Top 4 Mathematical Analysis Books
ฝัง
- เผยแพร่เมื่อ 13 ธ.ค. 2022
- In this video I will show you 4 mathematical analysis books. These are books you can use to learn real analysis on your own via self-study. You can also use these books to supplement any course you are taking on Advanced Calculus or Real Analysis at the undergraduate level. Knowing how to write proofs is very important before jumping into analysis, but these are always fun to look at even if you aren't an expert at proof writing. I hope you enjoy this video.
Here are the books.
Principles of Mathematical Analysis by Rudin amzn.to/3VicMKf
Advanced Calculus by Buck amzn.to/3EueMbI
Advanced Calculus by Fitzpatrick amzn.to/3VhmzQW
Understanding Analysis by Abbott amzn.to/3ACUDPl
Useful Math Supplies amzn.to/3Y5TGcv
My Recording Gear amzn.to/3BFvcxp
These are my affiliate links. As an Amazon Associate I earn from qualifying purchases.
**********Math, Physics, and Computer Science Books**********
Epic Math Book List amzn.to/3F98vT1
Pre-algebra, Algebra, and Geometry amzn.to/3FdbwSn
College Algebra, Precalculus, and Trigonometry amzn.to/3UKjvfb
Probability and Statistics amzn.to/3FaaxCq
Discrete Mathematics amzn.to/3P6jPE4
Proof Writing amzn.to/3XXukxo
Calculus amzn.to/3iEH3F3
Differential Equations Books amzn.to/3Fac5wi
Partial Differential Equations Books amzn.to/3uyk1SV
Linear Algebra amzn.to/3VHiN3G
Abstract Algebra Books amzn.to/3FzLZEr
Real Analysis/Advanced Calculus amzn.to/3VIO4Ua
Complex Analysis amzn.to/3P6kbuo
Number Theory amzn.to/3UEm3vw
Graph Theory amzn.to/3BfRd5m
Topology amzn.to/3BiAGhe
Graduate Level Books amzn.to/3uv1eIg
Computer Science amzn.to/3Hh8kaU
Physics amzn.to/3BhPCMp
These are my affiliate links. As an Amazon Associate I earn from qualifying purchases.
If you enjoyed this video please consider liking, sharing, and subscribing.
Udemy Courses Via My Website: mathsorcerer.com
Free Homework Help : mathsorcererforums.com/
My FaceBook Page: / themathsorcerer
There are several ways that you can help support my channel:)
Consider becoming a member of the channel: / @themathsorcerer
My GoFundMe Page: www.gofundme.com/f/support-ma...
My Patreon Page: / themathsorcerer
Donate via PayPal: paypal.com/donate/?cmd=_s-xcl...
***********Udemy Courses(Please Use These Links If You Sign Up!)************
Abstract Algebra Course
www.udemy.com/course/abstract...
Advanced Calculus Course
www.udemy.com/course/advanced...
Calculus 1 Course
www.udemy.com/course/calculus...
Calculus 2 Course
www.udemy.com/course/calculus...
Calculus 3 Course
www.udemy.com/course/calculus...
Calculus 1 Lectures with Assignments and a Final Exam
www.udemy.com/course/calculus...
Calculus Integration Insanity
www.udemy.com/course/calculus...
Differential Equations Course
www.udemy.com/course/differen...
Differential Equations Lectures Course (Includes Assignments + Final Exam)
www.udemy.com/course/differen...
College Algebra Course
www.udemy.com/course/college-...
How to Write Proofs with Sets Course
www.udemy.com/course/how-to-w...
How to Write Proofs with Functions Course
www.udemy.com/course/how-to-w...
Trigonometry 1 Course
www.udemy.com/course/trigonom...
Trigonometry 2 Course
www.udemy.com/course/trigonom...
Statistics with StatCrunch Course
www.udemy.com/course/statisti...
