yes, so choose a better book with better exercises.
I could write down the basic theorems of undergrad analysis on two pieces of paper, and we can pretend it's true cause some jewish guy said so. Or you can understand how mathematics, the language of gods, actually works.

>>16880776
If you have to ask, you don't know what you are doing. Try proving a theorem before reading the author's and maybe that will help you see the importance of exercises. If you want to be able to understand more advanced books, you will need the exercises to reinforece the material. Try that, open a non-friendly, advanced textbook. The problem with Abbott is that it is the kind of textbook for people who will only have a single "higher" math requirement, like those studying for secondary school teaching. Even Spivak's Calculus may have harder exercises than Abbott's.

>>16880792
OP here, nvm, i found https://math.colgate.edu/~mionescu/math323f12/.

I'll just attempt to do the homework problems he suggest in order to get an overview of the subject

>>16880776
In my opinion, it's better to not get hung up on doing exercises. A lot of the time, books have way too many exercises, and trying to finish them all, or even a sizeable amount, is such a daunting task, that it makes opening the book a chore. If skipping every exercise is what it takes to get through the book, then that's your better option.

>>16880850
This. However if the book is in a subject you want to get a deeper understanding of you have to do a lot of excercises or at the very least the recommended ones. But if you are just trying to move on to a different book after just skip them.

>>16880850
>A lot of the time, books have way too many exercises, and trying to finish them all, or even a sizeable amount, is such a daunting task
And Abbott isn't that sort of book. There are very few of them and if I recall correctly, none of them are the redundant sort.

>>16880776
Depends entirely on if you have an honest professor.

Why are zoomers scared of Rudin?

>>16880776
if you cant do the exercises in your head while your reading what's the point

>>16880776
Waste of time since it implies real numbers can be manipulated in any meaningful way. Real number arithmetic isn’t even properly defined lol. In b4 but it is. Then tell me what [math]\pi + e[\math] is and you’re not allowed to give a circular answer.

>>16882256
Limit of sum of rational sequence approaching those two numbers.

>>16880776
This is an arithmetic problem.
How much time do you have?
How much time can you spend for each problem?
5 mins, 10 mins, 30 mins?
Does it make sense?

>>16882294
What’s a limit?

>>16882294
That doesn’t make sense. Someone asked you what a number is. You say a limit. Naturally, the next question is, what is a limit if not a number? It’s a circular definition.

>>16882449
If you would open the book, you would know.

>>16882469
What is 69?

>>16882471
>book
toilet paper
>what is 68
You can’t have it both ways. If you define the real numbers in terms of sequences, or limits of sequences, then any subset of the reals must also be defined this way. So 69 is the limit of the “infinite” sequence {69, 69, 69, …}. And there is the problem. You used limits to define numbers, but then you end up with a circular definition. What is then a number? It’s a limit, we just admitted to that.

>>16882654
How do you define 69 as a natural number?

>>16882687
Ever counted apples before?

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anons what do we think of terry's analysis books and its excercises?

>>16882887
>hindustan

>>16882829
I have never in my life seen 69 apples together let alone counted them.

>>16883198
Clearly you’ve never made cider. You don’t know what you’re missing.

>>16883263
Clearly, I'm missing some apples.

>>16881105
>You VILL read za dense and difficult textbook when easier books exist and you VILL be happy

>>16884347
What's the best real analysis to learn from as a beginner? I have adhd and bad memory loss from covid, please help me.

>>16884410
Textbook*

>>16884410
>>16884418
Roughly in order of difficulty:

- Burn's Numbers and Functions: Steps into Analysis
- Erdman's A ProblemText in Advanced Calculus
- MIR Mathematical Analysis In Questions And Problems

Non-traditional (helper) books:

- Körner's Companion to Analysis
- Bressoud's A Radical Approach to Real Analysis
- Alcock's How to Think About Analysis
- Krantz's A Guide to Real Variables
- Gelbaum's Counterexamples in Analysis

Standard recommendations:

- https://4chan-science.fandom.com/wiki/Mathematics#Analysis

Imo, you need to have good grounding of algebra (inequalities, etc.), problem solving, proof, calculus, to not suffer.

If you check amazon, they will keep pushing for Jay Cummings' Real Analysis. I'm skeptical about the quality and the reviews.

Without doing the exercises it's like reading a graphic novel adaptation of a book.

>>16884435
Thx, ill try to look into them, i alrdy know differential equations so i know i have the prerequisite math down.

Its frustrating, i was planning on going through the abbott book because it has solutions, it sucks having adhd, my maximum attention span is around 27 minutes, i timed myself.

Thx for helping me out by reccomending those helper books, i really appreciate it.

>>16884449
Good luck, I just recommended a bunch of “through problems” book. Where you learn the concepts and proof the theorems through the exercises. Sometimes known as moore method or inquiry-based-learning.

