Nice rec! Looks like it would be my go-to reference if I needed it. Put on my Wish List [although my family never gets me anything on my wish list, they say it's all textbooks!]
Awesome! another book to add to my "to study later" list. I guess I'll have to make a review of my linear algebra soon, I forgot most of it and when I studied it back then I was young and not math-mature enough to approach the challenging and fun problems (that, and being a student with literally no time didn't helped that much lol). Now I just study this stuff just for the fun and enjoyment. I feel and I'm sure I'm missing some interesting topics out there. Now, how about some Differential Geometry and Tensor analysis? these are a couple of topics I've been considering to attack. So far I know that I should go with Diff. Geo. first. Anyway, thanks for the video. Keep it ℝ matey haha.
Have you ever read Stein and Shakarchi's "Fourier Analysis"? It's the first of a four part series on Analysis (Fourier, Complex, Real/Measure, Functional) and it's highly praised by mathematics UA-camr Daniel Rubin. It (or the series) may be a good candidate for your Hall of Fame if you agree with his assessment. I've only just begun the series myself.
I have not read their book on Fourier Analysis, but I do have their book III on Real Analysis! I've been interested in that series for a while, but have never actually sat down and tried reading them. Thanks for this. I'll give these a try!
No, unfortunately, I do not own that book, but it looks very good as well! I have been interested in getting it for the channel. That book is an introduction to proofs along with an introduction to many fields of math such as algebra, analysis, number theory, complex analysis, and more. It has partial solutions as well. It is written in a very similar way to this one in that it is very user friendly, modern and has many examples. I haven't put too much time into it, but I have skimmed through it and it looks awesome. Thanks for mentioning it. I'll try to get it at some point.
Can I or will I confirm this with 100% certainty? Nope! What I can guarantee you is that you will have a much, much easier time with this book than most other books on the same subject. This, in part, is because measure theory is mostly considered a subject for graduate students (and usually assumes real analysis at a bare minimum), while this assumes knowledge of only calculus. Compare this to the book by Capinski and Kopp. For instance, that book has a reputation for being very easy, and Johnston is much simpler than C&K. C&K does have a different goal and goes over different topics, but in terms of integration and measure, I would say Johnston is much easier. C&K also assumes knowledge of real analysis, while Johnston introduces the reader to many of the notions from real analysis. I hope this helps!
@@MathematicalToolbox Thank you for the expanded explanation, because I want to get into measure theory without a solid understanding of real analysis. I tried different books, but they are quite complicated. Thanks!
Thanks! That book looks good. I might get it for the channel at some point. While it is possible that it is the best in some regard, I would still recommend Johnston over Yeh for beginners. Perhaps Yeh can be used as a second book after Johnston. Thank you again for showing me this book!
Earphone users beware after the intro!
I apologize for the lack of focus in many parts of the video as well.
Nice rec! Looks like it would be my go-to reference if I needed it. Put on my Wish List [although my family never gets me anything on my wish list, they say it's all textbooks!]
Awesome! another book to add to my "to study later" list.
I guess I'll have to make a review of my linear algebra soon, I forgot most of it and when I studied it back then I was young and not math-mature enough to approach the challenging and fun problems (that, and being a student with literally no time didn't helped that much lol). Now I just study this stuff just for the fun and enjoyment. I feel and I'm sure I'm missing some interesting topics out there.
Now, how about some Differential Geometry and Tensor analysis? these are a couple of topics I've been considering to attack. So far I know that I should go with Diff. Geo. first.
Anyway, thanks for the video. Keep it ℝ matey haha.
Sure, I can do one on DG. I've got a very good book I've been wanting to read for some time now.
Hahaha, that's a good one.
Have you ever read Stein and Shakarchi's "Fourier Analysis"? It's the first of a four part series on Analysis (Fourier, Complex, Real/Measure, Functional) and it's highly praised by mathematics UA-camr Daniel Rubin. It (or the series) may be a good candidate for your Hall of Fame if you agree with his assessment. I've only just begun the series myself.
I have not read their book on Fourier Analysis, but I do have their book III on Real Analysis!
I've been interested in that series for a while, but have never actually sat down and tried reading them. Thanks for this. I'll give these a try!
His other book, “A Transition to Advanced Mathematics: A Survey Course” also looks excellent. Do you own that as well? Any thoughts on that one?
No, unfortunately, I do not own that book, but it looks very good as well! I have been interested in getting it for the channel.
That book is an introduction to proofs along with an introduction to many fields of math such as algebra, analysis, number theory, complex analysis, and more. It has partial solutions as well. It is written in a very similar way to this one in that it is very user friendly, modern and has many examples. I haven't put too much time into it, but I have skimmed through it and it looks awesome. Thanks for mentioning it. I'll try to get it at some point.
7:02 How would this compare to Pugh’s _Real Mathematical Analysis_ ? Is this actually more in-depth than Pugh?
Can you confirm that this is the easiest book on measure theory ?
Can I or will I confirm this with 100% certainty? Nope! What I can guarantee you is that you will have a much, much easier time with this book than most other books on the same subject. This, in part, is because measure theory is mostly considered a subject for graduate students (and usually assumes real analysis at a bare minimum), while this assumes knowledge of only calculus.
Compare this to the book by Capinski and Kopp. For instance, that book has a reputation for being very easy, and Johnston is much simpler than C&K. C&K does have a different goal and goes over different topics, but in terms of integration and measure, I would say Johnston is much easier. C&K also assumes knowledge of real analysis, while Johnston introduces the reader to many of the notions from real analysis.
I hope this helps!
@@MathematicalToolbox Thank you for the expanded explanation, because I want to get into measure theory without a solid understanding of real analysis. I tried different books, but they are quite complicated. Thanks!
Best book about lebesgue integration is J. YEH’s real analysis
Thanks! That book looks good. I might get it for the channel at some point.
While it is possible that it is the best in some regard, I would still recommend Johnston over Yeh for beginners. Perhaps Yeh can be used as a second book after Johnston.
Thank you again for showing me this book!