Thank you:)
![[TH] 2024 PMWC x EWC Group Stage Day 3 | PUBG MOBILE WORLD CUP x ESPORTS WORLD CUP](http://i.ytimg.com/vi/VnOqutfqWqU/mqdefault.jpg)
It’s so interesting looking at more complex math books. I’m barely beginning my mathematical journey with basic algebra and I’m super excited to get into higher level maths in the coming years.
@@maalikserebryakov lol
Learn some calculus in p6, you’ll understand it
That is great to hear! Don’t give up!
I would only recommend Baby Rudin as an intro to Real Analysis to someone that was my worst enemy. I think there are better (and more modern) alternatives. For example, Tao’s both volumes, Charles Pugh’s Real Mathematical analysis, or if you want to study graduate level real analysis, Sheldon Axler recently published a book on Measure, Integration and Real Analysis pitched at that level. All of them are way more pedagogical than Baby Rudin, they’re written in Anti-Bourbaki style, ie, they’re written to be understood first-hand.
Well, that’s just your opinion. The Rudin book is IMO the greatest introductory analysis book ever written, and people should take it seriously, live breathe and eat this stuff. If they can’t, they should find some other line of study. It’s that great. I remain in deep respect of it, so many years later.
Pugh is great- Axler also looks very good, but I'm not quite up to its level yet. See my post above about Ethan Bloch's introductory text. Also worth a look are the free undergraduate and graduate texts by Bruckner and Thomson - I've browsed them rather than studied from them, but they look like detailed, thought-provoking, and enjoyable presentations.
@@declanfarber it is terse to the point of being uninteligible and lacks motivation. Mathematics does not consist on a laundry list of definitions, proofs and theorems without motivation in-between. That’s what makes Baby Rudin good as a reference since you already know what’s going on. As a first exposure to the subject there are way better alternatives to learn from.
@@declanfarber That is just your opinion too. The lack of motivation and details isn’t great for a beginner. I avoided Rudin in undergrad and so did my PhD thesis advisor - it is not for everyone.
@@nickknight5373 never heard about those texts. Thanks for mentioning them. Pugh is phenomenal, and it does what Baby Rudin fails miserably: it is carefully written to be pondered and internalized, not as a laundry list with some discussion squeezed in between. The sad part is that most math texbooks fall into the latter category, since most derive from lecture notes written by instructors, ie, they’re not written to be read directly, but rather as a complement to those lectures. Other texts that avoid this pitfall asides from the ones I’ve mentioned are Spivak’s Calculus or Aluffi’s Chapter 0 and Algebra Notes from the Underground.
Who else was waiting for the easiest? 😜
Abbott
The Jay Cummings long-form textbook on Real Analysis would have been a great inclusion.
Yes!
@@TheMathSorcerer where would you have put it in the list?
@@TheMathSorcerer did you review the Zorich ?
My favorite goes always to Analysis book. In french system math major, if you choose "pure" math, you have to take Real Analysis (Analysys 4), Differential Geometry, and Abstract Algebra.
Calculus is mandatory in 2 first university years.
Your great math books remind me my university math battle and joy: doing math everyday ... many hours a day.
Hey, Math Sorcerer, have you ever heard of/considered doing a video on the Mathematics for Self-Study books by J.E. Thompson? Record has it that they're what Richard Feynman used to learn math and they were part of the reason for his nearly perfect math grades.
Oh wow I did not know that. I have several of those books and they are awesome!!! I will make a video on them. Thank you!
@@TheMathSorcerer NP.
This is fantastic I especially like the rudin book
A book I found very readable is, A First Course in Mathematical Analysis by David Brannan, (CUP 2006).
Really enjoyed this video. Have you reviewed Advanced Calculus by Avner Friedman. I'd be very interested in your opinion. Thanks
That second book is exactly what I've been looking for!
Mathematical analysis by apostol is really clear. I was frustrated by other books but this one I understood everything easily.