>>16884347
How is baby Rudin difficult? Holy fucking shit, gen Z is beyond repair.

>>16882887
Idk what to think about that book, i have read somewhere that it has very little to no graphs or drawings which in my opinion means that it must be very difficult in the explanation of concepts.

Does it have an associated solutions manual to it? If it does that would make it a better choice. If it doesn't then that would make it a bad book.

I would rather go over the book by abbott for real analysis. And if you go over his book once then i would go over it again twice jist to ensure that you truly understand the concepts.

Abbott has solutions on the internet, a solutions manual.

>>16882887
The first part where he defines all number objects from scratch, functions and sets, limits etc these are excellent. The actual calculus part I didn't like and he assumes you know topology later just kind of throwing out definitions.

The best real analysis text you will ever find is this one https://classicalrealanalysis.info/com/FREE-PDF-DOWNLOADS.php and that's the same book used by MIT's new analysis lectures on open courseware. Every limit proof, every continuity test, every derivative interpretation.

They have a version that drops the Riemann integral too assuming you want to continue on to measure theory http://classicalrealanalysis.info/documents/TBB-DRIPPED-AllChapters-Landscape.pdf

>>16884435
Peter Lax's Calculus book is probably the best beginner book because you begin with learning inequalities and the proofs are comical as he uses the infinite decimal abstract definition of real numbers so many of the early proofs are "these decimal numbers match these other decimals QED". No reason some engineering analysis can't do that instead of cauchy sequences

>>16886668
But isnt that jist a regular calculus book?

A better book to learn calculus from is mathematics for physicists by altland

>>16886770
It's single variable analysis w/differential equations so the same shit. Least upper bounds, squeeze theorem, continuity and everything has a proof.

Are there any other real analysis textbookss that have solutions withinn them?

>>16887859
Nope. Just give up.

Has anyone tried out going through lang's undergraduate real analysis textbook?

>>16884449
>Its frustrating, i was planning on going through the abbott book because it has solutions,
So why can't you do that? Trying to find an "optimal book" is procrastination bullshit when you already have a great one found. It's no effort but feels productive because you feel like you're "getting towards the goal" by looking for another better book.

>>16888592
Like i said the adhd causes procrastination, but i alrdy decided on abbot, i downloaded it.

>>16888609
Ah okay I thought you were saying you couldn't do Abbott for some reason. I went through some parts of Abbott some time back and will probably start again and hopefully finish the whole thing soon, if being in contact with someone else doing it would help with your procrastination issue let me know.

>>16888945
>>16888609
Also forgot to say, some things that helped me with similar problems: always keep the PDF open, always keep your desk tidy and your notebook where you solve exercises etc. in front of you with a pen, this way you reduce the mental friction and effort load in "starting" to engage with the book, you can even do it passively as a form of procrastination too. Like if you already have the book open and your notebook in front of you, it's considerably easier to be trying to solve an exercise or to read a part of it.

>>16888946
>>16888946
>always keep the pdf open
Ill keep that in mind.

>>16888945
Its a good thing you are gping through abbott twice, its always a good thing to go through a textbook twice.

I plan on going through Lang's complex analysis book twice or thrice because at university i failed complex analysis with a 30/100 average but he had pity for thoae whp failed and passed us.

>>16889342
No, going through a more advanced book like Rudin is a significantly better use of time.

>>16889342
I haven't really gone through Abott, just a few chapters and looked through
I had calculus/analysis like three times now (once hs twice uni) and I usually just did fuck all only enough to pass and get a "general" idea of things but I couldn't tell you how the fuck the integral actually works other than there being some "upper sums" and "lower sums" and it being a limit of that or something
>>16889345
Can you elaborate on this? Taking the above into account, and if I know a *little* bit of topology, should I just do baby Rudin or something? I can't help but always feel this need to "go through the basics fully" or whatever but I think I might just be hamstringing myself because I just end up spinning in these "relearning fundamentals" circles. Same with linear algebra lol, did that "twice" but feel like I have significant understanding holes, but also going through an entire linalg textbook like LADR seems like it will be somewhat of a slog idk, maybe I should just bite the bullet and go through it fast to get it over with.

>>16889345
But rudin doesnt have solutions, how could i verify my proofs without solutions anon?

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>>16889351
I think what you are looking for is a conceptual understanding of linear algebra, pic related is just an exposition of linear algebra for physicists to read through, with a few exercises.

I dont see it as a bad thing, to go through abbott's real analysis twice or thrice, the more times you go through it, the more you memorize and understand real analysis.

Try downloading and reading through pic related, it should deepen your understanding of linear algebra.

>>16880776
Do as many exercises as it takes for your to feel confident you understand the material.

I wish someone made a real analysis textbook for physicists, where it has lots of applications tp physics to stay better motivated.

