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Learn Real Analysis With This Excellent Book
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Күн бұрынIn 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.
Here is the book: amzn.to/3VkaNoN
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Thank you:)
@terrylewis5786 Жыл бұрын
Wait a darn minute! This great book only cost $16 ! An easy decision to purchase. This is a no-brainer. Thx 😊
@seanhadley5452 Жыл бұрын
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!
@PTGaonkar Жыл бұрын
Real analysis is one of the reason for me to get into mathematics
@sophiaisabelle0227 Жыл бұрын
The Real Analysis will certainly help out a lot of people. Thank you for your consistency.
@TheMathSorcerer Жыл бұрын
:)
@thegoofiestgoooberr 10 ай бұрын
@@TheMathSorcererwhich do you think is better between this and kolmogorov? (i already have kolmogorov)
@Crazylust Жыл бұрын
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.
@benhill3098 Жыл бұрын
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!
@poincare5350 Жыл бұрын
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 Жыл бұрын
"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.
@user-hy6cp6xp9f Жыл бұрын
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 :)
@gopalparam6401 Жыл бұрын
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 Жыл бұрын
As a math major I absolutely endorse your point!
@jidrit999 Жыл бұрын
bhai online free pdf hai
@extreme4180 7 ай бұрын
@@jidrit999 hm whi toh aur uska print karwaane pe bhi sasta padega T_T and i prefer rudin
@SequinBrain Жыл бұрын
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.
@georgesealy4706 Жыл бұрын
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 Жыл бұрын
"Alright, ε-δ Proofs, come at me now!"
@adumont Жыл бұрын
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
@hhht7672 Жыл бұрын
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 Жыл бұрын
He seems like a great author! Would you recommend the proofs book to someone who has never done proofs before?
@TheLethalDomain Жыл бұрын
@@11seth11b No doubt about it. Begin with his book of proofs and then jump into his book of real analysis.
@guillermo3412 Жыл бұрын
you love whaaaaat
@11seth11b Жыл бұрын
@@TheLethalDomain sounds like a plan! Thank you
@hhht7672 Жыл бұрын
@@11seth11b for sure! It's very beginner friendly
@brianpoi5117 Ай бұрын
Cummings' book is downright enjoyable to read in the evening. I should have taken real analysis 30 years ago before I went on to graduate school and had to learn elements of real analysis as I went along. I wish I had this book back then.
@swordofstrife1174 Жыл бұрын
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 Жыл бұрын
would you recommend i read an intro to proofs before trying cummings's book? or just jump in?
@stephenhu2000 Жыл бұрын
@@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
@charleswoodard8478 Жыл бұрын
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.
@RaviShankarMishra-dz5zy 24 күн бұрын
Really, it is an amazing book on UG real analysis. Sir J Cummins is extraordinary , he knows exactly what an UG student wants to know. Its cost is affordable for its unparalleled value.
@StaticBlaster Жыл бұрын
I have "proofs" by Jay Cummings. It's a pretty good book.
@TheMathSorcerer Жыл бұрын
yeah I like that one too:)
@tideoo8823 Жыл бұрын
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 Жыл бұрын
Where is the review of Abbott's Understanding Analysis? 😢
@ryans7536 Жыл бұрын
This is the book we used when I took real analysis, it’s an excellent book and very well written!
@gloriosatierra Жыл бұрын
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.
@Pteromandias Жыл бұрын
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.
@adoxographer Жыл бұрын
I agree. I used this book and it is excellent. He also has one on introduction to proofs.
@ChickensBreast Жыл бұрын
I failed Real Analysis. I will take a look at this book during winter. Thank you for the recommandation Mr. Sorcerer.
@TheMathSorcerer Жыл бұрын
Awesome! I think it will help you a ton. Good luck☺️
@mcmulazz1060 7 ай бұрын
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.
@joehudson440 Жыл бұрын
Hi math sorcerer. I admire your motivation of mathematics because it aspire students to pursue further studies in math.
@thomasblackwell9507 Жыл бұрын
That edition of Earl Swokowski’s Calculus gives me flashbacks to a happier time, thank you.
@williamsteph2104 Жыл бұрын
Very cool to see so much diligence put into a textbook!
@briang.valentine4311 Жыл бұрын
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.
@AbElsaied Жыл бұрын
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 7 ай бұрын
I agree
@edgardgrydnyev3508 Жыл бұрын
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 Жыл бұрын
Hey yes I will do that! I have a few geometry books as well as some on differential geometry. Thank you for this comment!!!!
@williamhutsch851 10 ай бұрын
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.
