Learn Real Analysis With This Excellent Book

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In this video I will show you a very interesting real analysis book. This book is excellent for anyone who wants to learn Real Analysis on their own, or anyone who is taking an Undergraduate level course on Advanced Calculus/Real Analysis. The book is titled Real Analysis: A Long-Form Mathematics Textbook and it was written by Jay Cummings.
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24 ноя 2022

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Комментарии : 188

@terrylewis5786 Год назад

Wait a darn minute! This great book only cost $16 ! An easy decision to purchase. This is a no-brainer. Thx 😊

@benhill3098 Год назад

I got that real analysis book a few months ago. I didn't know what to make of it then, but I'm glad it has been approved as an excellent choice! I'll definitely use this book as a supplement for my future undergrad studies on the subject, along with the works of Fitzpatrick and Buck (which I will receive next week), Tao, Ross, and more. I appreciate the organization and clarity of this book by Cummings and the author's acknowledgment of their students in the book's editing. Thanks!

@seanhadley5452 Год назад

A coworker gifted this book to me! It has been absolutely invaluable for my analysis class! Its been an absolute pleasure to read! Truly enjoyable. You're almost downplaying how fun and humorous this book is! Anyone taking an analysis course should have this book on hand!

@williamsteph2104 Год назад

Very cool to see so much diligence put into a textbook!

@purelyconstructive Год назад

Always coming through with the amazing book recommendations!

@ikechukwumichael1383 Год назад

I love you videos. Thanks for making Mathematica open source

@Pteromandias Год назад

Oh good. I just saw this video. Having watched some of your videos about good math books I looked back at my shelves to see if I had any. I have a Serge Lang book and some others, and decided to take a few back with me where I am staying in Antarctica for the next year. I picked up this book and the companion book about proofs a while back, and they looked interesting so I packed them both in my travel bag. A the plane is taxi-ing right now, I am happy this one is sitting in the overhead bin as I write. Glad to see I made a good choice.

@numericalcode Год назад

Really good view of the actual content in the book. Thanks!

@adumont Год назад

Thanks for this review. I studied maths a long time ago, and this review made me want to buy the book! When I saw it was that affordable, I couldn't resist. I'm sure I'll enjoy it a lot! I hope Jay will keep writing such excelent Maths books. I'd love to read one on Topology or Álgebra. Right now I can't wait for this to arrive and start reminiscing my Math studies. Thanks again

@Diranlou Год назад

Great! thank you for introducing the book.

@argonwheatbelly637 Год назад

Wish I had this when I took RA. This looks great!

@Crazylust Год назад

I have this book and there’s no answers to the exercise. It’s stupid to not have answers to the problems since I learn by examples and that defeat the purpose to learning without any solutions. However, if this book have answers to the exercise, it would’ve been a 10/10. For me, it’s a 7/10.

@joehudson440 Год назад

Hi math sorcerer. I admire your motivation of mathematics because it aspire students to pursue further studies in math.

@andreashartel5577 Год назад

Thanks for this video! Would love to see a video on Cummings' Proofs book!

@Maths_3.1415 Год назад

Thanks for recommending these types of books sir :)

@user-hy6cp6xp9f Год назад

Your channel is a little wholesome gem. I have always loved math, but was not able (or maybe not focused enough) to major in math. I love the quiet little world of solving problems and collecting books, divorced from the politics and stress of the world. Keep it up and keep smelling books for us :)

@nerd26373 Год назад

The Real Analysis will certainly help out a lot of people. Thank you for your consistency.

@TheMathSorcerer Год назад

@thegoofiestgoooberr 8 месяцев назад

@@TheMathSorcererwhich do you think is better between this and kolmogorov? (i already have kolmogorov)

@satyavivekanandbattula1091 Год назад

Thank you Sir. For sharing about that book. Useful video.

@charleswoodard8478 11 месяцев назад

This book has been, for the most part, a pleasure. I enjoyed the derailment in series for Cesaro summability, which gives the reader a firmer intuition of a particular arrangement of a conditionally convergent series.