Great video! I have been trying to brush up on real analysis that I learned ~ 2 years ago before I start studying complex analysis next semester. I have a paper copy of “Baby Rudin” that I have been reading through, and although I love the rigor and structure of the book it is definitely a hard read. After reading through a chapter, thinking I understood it, I still have no idea how to tackle the exercises. Maybe it’s just me, but I am struggling a bit. I really feel what you said at 1:26. Though I was able to find a compilation of solutions to the book online. I will definitely look into Abbott’s book 8:20.
I'm currently (after a looooong gap) reviewing Real Analysis, primarily using Ethan Bloch's text. I have some issues with it, especially compared to Pugh's very friendly and breezy presentation: Bloch takes slow and steady to an extreme, and has a notion of simplicity which entails using some very inefficient proof methods; it's also 1D only. On the other hand, it has a clarity and a breadth and depth of perspective that I haven't seen in other texts, especially with regard to building up the real numbers, but also throughout the text. It also has a particularly strong didactic quality arising from its target audiences, which are both undergraduates but also secondary school teachers looking to solidify their foundations.
Another good looking text is the introduction by Bruckner and Thomson - I haven't studied from it, but it's free and gives the impression of a very thorough and thoughtful presentation. They also have a graduate text which looks fabulous, but I'm not ready for it yet.
Here in France we have some fantastic mathematics books, most of which have never been translated.
It helps to know that there are several streams of mathematical education:
1) A two year intensive course as a preparation for the engineering schools ("Grandes Ecoles"). Once you get into one of these schools the schools have their own curriculum. In fact they throw so much at the students it is almost impossible to follow everything.
2) The more "leisurely" "licence" which is a 3 year degree (like a bachelor's). There is a lot of stuff to learn. In particular they teach differential forms in 2nd year.
I'd like to give you a feel for it by a scan and OCR of the table of contents of one of the best series of books for the Licence : By J.P. Marco, L. Lazzarini, H Boualem, R Brouzet, B Elsner, L Kaczmarek and D. Pennequin. I can do that in 2023 when I have access to a scanner and OCR software.
The books have very detailed proofs of most theorems: very little handwaving.
The French system has a particular style: emphasis on rigour and formality and they expect you to master one level before moving onto the rest. The abstract aspect may be going a bit far at times, in that visualisation is discouraged.
If you sweat through all of this, you will be able to prove theorems with a high degree of rigour.
After the licence there is the maitrise where more advanced subjects are dealt with, and I get the impression that you can often start to enter into the word of research, at least for some subjects, but not for stuff like Grothendieck.
what are some titles of those books for L1 informatique
I'D like to see another live stream. I missed the last one. I like Blitzer books and didn't know about them until I saw these videos. Now I've ordered the Sullivan book Algebra & Trigonometry.
Oh Sullivan is so good! That's a GREAT choice!!
It's funny you mentioned a live stream. I was thinking I should do one!
@@TheMathSorcerer I hope I don't miss it next time. These videos are so good about giving us ideas what math books we might be interested in.
Can you do a similar video for linear algebra, probability & statistics?
I graduated with my bachelor's degree in mathematics on Saturday which I'm pretty excited about. I plan to attend graduate school for mathematics during the fall semester of 2023.
congrats!
Congratulations! Math grad school can be hard esp managing your time if you are a new TA, Make friends! And understand what the department requirements are: how many sequences you have to take, how many prelims, and so on.
Consider reviewing
2-Volume Mathematical Analysis, by Zorich
3-Volume Analysis, by Herbert Amann
And for the serious mathematicians:
9-Volume Treatise on Analysis by Jean Dieudonné
Hello, great video! What is your opinion on Kolmogorov's analysis book?
I used Apostol Mathematical Analysis and Dellillo Advanced Calculus with Applications back in the 1980s. I hoped you would look at those.
Excellent excellent books I will definitely look into them
The 2nd edition of Abbott's book is a bit thicker with some added content. As far as solution availability, Springer has solutions to the exercises for professors. That's all I know about solution availability.