@schrodingcheshirecat Жыл бұрын
I purchased both this and his proof (long form) books. highly recommend both
@RhynoBytes857 Жыл бұрын
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!
@ikechukwumichael1383 Жыл бұрын
I love you videos. Thanks for making Mathematica open source
@wilhufftarkin8543 Жыл бұрын
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.
@argonwheatbelly637 Жыл бұрын
Wish I had this when I took RA. This looks great!
@mukfu Жыл бұрын
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)!
@meshackgaolathe6492 Жыл бұрын
This book reminds of the Engineering Mathematics book by Stroud. It will stay around for a long time
@TheMathSorcerer Жыл бұрын
Hmm, I don't think I've seen that one yet. I will look for it. Thank you!!!!
@purelyconstructive Жыл бұрын
Always coming through with the amazing book recommendations!
@andreashartel5577 Жыл бұрын
Thanks for this video! Would love to see a video on Cummings' Proofs book!
@numericalcode Жыл бұрын
Really good view of the actual content in the book. Thanks!
@erichong3430 Жыл бұрын
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.
@shaneyaw4542 Жыл бұрын
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 Жыл бұрын
My favorite is "trivially obvious".
@boogerie Жыл бұрын
Now can you do a review of the author's proof-writing book?
@TheMathSorcerer Жыл бұрын
Yup will do!
@user-rz4sd3xt7f Жыл бұрын
I wish i had this book during my undergraduate course
@Maths_3.1415 Жыл бұрын
Thanks for recommending these types of books sir :)
@athanasiospapoutsis9978 Жыл бұрын
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!
@academyofuselessideas 8 ай бұрын
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!
@raul0ca Жыл бұрын
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
@RealPi Жыл бұрын
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
@JB-in4dj Жыл бұрын
I had him as a teacher! Very clear.
@TheMathSorcerer Жыл бұрын
Awesome!!!
@TheMathSorcerer Жыл бұрын
You could have him sign your book! Lol
@JB-in4dj Жыл бұрын
@@TheMathSorcerer Lol yes I can ask! haha
@magicmagic8188 8 ай бұрын
Based on the author I can already tell the book is climactic from front to end
@seanhunter111 10 ай бұрын
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".
@satyavivekanandbattula1091 Жыл бұрын
Thank you Sir. For sharing about that book. Useful video.
@jennifertate4397 Жыл бұрын
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 8 ай бұрын
@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 8 ай бұрын
@@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 8 ай бұрын
@@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 8 ай бұрын
@@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.
@viniciuscilla 7 ай бұрын
In Brazil we use the book "Análise Real" from Brazilian mathematician Elon Lages Lima
@sanjursan Жыл бұрын
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 Жыл бұрын
Very interesting idea, thank you!!!!!!
@Diranlou Жыл бұрын
Great! thank you for introducing the book.
@jaydenclowers2616 Жыл бұрын
This book in more connecting then the others you have mentioned in other videos
@maowiisenseii1470 Жыл бұрын
I say, this book + the long form proof are rival-able to baby Rudin: gold star!!
@walter274 9 ай бұрын
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.
@dominikriegler 4 ай бұрын
5:39 Transition from 3rd line to 4th line: Division by 0 . If x=y and you have y(x-y) on the right side of the equation and (x+y)(x-y) on the left side, and you "cancel"(x-y) where by definition above if x=y, you would devide by 0, so therefore you end up getting 2=1 which obviously isn't correct. Even the 3rd line isn't correct anymore. If x=y, then (x+y)(x-y)= y(x-y) is obviously also not correct anymore. How can x+y be the same as y if x wouldn't be zero (if we wouldn't know that yet). That equation is just so wrong. Zero just gets you in trouble. What you end up getting are insane equations like this. Its better to stay far away from these "2=1 proofs" and do something meaningful instead. For example: reading a math book. As for this book: quickly go to the next chapter. I really have a headache now just by watching this "2=1 proof" it's insane!
@definitelynotvj Жыл бұрын
I want this now!
@paradox_1729 Жыл бұрын
Ah at last you come to these two. I have been wondering if they were a good book for a while.
@williamkendall5502 Жыл бұрын
A book with no answers to check yourself is just guessing at mathematics as you don’t know if you got it right or wrong, so it’s really kind of useless and I never buy a math book without at least the odd answers at the back so I can check myself. I am one of those that will work my best to do all the problems I can but then also need to verify that I have it correct otherwise I’m just guessing. Plus a book with proofs at the end may show you other methods for doing proofs than what you did it. Not having the answers in the back of a math book is pure laziness on the part of the instructor and doesn’t teach anyone anything as there is no way for them to verify their answers other than spending hours googling them. The mathematics student that applies themselves will do the problems on their own and then check the answers in the back of the book. The lazy ones won’t go anywhere anyway if they just look at the answers so I’m not really too concerned about them.