@poincare5350 Год назад

I bought this book more than one year ago. In those days I was thinking that this book could support me to finally learn RA by my own. Unfortunately, my scholar obligations (PhD in electrical engineering) has demanded a lot of time to me, I finish every day exhausted. I hope when this finishes I can approach to this book, and be able to get the basics of RA.

@ahmedabbas3998 Год назад

"Elements of Real Analysis" Narayan, Shanti is unique for its clarity and the number of examples and fully solved problems. Indians do excel in writing lucid math books.

@pavangaonkardonigadde Год назад

Real analysis is one of the reason for me to get into mathematics

@StaticBlaster Год назад

I have "proofs" by Jay Cummings. It's a pretty good book.

@TheMathSorcerer Год назад

yeah I like that one too:)

@ryans7536 Год назад

This is the book we used when I took real analysis, it’s an excellent book and very well written!

@mukfu Год назад

Thank you. I'm a self learner and want to study a bunch of math but stuck on note taking strategies, both from the perspective of note taking for individual topics but then more systemically so it can be referable and searchable. Example issues are do I try to build a table of contents, do I use loose leaf so I can create my own "books", do I use notebooks, etc . I don't think digital approaches make sense b/c their too cumbersome and slow in the note taking process. A video on best practices, tips, tools, etc for someone who is building their own curriculum (based on your recommendations I should add)!

@mcmulazz1060 5 месяцев назад

I bought both the book and the book stand in your thumb nail! The funny part is that it was before I saw this video lol. Every self study student needs one of those book stands.

@tideoo8823 Год назад

I bought this book exactly a couple weeks ago! I was surprised not many people have heard of it and was wondering what other people thought about it. So the timing of your video is uncanny. Thanks!

@navierstokes2356 Год назад

Where is the review of Abbott's Understanding Analysis? 😢

@athanasiospapoutsis9978 Год назад

This is an amazing book, very pleasant to read. I bought both "Proofs & Real Analysis". I would love to see a book from Prof Cummings for Multivariable calculus!

@schrodingcheshirecat Год назад

I purchased both this and his proof (long form) books. highly recommend both

@AbElsaied Год назад

Really great video as always thank you. You may consider making a video or video series about books which is really for teaching not just dropping information and theory after each other (like most of the main stream books). Some books have friendly tone, verbose and talkative with clear conscious concepts (the one I miss most) and friendly approach to a first time reader for the subject so it would be great if you cover different areas and subjects with such books.

@coolrunnings617 5 месяцев назад

I agree

@vjjorque1610 Год назад

I want this now!

@SequinBrain Год назад

0:15 Before my first book, I knew there was no way anything I did would be an improvement on any book currently written, mostly due to the low probability that I've read every book that's out there for comparison. So, knowing this, what you CAN do is supply your own combinations of words and symbols that you've found helpful, faster, unique, or any other beneficial quality to create your work. If nothing else, since what you know comes from what you've studied, there's a low probability that your readers have read the same things, and those tricks and explanations will be entirely new to them. Or, you could create an explanation that you've never seen before, then you know for sure no one will have seen it. Just food for thought if you get bored and decide to cogitate publishing anything.

@jferfreiccp Год назад

Thank you 👍🏼☺️

@adoxographer Год назад

I agree. I used this book and it is excellent. He also has one on introduction to proofs.

@gloriosatierra Год назад

Nice book but it is more of a workbook. The beginning of Series Chapter reads like notes. I want history, drama, definitions, speculations, insight… you know, what Mathematicians crave.

@wilhufftarkin8543 Год назад

Cool, I wanted to suggest that you make a video about this book. This is how a math book for beginners has to be written.

@erichong3430 Год назад

I'm not sure if its still the case, but gold standard for real analysis during my college year was Rudin. Its a great companion text if you're taught by someone who knows what they are doing. But it can also be a source of tremendous pain if you're not, or if you're trying to learn it alone.

@georgesealy4706 Год назад

Thanks for this review of this book. I put it in my Amazon shopping cart. It always bugged me that I was not better at Real Analysis. I was an engineering student firstmost and when I reached my junior and senior years I was engaged in other high-powered courses. Later in graduate school, I got involved in higher mathematics; frankly, I didn't have a well-grounded background in it. So here is another reason to buy this book: how about an old guy who has a score to settle and an itch to scratch. LOL.