>>16889402
>t. fucking pdf hoarder
Pick up a pencil.

>>16889402
check out Zorich

>>16889351
I don't know what's there to elaborate. Doing a new book instead of one you have already done or mostly done is just better use of time. Rudin is more rigorous, has way more interesting exercises than just completing proofs of standard results, is terse, which makes it faster for a reread, has more topics. The only reason to use Abbott would be if you're not prepared for Rudin, which shouldn't be the case if you have done at least half of Abbott.

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>>16889400
Really good with honest applications

>>16889402
>>16889509
I missed lol

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>>16889501
Oh sorry I think I might have misread it as you saying going through a more advanced book *twice* is better. Or maybe not, I'm not entirely sure now, maybe I just wasn't sure about the extent to which Abbott and for example Rudin can differ while still going over the same type of material. I suppose your reply answers my question either way, thank you. I think I will try to give Amann & Escher a go instead of Rudin though.

>>16889673
GL anon

>>16889679
thank you anon you too in whatever you will be doing

Try reading another analysis text at the same time, it should help you understand things a bit better.

>>16887859
spivak calculus and key to spivak calculus.

I wish i was faster at self studying, i can read really fast but problem solving is slow

Mathematical Analysis by Brennan has full solutions at the back.
Fundamentals Of Mathematical Analysis by Haggarty has full solutions at the back.
Real Analysis by Howie has full solutions at the back.

Brennan's book is by far the easiest book that I've listed. It was written specifically for adult learners to teach themselves Analysis as part of the Open University's mathematics distance learning degree programme in the UK. Howie's book is slightly easier than Abbott's. I haven't worked through Haggarty's book but I've flicked through it and it looks decent.You haven't heard of these books because they're British and most people online only recommend American books.

>>16880776
analysis is my fav since thats when everyone does the shinanigans to understand it like calc 1-3 and linear algebra even though conceptualizing mutli dimensional spaces is easy as fuck with a PRI NVIQ of 115+ lmao

>>16891493
Ty for this anon, ill be looking into the first book, ill most likely read it alongside abbott, that or ill read through analysis by ross while going through abbott

>>16886668
So I checked his book. It’s very weird. I don’t think I have seen other calculus books with so much focus on applications and numerical calculations. Feels like reading a computational physics textbook at times. He spends more time on application compared to other analysis book with applications like Courant’s or Zorich’s.

>>16891742
Its better go through mathematical analysis by brannan if you want a more detailed overview of calculus. And its better to go through mathematics for physicists by Altland if you want to peruse through regular calculus applications.

Abbotts first chapter is hard to understand, i hope i figure out more from solving the problems, he writes too terse at times amd he doesnt make enough graphs that would help in understanding what is going on.

>>16892156
Someone should write a Visual Real Analysis for Retards book.

>>16880850
this is why when i go to the gym i just put the treadmill on and let it run while i walk around and look at each piece of equipment then leave
otherwise going to the gym can become a chore

I'll be doing five problems from chapter 1 tommorrow, its too bad i still don't fully understand chapter 1 of abbott. I'll let yall anons know how it goes in terms of understanding.

>>16892714
Best of luck to you

>>16880792
>If you have to ask, you don't know what you are doing.
are you retarded? if they knew what they were doing why the fuck would they ask in the first place? i can't imagine what sort of smug reject sits at home with a million cocks down their throat and thinks this is a smart or insightful thing to say. but that person is you.

>>16893851
>>If you have to ask, you don't know what you are doing.
Is that the complete extent of the post you are replying or does it subsequently provides some hints about how to know what one is doing when reading some mathematical textbooks? Elaborating on those hints: depending on the reader's goals, he could do with only the main text and without exercises at all or, on the contrary, he could need all the exercises and more, that is, complementary exercises from external sources to the book. That is why asking OP's question to /sci/ ends up getting stupid answers, because of the lack of crucial information and background in said question

I did it, i did the five problems in my head, i understand supremum and infimum a bit better now, i had tp use the solutions to verify if my answers were correct.

Now ill be moving onto chapter 2 of abbott's book, sequences and series.

>>16894022
>i had tp use the solutions to verify if my answers were correct
Then, you didn't do it.

>>16894039
I did the problems first then i checked the solutions to see of my answers were correct, which they were. I dont understand what you are trying to say. Using solutions to verify if tou got the answer correct isnt wrong, unless you are the type to blindlt answer questions and falsely believe that you are always correct, in that case you are not truly educating yourself, your jist blidnly answering problems correctly and incorrectly.

>>16894053
>Weil's after proving Fermat's theorem
>Hmm, now let's look at the solution manual.

