I used this book in my honors calculus course, I recommend it to people who really want to be more familiar with calculus and who are building steps to approach real analysis.
That book is a masterpiece and should be read by anyone who loves mathematics. The explanation of the logarithmic and exponential function is the best among all math books.
Thank you for this video, it brought back great memories. We used this text with the great Professor Tom Storer in the Honors Calculus sequence at University of Michigan many years ago.
I really like the definition of trigonometric functions that appears in this book. The only book that gives a perfectly rigorous definition, yet related to our geometric intuition. I prefer that over using Taylor series or differential equations as a definition. You can define like that of course, but then problems like "can you square a circle" don't make much sense.
perfect example of what a good writer can do with a subject. the only way anything would remain unexplained would be due to the infinite ramifications of the subject. I wish I had more time to read it, but the small part of what I read at the beginning was pure beauty and art.
Do you think this book and Abbott are good to prepare for my first class in real analysis next semester? I already know how to prove things since i took a rigorous linear algebra class (with Axlers book) and I am kind of familiar already with epsilon delta.
With certain high profile books, like this one, it'd be great if you did a mini video series. Introduce the book then work selected problems in it and talk about why they're interesting. It'd be good content for sure.
I did my undergrad at Waterloo, i dont remember what the required book was but i remember getting this later in my undergrad from a profs recommendation
Hey Prof. I've been following your channel ever since I started studying Math at 26y/o, I would love to watch videos where you go through questions you find interesting like you did in the past.
Hi Math Sorcerer!I am a 16 year old high school student.I have learnt single-variable calculus on my own and planning to study real analysis in December and January and then study this book.I am grateful for your informative videos
Yeah this is actually a common feeling among students. It's one of the most hated things in Calc 2. I disliked the disk/shell at first, but then later grew to love it.
I've been using this book for Calculus 1. It is a good book but it was not my favorite as it lacked some content that i was looking for I really like Calculus with analytic geometry by Earl W. Swokowski And the Thomas Calculus new edition The best
I was looking at some of the solutions in chapter 18, and I was thinking they looked like they were solved by a math program. How the heck could I come up with some of those solutions with just a pen and a paper? Looks difficult. LOL.
12:25 . Love to see that. But I wonder how it's possible that the knowledge is yet not widely spread that power towers are calculated from top to bottom? For me, they are second nature. So I thought that's obvious. Yesterday, I watched a video about Goodstein sequences and Gödel's incompleteness theorem and let me tell you, it was fantastic. I'm constantly looking for bigger and bigger numbers and when the host of the video on Numberphile said ua-cam.com/video/0Le7NgS-wO0/v-deo.html , Grahams number's growth rate is small compared to this one, I couldn't believe it. Not only does adding one single up-arrow make all the difference, it pushes it into a different category. And Graham gives you G(n) arrows for the next G(n+1) number. Watching the Godstein sequences, I really think that this is the holy grail of fast growing sequences. However, it's said that this sequence comes back down to zero because of the -1 s it has. No matter how insignificant small, but given enough time, the -1s start to overhaul that big number at the front. I'm wondering, is there a book about Goodstein Sequences? It's said on wikipedia, that in terms of fast growing hirarchies, fε0(n) is the first function in the Wainer hirarchie, that dominates the Goodstein sequece. You could view this as an upper bound. It also surpasses the ω hirarchy until it's bound by ω^^ω or written differently ω ↑↑ω (a power tower with ω's which has a height of ω), also called ε0, as an upper bound. Isn't that amazing? So, if you do know a book with an explaination about the Goodstein sequence, it would be amazing. I'd love to read about that after finishing the current book I'm reading (Concrete Math) by Knuth, Graham, Patashnik and the next book I'm going to read after that one (TAOCP by Knuth).
Please check once jee advanced mathematics books , like 2 of them are really hard , 1st ) black book by Balaji publications 2nd) problems in iit mathematics by A das Gupta, U would definitely like to do thoes books
I bought this as a first time calculus learner on my own and it was just increasing my neurons at each problem
lmao best comment
the book which has made people switch careers🥶🥶🥶
Yes lol
how ? explain?
@@arifaahmed5454the book introduces serious real beautiful mathematical thinking. Many people can’t handle it
Also Rudin
😂😂
I used this book in my honors calculus course, I recommend it to people who really want to be more familiar with calculus and who are building steps to approach real analysis.
That book is a masterpiece and should be read by anyone who loves mathematics. The explanation of the logarithmic and exponential function is the best among all math books.
Velleman has his own Calculus book and it’s really, really cool! It’s subtitled: “A Rigorous First Course”.
My math prof for analysis, Ed Perkins at UBC, in the 1980s told me this was his favourite calculus book. I've always wanted to check it out.
That's awesome. You should definitely check it out.
I have the Fourth edition and the Combined Answer book. Great book. Pretty sure this is one of the first books I bought on your recommendation.
Awesome!!
Thank you for this video, it brought back great memories. We used this text with the great Professor Tom Storer in the Honors Calculus sequence at University of Michigan many years ago.