I have the 2nd edition of the Abbot's book published in 2015 which I bought from Springer Verlag (German publisher). Every year from March to June/July, Springer's yellow book sales offers some mathematics books at a discount of 50%, many are worth buying at such a low price. I also have the instructor solution manual for the 1st edition printed 2004. I was previously going to read Abbott's book but now I think I shall start Buck's book instead. Thanks for the video advice.
Oh wow that is interesting about the sales. I will have to check that out. Thank you:)
i just got it online for free, just search the book name followed by pdf....
Have you ever covered Khinchin's "Eight lectures on mathematical analysis"?
I can't remember that (I suppose that because it's very hard to find in paper), so I decided to write about, I think it is really worth the mention.
I recognized it at the 1:28 moment as the very opposite to Rudin. Whole book is dedicated to the simplest possible explanation of essentials and motivation behind the proofs and the way calculus is organized taken as a whole.
In case if anyone reading this haven't heard of it, but already interested in this, the preface says about the book better than me:
"We frequently encounter a situation in which an engineer, teacher, or economist who has at some time studied higher mathematics in a “simplified” course begins to feel the need for a broader and, what is more important, a more solid foundation for his mathematical knowledge. This need, whether it arises out of specific research by the specialist in his own scientific field or comes as an inevitable consequence of the general widening of his scientific and cultural horizons, must of course be satisfied. It might be supposed that the specialist might easily satisfy his need; he could merely take any comprehensive text on mathematical analysis and study it systematically, making use of the rudimentary knowledge he has already acquired. However, experience shows that this method, which seems so natural, almost never leads to the desired goal but instead often brings disillusionment and a consequent paralysis of any further effort. For such a student usually has only limited time at his disposal and therefore cannot undertake to work systematically through a full-length textbook. On the other hand (and this is probably the most important factor) he does not yet have a firm grounding in mathematics, and therefore he cannot, without outside help, pick out the essentials. He will be compelled instead to devote his attention to irrelevant details, and in these he will finally get lost, unable to see the forest for the trees."
"I renounced from the very beginning any idea of presenting even a single topic in full detail: instead, I limited myself to a vivid and concrete presentation of the essential points and spoke more of goals and perspectives, of problems and methods, of the connections of the fundamental notions of analysis with each other and with their applications, than of individual theorems and their proofs."
"This book has the same goal as the course of lectures I have just described, and tries to realize it by the same means. The reader should therefore be warned from the very beginning that he will not find here a complete presentation of a university course in analysis, or even of individual topics selected from such a course. I have set myself the task only of giving a general sketch of the basic ideas, concepts, and methods of mathematical analysis. But I have tried to make this sketch *as simple and as easy to retain as possible*, to make it something that can be read and assimilated by anyone familiar with even the crudest exposition of the subject, and one which, once assimilated, should enable the student to study the details of any part of the subject independently and effectively.
At the same time, I hope that this book may also be of real benefit to many students in the mathematics departments of universities. Neither a text nor a lecturer, limited as they both are by the exigencies of time and the program, can pay enough attention to the discussion of fundamental questions; both are compelled to concentrate on the exposition of all the details of the material they cover. And yet everyone knows how useful it is sometimes to turn one’s eyes away from the trees and look at the forest. I would like to believe that this book will help to reveal that broader view to more than one future mathematician who is studying analysis for the first time."
Here is the book in for free: archive.org/details/khinchin-eight-lectures-on-mathematical-analysis
🥰
P.S. I also highly recommend these essays by him, very interesting to read for a bunch of reasons: it's about teaching math; it's aged by 70-80 years, but its range of aspects is not so, and some are still issues of the day; etc. archive.org/details/khinchin-the-teaching-of-mathematics
What about Terrence Tao's Real Analysis book I and II? I thought these were great. Where would you put Terrence's book in terms of difficulty mentioned in this video?
What is the conceptual difficulty with Real Analysis?
My exposure to Real Analysis was limited to the introductory material in my Freshman Calculus text (Marsden & Weinstein) which gave basic arguments that differentiation and integration are legal operations. It was very geometric and intuitive.