@douglasstrother6584 Год назад

"Alright, ε-δ Proofs, come at me now!"

@briang.valentine4311 Год назад

The first graduate year "real analysis' texts usually cover choice axiom and continuum hypothesis is first chapter, then Lebesgue measure, Lebesgue integration, topological spaces and their relations to metric spaces, abstract analysis on Hilbert and Banach spaces, product measures. This book would be good for the first semester of the typical undergrad "advanced calculus" course.

@gopalparam6401 Год назад

Dear Math Sorcerer, Greetings from India and I want to thank you once again for inspiring others to learn not just mathematics, but learn in general. I subscribe to the notion that "true knowledge is without borders" and mathematics is no exception. It should include proper and just compensation for the tremendous effort that authors have exerted in writing the book. However, the book seller market place is fraught with inequalities. Since you are discussing Mr. Cummings work, a book that is on my wish list I would state the following. His Real Analysis and Proofs book sell for around $ 17 each in the USA, but in India they are $21 (reasonable) and $50 (unreasonable) respectively. The exorbitant price difference of almost three times the price for a preparatory book to Analysis, which is proof writing, in a country where it should be cheaper by the sheer size of the market place, smacks of price gouging that is inexplicable. I have brought this to Mr. Cummings attention and want to share this with you to have calm and reasoned discussion to solve these unfair pricing policies. Thank you once again for your wonderful guidance.

@AnandKumarRavi Год назад

As a math major I absolutely endorse your point!

@jidrit999 10 месяцев назад

bhai online free pdf hai

@extreme4180 5 месяцев назад

@@jidrit999 hm whi toh aur uska print karwaane pe bhi sasta padega T_T and i prefer rudin

@thomasblackwell9507 10 месяцев назад

That edition of Earl Swokowski’s Calculus gives me flashbacks to a happier time, thank you.

@jaydenclowers2616 Год назад

This book in more connecting then the others you have mentioned in other videos

@seraphimwang Год назад

Thanks!

@TheMathSorcerer 10 месяцев назад

thank you!

@paradox_1729 Год назад

Ah at last you come to these two. I have been wondering if they were a good book for a while.

@swordofstrife1174 Год назад

This is the book I used to learn real analysis! Its honestly amazing, the explanations are so clear and this guy has a great sense of humor

@jamieg2427 Год назад

would you recommend i read an intro to proofs before trying cummings's book? or just jump in?

@stephenhu2000 Год назад

@@jamieg2427 I'd probably just jump in. If you're feeling like you need more background, then go do intro to proofs instead. Cummings himself has a proofs book which is also good, and book of proof is excellent and free online

@user-rz4sd3xt7f Год назад

I wish i had this book during my undergraduate course

@hhht7672 Год назад

I love Jay Cummings he also wrote an intro to proofs book that I’m using for class right now, it’s real good and the humor really keeps you going

@11seth11b Год назад

He seems like a great author! Would you recommend the proofs book to someone who has never done proofs before?

@TheLethalDomain Год назад

@@11seth11b No doubt about it. Begin with his book of proofs and then jump into his book of real analysis.

@guillermo3412 Год назад

you love whaaaaat

@11seth11b Год назад

@@TheLethalDomain sounds like a plan! Thank you

@hhht7672 Год назад

@@11seth11b for sure! It's very beginner friendly

@academyofuselessideas 6 месяцев назад

I've read the Proofs book by Jay Cumming and I found it really refreshing. I checked out the first pages of this analysis book and it also seems great... Jay Cummings's love for mathematics transpire through his books... I wonder how was the experience of people self studying real analysis from this book, and how they felt about their journeys!

@JB-in4dj Год назад

I had him as a teacher! Very clear.

@TheMathSorcerer Год назад

Awesome!!!

@TheMathSorcerer Год назад

You could have him sign your book! Lol

@JB-in4dj Год назад

@@TheMathSorcerer Lol yes I can ask! haha

@maowiisenseii1470 Год назад

I say, this book + the long form proof are rival-able to baby Rudin: gold star!!