I really like the definition of trigonometric functions that appears in this book. The only book that gives a perfectly rigorous definition, yet related to our geometric intuition. I prefer that over using Taylor series or differential equations as a definition. You can define like that of course, but then problems like "can you square a circle" don't make much sense.
perfect example of what a good writer can do with a subject. the only way anything would remain unexplained would be due to the infinite ramifications of the subject. I wish I had more time to read it, but the small part of what I read at the beginning was pure beauty and art.
Wow those worked solutions are a gem ! Self-study is possible.
Read this and worked through some of the problems a while ago. I'm back to it now to attempt to complete all of the problems!
Do you think this book and Abbott are good to prepare for my first class in real analysis next semester? I already know how to prove things since i took a rigorous linear algebra class (with Axlers book) and I am kind of familiar already with epsilon delta.
Definitely !!
There is book by how to think about analysis by lara alcocok. check that
With certain high profile books, like this one, it'd be great if you did a mini video series. Introduce the book then work selected problems in it and talk about why they're interesting. It'd be good content for sure.
I did my undergrad at Waterloo, i dont remember what the required book was but i remember getting this later in my undergrad from a profs recommendation
Was it for the advanced sections (147/148/247)? I did the regular stream so I have PMATH 333 coming up, hopefully Spivak will help. 🤞🤞
@ansonpang8468 nope 130s series. I only got interested in maths, academics aside, after I started my master's (not in maths, but related)
I'm a programmer and I feel like I want to buy it.
Spivaaaaaaak!*
*Like Sheldon screams Wheeaaaton!
Calculus of Manifolds is his (Mr.Spivak's) other book. Nice one. This one is also good one. 👌🤘👍. Thanks bro. 🤝🙏
Hey Prof. I've been following your channel ever since I started studying Math at 26y/o, I would love to watch videos where you go through questions you find interesting like you did in the past.
Hi Math Sorcerer!I am a 16 year old high school student.I have learnt single-variable calculus on my own and planning to study real analysis in December and January and then study this book.I am grateful for your informative videos
You are insane dude😭
I aspire to be someone like you🙏
@keanusamuel4392 Thnx buddy
Really good book. I learned from iit rigorous Analysis. Only thing i do not like is the way it introduses and presents Taylor Series .
My analysis 1 book as a physics student. it is quite nice
A book which is something between "Calculus" and "Real Analysis". A great book, and the problems were amazing!
Yeah those problems are pretty awesome.
Infinite series, power series, and Taylor series taught me to hate math.
Yeah this is actually a common feeling among students. It's one of the most hated things in Calc 2. I disliked the disk/shell at first, but then later grew to love it.
❤🎉
:)
I've been using this book for Calculus 1.
It is a good book but it was not my favorite as it lacked some content that i was looking for
I really like
Calculus with analytic geometry
by Earl W. Swokowski
And the Thomas Calculus new edition
The best
This book is goated
My dad has that book
I was looking at some of the solutions in chapter 18, and I was thinking they looked like they were solved by a math program. How the heck could I come up with some of those solutions with just a pen and a paper? Looks difficult. LOL.
Stewart!
12:25 .
Love to see that.
But I wonder how it's possible that the knowledge is yet not widely spread that power towers are calculated from top to bottom?
For me, they are second nature. So I thought that's obvious.
Yesterday, I watched a video about Goodstein sequences and Gödel's incompleteness theorem and let me tell you, it was fantastic.
I'm constantly looking for bigger and bigger numbers and when the host of the video on Numberphile said
ua-cam.com/video/0Le7NgS-wO0/v-deo.html
, Grahams number's growth rate is small compared to this one, I couldn't believe it.
Not only does adding one single up-arrow make all the difference, it pushes it into a different category.
And Graham gives you G(n) arrows for the next G(n+1) number.
Watching the Godstein sequences, I really think that this is the holy grail of fast growing sequences.
However, it's said that this sequence comes back down to zero because of the -1 s it has.
No matter how insignificant small, but given enough time, the -1s start to overhaul that big number at the front.
I'm wondering, is there a book about Goodstein Sequences?
It's said on wikipedia, that in terms of fast growing hirarchies,
fε0(n) is the first function in the Wainer hirarchie, that dominates the Goodstein sequece.
You could view this as an upper bound.
It also surpasses the ω hirarchy until it's bound by ω^^ω or written differently ω ↑↑ω (a power tower with ω's which has a height of ω), also called ε0, as an upper bound.
Isn't that amazing?
So, if you do know a book with an explaination about the Goodstein sequence, it would be amazing.
I'd love to read about that after finishing the current book I'm reading (Concrete Math) by Knuth, Graham, Patashnik and the next book I'm going to read after that one (TAOCP by Knuth).
I found his book "Calculus on Manifolds" to be perhaps the most clear, wonderfully concise advanced math text I have ever read.
Gee I wonder if spivack is a mason pufft.....
lim f(x+1) - f(x) = L (x ->infinity). Calculate lim f(x)/x (x -> infinity). Spivak wont help you in this simple question. Sorry.
Please check once jee advanced mathematics books , like 2 of them are really hard ,
1st ) black book by Balaji publications
2nd) problems in iit mathematics by A das Gupta,
U would definitely like to do thoes books
Ooo