@spacetimemalleable7718 Жыл бұрын
Higher level math books don't have the proofs because the student is then FORCED to THINK! It's the journey, NOT the destination. You find a satisfaction after solving the problem/proof. One usually knows when his/her proof is correct by poking holes in it. If , in fact, it is wrong, then it's back to drawing board.
@skillybiskuit12 Жыл бұрын
I have this. The first page reminds me, mathematicians can be funny. At times.
@victorpinasarnault9135 3 ай бұрын
Zeno's paradox for real numbers? That is new to me.
@FrancoisPesce Жыл бұрын
Nice review! Seems like their students missed a typo on page 63 (8:15 in your video) paragraph 3: "Quesiton" instead of "Question". 😅
@GhoshA Жыл бұрын
Real Analysis by S. K. Mapa is also a student friendly book. One can look at it once.
@joshuatovar6298 Жыл бұрын
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?
@mohammadmahmoud7208 Жыл бұрын
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?
@marcelocortez3312 Жыл бұрын
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!
@bengtbengt3850 Жыл бұрын
Great video as always. Are you going to do a review on Folland's Real analysis?
@TheMathSorcerer Жыл бұрын
great idea!!!!!!!
@jferfreiccp Жыл бұрын
Thank you 👍🏼☺️
@seraphimwang Жыл бұрын
Thanks!
@TheMathSorcerer Жыл бұрын
thank you!
@PrudentialViews Жыл бұрын
Does anyone know what math concepts I should know before learning real analysis?
@brandonfox9618 Жыл бұрын
I actually own that book that I got years ago!
@benjaminhogan3157 Жыл бұрын
Jay Cumming's also has a long form proof book...check it out.
@rk99688 Жыл бұрын
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)
@ihmejakki2731 Жыл бұрын
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?
@cannong1728 Жыл бұрын
Hah! That's my Calculus textbook from college...which I still have! Good ole Swokowski!
@8383N8 Жыл бұрын
Happy Thanksgiving! Where are the Math Book🏆 Awards?🏆
@osvaldo701 Жыл бұрын
Books do not need answers to exercises, it is better to do it by your own
@wachox Жыл бұрын
Hi, question, would you recommend buying the electronic kindle version ? What are your thoughts on using electronic math books for study ?
@TheMathSorcerer Жыл бұрын
They can be good. I think it's personal preference. I definitely prefer physical books:)
@wachox Жыл бұрын
@@TheMathSorcerer thank you very much for the reply, PS I like the Spanish videos, greetings from Mexico
@awildstevey Жыл бұрын
Aye! I used this text as a resource during my undergrad
@fndTenorio 6 ай бұрын
Hey Sorcerer, please review "The way of analysis" by Strichartz, it's a very peculiar book.
@bspain1637 Жыл бұрын
You can't self-study without solutions to check and verify your understanding is sound
@xaviergonzalez5828 Жыл бұрын
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!
@noahribes 15 күн бұрын
Is it necessary to have a strong background on calculus to read this book ? I'm currently reading for fun the book by the same author "Proofs: a long-form mathematics textbook" and I would love to keep reading his other book on analysis once I finish this one
@alexar6860 Жыл бұрын
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!
@TepsiMorphic Жыл бұрын
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.
@NoobleeGt Жыл бұрын
Hello, Thanks for this review! If you had to choose, would you go for Jay Cummings book or Terence Tao's one?
@TheMathSorcerer Жыл бұрын
Jay Cummings definitely
@NoobleeGt Жыл бұрын
@@TheMathSorcerer ok, that will be my choice then ;)
@jidrit999 Жыл бұрын
is terrence tao harder for first cource ? @@TheMathSorcerer
@DingDong-fq2mo Жыл бұрын
Thanks. I'm interested in a review of his proofs book.
@Dxxxxxv Жыл бұрын
If there is real analysis, then what is fake analysis?
@like_that4966 4 ай бұрын
Real analysis mean analysis of the real number line, not true analysis and there's no fake analysis there is complex analysis tho, where it's the analysis of the complex number line
@denersdef4163 2 ай бұрын
Calculus
@andjdjdjd Жыл бұрын
Would you recommend this book as a good summer read for someone who will be studying maths as an undergraduate? Thanks.
@TheMathSorcerer Жыл бұрын
Yes, definitely
@navierstokes2356 Жыл бұрын
By the way, look at that meme in the book 9:07 hahaha
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