@RhynoBytes857 Год назад

How does this compare to Understanding Analysis by Stephen Abbott? I've also heard that one is very easy to read, and if you haven't looked at it yet, I'd love to see a review on it!

@williamhutsch851 9 месяцев назад

Not the biggest fan of books without solutions. Yes it is important to put time into constructing an answer, but something equally important is being able to either validate or even understand the thinking required to achieve a appropriate solution.

@rk99688 Год назад

Can you also do a video on topics and books that I can study with the knowledge of Real Analysis (e.g Topology, Differential geometry)

@meshackgaolathe6492 Год назад

This book reminds of the Engineering Mathematics book by Stroud. It will stay around for a long time

@TheMathSorcerer Год назад

Hmm, I don't think I've seen that one yet. I will look for it. Thank you!!!!

@edgardgrydnyev3508 Год назад

Hello math sorcerer I don’t think you will read this but I have seen you show books on many topics, however I haven’t seen you show many books on geometry and none in geometry that is above high school. Could you show some books in differential geometry or in fractal geometry someday?

@TheMathSorcerer Год назад

Hey yes I will do that! I have a few geometry books as well as some on differential geometry. Thank you for this comment!!!!

@brandonfox9618 Год назад

I actually own that book that I got years ago!

@DingDong-fq2mo Год назад

Thanks. I'm interested in a review of his proofs book.

@alexar6860 Год назад

Hi, Thanks for another review!, i wanted to ask, I'm a freshman in mathematics, but i also like physics, what are your thoughts about double majoring math and physics?. Much props from Venezuela!

@bengtbengt3850 Год назад

Great video as always. Are you going to do a review on Folland's Real analysis?

@TheMathSorcerer Год назад

great idea!!!!!!!

@boogerie Год назад

Now can you do a review of the author's proof-writing book?

@TheMathSorcerer Год назад

Yup will do!

@FrancoisPesce Год назад

Nice review! Seems like their students missed a typo on page 63 (8:15 in your video) paragraph 3: "Quesiton" instead of "Question". 😅

@awildstevey Год назад

Aye! I used this text as a resource during my undergrad

@mohammadmahmoud7208 Год назад

I'm planning to self learn real analysis, I'm going to get Bartle and Sherbert's book "Introduction to real analysis". Would you recommend this book more, or should I have both where they supplement each other?

@walter274 7 месяцев назад

I had analysis from fitzpatric also. I don't think my prof had taught it before, and he just wrote the book on the board. He was very helpful 1 on 1, but the book the lectures weren't great. Now as some one who has taught college level math, i always feel that the first time i teach a class it's a bit of a disaster, so i wonder how he did the next time he taught it.

@jennifertate4397 Год назад

I'm currently self-studying Cumming's second edition of Real Analysis! And yes, it's a joyful and more natural-like way of learning analysis, written very much unlike the other RA textbooks I have. More solutions are coming, according to the author (whom you can email), but the book has more "hints" than answers, and hardly any of either. Otherwise, I also recommend it highly.

@academyofuselessideas 6 месяцев назад

@jennifertate4397 Someone recommended this book to me recently, I was wondering how was your journey of selfstudy with this book, or selfstudying analysis in general!

@jennifertate4397 6 месяцев назад

@@academyofuselessideasYes, I have this book. It's great, and humorous. I've studied Chapter 1 so far, but am taking a detour to practice and learn more about proofs.

@academyofuselessideas 6 месяцев назад

@@jennifertate4397 usually mathematicians use Real Analysis (and basic Abstract Algebra) as an excuse to teach the methods of modern mathematics to students. So, it is beneficial to know more about how to read and write proofs.... Are you also using the Jay Cummings books to learn more about proofs? I read that book and I found it pretty cool... Jay Cummings loves math and explains it in a very engaging way.

@jennifertate4397 6 месяцев назад

@@academyofuselessideasI'm using Cummings along with 3 others including Richard Hammack's Book of Proof, which I like the most. It's also available for free online in PDF form I think. I bought the hardcover for a reasonable price. And all odd-numbered problems have very good clear solutions. Excellent for self-study.