I would like it if you mentioned the publishers of the books you review. I have learned what to expect from, say, Wiley, or Springer, or Addison-Wesley, or Dover, in terms of design, editing standards, organization, and so forth. To me, the publisher is an important feature of any book.
@TheMathSorcerer; what about maths-for-dyscalculia ?
On other topic, the TH-cam Channel Math the Beautiful had an excellent presentation on tensor operations. The author piblished a book which was based on this series.
Thank you very much for the wonderful channel!
Bellísimos todos!, en español solo conozco Rudin.
Thanks. I thought Advanced Calculus is a Calculus book. Now, I am going to start reading Buck's book soon.
Excellent!
Yes, math sorcerer please make a video on J.E THOMPSON'S maths self study books.
Specialy trig and calculus
Baby rudin is very good! The second chapter on topology is awesome too!
If you've read it before, what do you think of "Analysis with an introduction to proof" by Steven R. Lay?
I've read that book cover to cover. It's a very gentle introduction to single variable analysis..... almost too gentle. It's an excellent first book and prepares one for more difficult textbooks... maybe supplement it with Schaums Outline "Real Variables" for harder problems with solutions.
About Bartle's and Spivak books, what position would they be ranked?
What about the Terence Tao ones?
How about A Course of Pure Mathematics by G. H. Hardy?
Greetings Mr.Professor,
Thanks for the Wonderful Overview of Textbooks on 'Analytical Mathematics' .
Good Pick/Choice = Fitzpatrick - Advanced Calculus.
Take Care,Professor.
With regards,
RanjithJoseph (R.J)
Mathematical Analysis by Tom M Apostol is a worthy inclusion. Its not too tough but it definitely prepares one for Analytic Number theory.
A few suggestions I have are Herbert Amann, Zorich and Courant. These titles are quite popular in Switzerland.
A very good follow up to Abbott that does multivariable (correctly IMO) is by Jerry Shurman's "Calculus and Analysis on Euclidean spaces". Those two books along with Linear Algebra Done Right by Axler give an excellent foundation. Duren's Invitation to Classical Analysis covers some interesting topic that Abbott didn't do in his book like Zeta functions, Bernoulli polynomials, Peano curves, Elliptic integrals etc. and makes a good supplement.
Your thoughts on Bartle-Sherbert?
Have you looked at Frank Dangello and Michael Seyfried Introductory Real Analysis?
I think is pretty good, clear explanations, examples and includes solutions!!!
Great posting, Congratulations and Thank you!!!
Have you reviewed Stromberg’s _An Introduction to Classical Real Analysis_? I’ve heard that’s one of the most elegant analysis books ever written and includes some of the best problem sets out there.
_ACICARA_ , _Introduction to Calculus and Real Analysis_ by Hijab, and _Fundamentals of Abstract Analysis_ by AM Gleason. Gleason was a full-blown genius with the humility of a saint: he stated exactly how many years it’d take him to solve a Hilbert problem (8) and why, then solved it in 8 years. He was once described by Turing as the “brilliant young Yale mathematician”. His analysis book contains all or almost all solutions to problems in the back. He has possibly the clearest writing style of any mathematician I’ve read. And he seemed like a genuinely kind man.
You should check out about nonstandard analysis by Alain Robert
Concerning the blue book, What's the use of a book that doesn't explain it's thinking, and without examples that actually cover the possible complex permutations of the concept it's teaching? It's kind of useless or very tedious and not realistic if the exercises clearly outstrip the lessons
Well you started to compare single and multivariable aspects dealt with first 2 or 3 books but in general rudin apostol strichartz books cover the cases of complex variable aspects as well such that those theorems also cover complex variables. That's a good advantage. Because we don't need to cover semester full of complex analysis in this process.
I also read Baby Rudin theorem-by-theorem. Yes, it was hard. And it was slow going. But worthwhile. Papa Rudin is harder and Grand-daddy Rudin is beyond me (currently). The Rudin books have become a goal for me to get through and its been more difficult since leaving school.