>>16894059
Im guessing you have a phd in mathematics from some top university if you never had to use a solutions manual once in your life. Let me guess, you got all A's in your courses, graduated top of your class and now your a professor at some top university

>>16894070
Exactly, everyone else who doesn’t have solution manual basically failed all math courses. Those other lecture notes, textbooks, problem books are useless and don’t teach anything because they don’t have solution manual.

>>16894053
The point of formal proofs is to verify logic without doubt. If you cannot figure out your proofs are correct without a solutions manual (which is meant for the instructor not the reader), then there's literally no reason for you to learn formal math. It's like buying a car but not learning how to drive one.

>>16894081
>>16894079
Don't listen to this shitty advice, if you need a solutions manual to verify if you got things correct, then use it.

You're self studying on your own i'm guessing, you need as much help as you can get, you can't just go to office hours to help you out.

I just did two more problems from abbott

>>16894081
That doesn’t make sense. Surely the instructor would need the solution manual even less by your logic.

>>16892714
Did you manage it?

>>16895245
I managed it, i either read or do problems from abbott every 2 days. Im going through a small 180 page textbook on vector analysis at the same time as abbott.
On A days i gp tbrough the vector analysis textbook, on B days i go through abbott.

Im following link related syllabus for abbott so i only have to do 5 to 6 problems per chapter, i basically do the homework problems only that they assigned to their class, that way i dont have tp do every single problem in abbott. I jiat want a decent understanding of real analysis so i can move onto complex analysis by Lang.

https://math.colgate.edu/~mionescu/math323f12/

>>16895245
Im starting to read chapter 2 now, on this thursday ill start to read chapter 2, tommorow is vector calculus by Matthews.

If you need a solutions manual for abbott to help verify your answers heres a link to it. I used it to verify my solutions for chapter 1.

https://uli.rocks/understanding-analysis-solutions/main.pdf

>>16895253
>https://uli.rocks/
I checked his webpage. Honestly he sounds unhinged. Be skeptical about his solutions.

I read up to chapter 2.2 today

>>16895242
Instructors are not gonna waste their time solving kiddie exercises to teach a class. Also, instructors are literally the only one who can get a copy legally by requesting a copy from the publisher; they are not sold or published anywhere else.

>>16884435
that's a good list

Today's the day I start doing problems from Abbott again, ill try to do 2 problems, real analysis is boring, so far it doesn't interest me, I just need it to get through complex analysis as a prerequisite

>>16900276
Ah yes, because complex analysis is known to be very engaging and interesting, instead of a continuation of the same bullshit.

>>16900329
All of math is boring, prove me wrong

>>16900276
Your attitude is all wrong. You're trying to take a shortcut but shortcuts in mathematics don't work. You'll just end up with bad foundational knowledge and you'll suffer later. My advice would be to learn real analysis in earnest and put more effort in. Earlier in the thread you said chapter 1 of abbott was challenging for you which tells me that you haven't taken an intro to proofs class or read a proof writing book. Anyone who has taken an intro to proofs class would make quick work of chapter 1. Grab hammack's book of proof, work through it (you can ignore the counting/combinatorics chapter), then pick up abbott and do all the odd questions at least is my advice. Also don't use some rando's solutions. He might be wrong and then what? You've internalised some guy's mistake. Some might even say that using a solutions manual at all is bad because it acts as a crutch. What you should do is write a proof and then go over the proof line by line and be able to justify every line without any doubts. Also there's no fun in reading other people's proofs. I find that my own proofs are always better because they're my own and I can understand them quickly even if they're longer or uglier. With other people's proofs, I have to re-write them and break them down especially if they're terse which makes me expend extra energy.

Anyway, why are you rushing? What's so important about learning complex analysis?

>>16901106
Lmao, why larp as some math learning expert? He reads a book, does the problems, compared with the solution. Imagine finding anything wrong about this.

>>16882972
classic publisher

>>16901125
>He reads a book,
No problem with that
>does the problems,
He's doing 2 problems per chapter. No one learns mathematics by doing that little. He needs to do more problems.
>compared with the solution.
He's not comparing with official solutions or solutions made by a reliable mathematician/professor/lecturer. He's using some random person's "solutions manual". There /is/ an official solutions manual made by abbott himself btw. He's not using that one. He's using this >>16895253 . Made by this guy who hasn't got a degree in mathematics and claims to be self-taught: https://uli.rocks/about/
Besides solutions manuals are crutches no matter what you say and no serious mathematician would disagree.

>>16880776
The official instructor solution manual is online. Was it lacking in some way? Perhaps for older edition, incomplete, not clear, etc.

>>16880786
Analysis is a decision tool to take an action using assumptions with an confident confidence percentage from a dataset that minimized the number of samples and sampling time.

>>16889398
nta but is pic related the kind of LA intro for people who have already done a course/book on it or can I use this as my first LA book?

>>16904285
For those who have already done it, its easier to understand that way

>>16904613
kk, I think I'll go with Lay then