@yasin-ali 8 месяцев назад

Thanks for this. How do these compare to Tao?

@ChickensBreast Год назад

I failed Real Analysis. I will take a look at this book during winter. Thank you for the recommandation Mr. Sorcerer.

@TheMathSorcerer Год назад

Awesome! I think it will help you a ton. Good luck☺️

@NNKNTA Год назад

Thank you for video. Is this book the same pure like Introduction in real analysis by G.Bartle , R. Sherbert?

@RealPi Год назад

I grew up with Little and Big Rudin, like most mathematicians but I really like Terence Tao's analysis books (1 and 2) as well. Hadn't heard of Cummings, for some reason, looks interesting, thanks

@viniciuscilla2865 5 месяцев назад

In Brazil we use the book "Análise Real" from Brazilian mathematician Elon Lages Lima

@ihmejakki2731 Год назад

Robert Adams' Calculus is used in many European universities as a standard for calculus courses, but I rarely hear you mention it! Do you have thoughts on the book?

@victorpinasarnault9135 Месяц назад

Zeno's paradox for real numbers? That is new to me.

@xaviergonzalez5828 Год назад

I'm gonna order it! Still stuck in continuity and differentiability (I dunno if I wrote correctly). Does real analysis cover all of those topics?? Thank you Sir!

@TepsiMorphic Год назад

Can you do "How to Prove it" by Daniel J. Velleman? I've read that book last summer and would love to hear your opinion on it.

@GhoshA Год назад

Real Analysis by S. K. Mapa is also a student friendly book. One can look at it once.

@raul0ca Год назад

I looked at the price and wondered when Amazon started doing Black Friday sales on Real Math Books but no that's the Real (non-Imaginary) price

@seanhunter111 9 месяцев назад

The dedication of his proofs book is also really cool. It's something like "To my loving wife, who read this whole book, apart from the maths parts".

@benjaminhogan3157 Год назад

Jay Cumming's also has a long form proof book...check it out.

@sanjursan Год назад

Sounds like a good book: the anti-Bourbaki book! But how about starting a short series on reading and writing math short hand. I like to take an interesting sentence, or a theorem perhaps, in English, and re-write it in math. Set theoretical stuff is so much easier to follow in math than than English once you get used to it. What think you, Sorcerer?

@TheMathSorcerer Год назад

Very interesting idea, thank you!!!!!!

@marcelocortez3312 Год назад

I'm aware I should be better at analysis... I really love buy this book, even though the price is good, shipping to my country is expensive:( Such good book though!

@magicmagic8188 6 месяцев назад

Based on the author I can already tell the book is climactic from front to end

@PrudentialViews Год назад

Does anyone know what math concepts I should know before learning real analysis?

@fndTenorio 5 месяцев назад

Hey Sorcerer, please review "The way of analysis" by Strichartz, it's a very peculiar book.

@isacharjones 7 месяцев назад

Is this better than Stephen Abott's book on Real Analysis for independent learners?

@shaneyaw4542 Год назад

Any math or physics textbooks that have the following words are useless: 1.) it is obvious; 2.) it is simple; 3.) clearly; 4.) the proof is left as an exercise.

@yamishogun6501 Год назад

My favorite is "trivially obvious".

@anonym498 Год назад

I'm taking an online course on real analysis from MIT and professor said we will learn to write proofs along the way. A little bit confused if should I take it

@thelilpippin Год назад

Could you recommend a real analysis book with solutions?

@cannong1728 Год назад

Hah! That's my Calculus textbook from college...which I still have! Good ole Swokowski!

@joshuatovar6298 Год назад

How do you avoid plagiarism during exam when the solution to a test problem is exactly the same as you've learnt it in a book or in class? Do we have to give credit all the time?

@TDG361 Год назад

I don't have a strong background on calculus, and been looking for a way to make it stronger, would you recomend me to use this book as a way to strenght my understanding of calculus and analysis? This seems to be a great book.

@tideoo8823 Год назад

You could try out Spivak's Calculus! A lot of people love that book and it has a bit of real analysis in it.