What is Grand-daddy Rudin? I assume Real & Complex Analysis is Papa Rudin.
@@enisten 'Functional Analysis'
Next videos, top 4 linear algebra books
Springer math books look so good. :)
Help me I need a book to understand black scholes model
You need the full Calculus sequence from Single Variable to Multivariable, Linear Algebra, Differential Equations, then Partial Differential Equations
@@lukeatlas5337 thx!
rudin real and complex analysis, folland real analysis, brezis functional analysis, sobolev spaces and pde are some good books owo
I remember when it took 2 days for me to go through a couple sections of Rudin a while ago lol. I switched to Elon Lages Lima since then.
Bartle is easy and intuitive. I did beginners calculus with Loomis, then bought other books to do the problems, mostly. Older editions of Bartle include the Cantor set. I think the latest ones don't.
No love for Bartle and Sherbert? That was my book back in college.
Good list but I MUST add “Elementary Classical Analysis,” by Jerrold Marsden. This was THE intro analysis book at UC Berkeley and other UC campuses in the 1970’s and 1980’s. Marsden was my prof at Cal, and in the nineties (I believe ) he went down to CalTech. A great mathematician and teacher. His book is the best intro analysis text I’ve encountered. Its format is extremely student-friendly. He gives the main theorems followed by helpful applications, but delays the proofs of chapter theorems to the end of each chapter after the student has used the theorems in many problems, and after his nice examples. His proofs are very detailed and carefully explained-Marsden knew this course was probably each student’s first-ever exposure to the topology of R^n, as well as to to “calculus proofs” using epsilon-delta, so he treads gently for the smart-but-inexperienced. I have cherished my copy for 48 years!
Lang’s analysis has all the solutions so it’s good for self study. How good do you think that book is?
Plss can you review Real analyis brilliant version by DR Sharma???👍
Two books that were omitted:
For the single-variable calculus, Spivak's Calculus.
That seems generally admired.
For multi-variable calculus, or calculus or analysis on vector spaces, there is
Lang's Undergraduate Analysis.
I like that book, but opinions do seem to differ.
I wonder how Math Sorcerer would compare it to Rudin or Buck.
Lang has a sequence of five books:
A First Course in Calculus (single-variable; few if any proofs)
Calculus of Several Variables (multi-variable, over R^m, R^n; some proofs)
Undergraduate Analysis (over normed vector spaces; everything is proved)
Real and Functional Analysis (Lebesgue, etc.)
Introduction to Differentiable Manifolds
The first text is really easy, just about anyone with a half-way decent high school education should be able to read and understand it.
After that, the level goes up.
The last two are at the graduate level.
(He also has a book on Complex Analysis, which I would rate at the college senior level.)
I know of stephen abbot too
rudin is the best book, i do all the exercises 2 days before my midsems and it really teaches me how to write crisp proof and solve problems. Obviously u dont want to start learning analysis from this book. It is good for reviewing stuff or revising the,, professors are best for teaching, kudos to them!
You must read "Curso de Analise Vol. 1 and 2" by Elon Lages Lima
Issue:
What is a differential of an irrational argument?
Let a= some rational approximation, and A be the irrational number itself (if that makes sense).
Then A - a > dA and there is no way a + dA > A
should i take real analysis before complex analysis?
I think it depends on the complex analysis course and/or book. Some complex analysis courses/books require or recommend real analysis, or even topology. Others require just multivariable calculus. Often these latter course/books have "complex variables" in the title instead of "complex analysis" but that isn't a hard and fast rule.
Rudin's book is not of the same level as ' Abbott' and the advanced calculus books. These last three are in a level way below the Rudin's book. Rudin's book is a "baby book" in real analysis, one of the hardest courses in math.
A treasure in hand.
I want to improve my math but I don’t even know where to start can anyone help me??
