did this this the age of 17 its quiet impressive !!!

[ulysses_grant]

Great one! I'll definitely check this one out!
As far as I had been using it, Susanna Epp - Discrete Mathematics with Applications is my current best of all time math book.

[monkeeseemonkeedoo]

Wasn't expecting to see this in my recommended. Thanks for sharing, will check it out

[chrislang]

An excellent text, which I've used as an instructor; beautifully put together and crystal clear throughout. There are many books on Fourier analysis, but this text really does stand out.

[jmguevarajordan]

Congratulations for your review. That book is indeed the best one in the Princeton's serie on analysis by Stein and Shakarchi. However, Stein's presentations of math analysis is not the easiest or the most pedagogical one. Of course, once you know the material presented in Stein's books, those books become excellent references.

[thcoura]

If I may share a word of wisdom. You traveled a long path in education to reach your journey in graduation. So, if you read a book and don't get something you are not dumb or stupid. The book is the problem. Look for others about the topic. There are many ways to explain a subject and no author is perfect.

[karthicka]

Great one! I feel like a book walkthrough, I wish we get to know more of your experiences and notes sharing in future

[mathmusicstructure]

I recommend A. P. French's "Vibrations and Waves" from the MIT series as an introduction to the physics side. The book from the video and French would be a very effective combination.

[michealjackson]

Butzer and Nessel Fourier Analysis and Approximation

[dijonstreak]

loved this on a very cool expose'....loved your sincere enthusiasm...great job buddy...the book s expensive

[jayantshaq]

Great video. Your love for the book and the subject really shines through.

[turdferguson]

My favorite math book of all time is Probability Theory: the Logic of Science by ET Jaynes.