First, focus on a specific part of math that you want to learn or improve your ability to handle. Think of something you struggle with.
Once you've thought of a few topics you'd like to work on, look for something that has an extremely easy explanation of it. The explanation doesn't have to be from a really old or famous book. It could be from a TH-cam video, or it could be from a post on a math tutorial website.
Try to follow along a few example problems on one specific topic. If they don't make sense, either revisit the explanation or try to come up with your own interpretation of it.
If necessary, show that something hold true in a particular case. Then check to see if you can make a general rule out of that case. If it holds true for some cases, but not all, then state the type of cases that it does hold true for.
Afterwards, try to solve more problems using the "trick" you either took from someone else or had to come up with yourself. Once you are sure you've got the method right, go ahead and solve more problems and go through many more exercises in varying difficulty levels until you feel confident that you can approach any question on that topic.
If you ever come across something that seems like you're not quite getting, be it because you're missing important prerequisite knowledge, or because you think it's not being explained simply enough, then check the following:
1. Find out if there are any other topics you should have learnt about prior to the one you want to aim at, so as to cover any gaps in your knowledge
2. Look for another learning resource that has an explanation for the same topic
3. Make sure to pay very close attention to explanations and put as much mental effort as possible to getting a clear "picture" of what you're trying to learn about
If everything else fails, try to see if there's an easier, but related problem you can solve that can give you an idea of how it worksm
There are legendary volumes on Analysis from G. M. Fichtenholz, which saved lives of many mathematicians.
I think this series is based on the Rudin book. One of the few complete Real Analysis series I could find: th-cam.com/video/sqEyWLGvvdw/w-d-xo.html
Wow that is so cool, thank you for sharing.
@@TheMathSorcerer np. video quality is not good, which you'll see people asking for updated versions in the comments, but it's the best we have for now, and better than just trying to figure out the book on your own.
Working through Analysis theorems is easy. Solving all the problems is another story. You can understand the theorem, know in principle that it's applicable to a problem, but still not see the trick to get the solution.
Your channel is costing me so much money...
Huh, no Apostol?
Rudin's book is great for someone who already knows analysis
Patrick fitzpatrick I know who that is I don't know him personally but I know of him
Just tossing in my 2 cents, Baby Rudin is tough for a first intro.
Abbott is nice but to mild or do not support all aspects of a undergrad Real analysis class
Anyone else think that Schlomo Sternberg's book on real variables is even tougher than Rudin?
Real Analysis by SK Mapa is a decent book on the subject. I would recommend you to have a look at it.
Dear Math Sorcerer,
Please help me! I can't stop buying Math books!!! 😅🤣❤️
Seriously! It's so addictive! 😅
Maybe you should do a video on budgeting tips for bibliomaniacs! 😅
Haha I know the feeling. I've been buying other types of books now too! I need to stop LOL. I recently got a philosophy book and a book on bees.
@@TheMathSorcerer That's funny, because Philosophy & Entomology books were what I used to collect before you got me into Math books!!!
Apostol>Bartle> Rudin
first
Clearly these books are options, but not for students at a run of the mill US university.
Is baby Rudin harder the papa Rudin?
Papa Rudin is way more advanced.
No, technically papa Rudin will be more difficult because it includes Complex Analysis topics. Baby Rudin will be easier because it stays within the Reals. Although the math prof that trained me said papa Rudin is his favorite book, but he said that kind of book is only appreciated after you truly understand analysis very well.
Luckily in Europe we don't have Calculus and Analysis separetely. When you start your journey of math major, every subject is proof based and hard like Real analysis.
Rudin's book is absolute garbage if you're new to analysis. It's almost a meme at this point that people still recommend this garbage. It's not suited for researchers either, as there is a plethora of better books for this purpose. It's a hybrid suited for basically no one.
BEFORE GOING TO AMAZON/ABEBOOKS when books are recommended by even small channels the jump in views that a book gets can spike the price by a lot. It might be worth holding off until they go back to normal, or checking the uni library