Brainlet in training

Tao

>>8531954
Last year physics undergrad here, took real analysis as an optative, one of the worst experiences in my life. I'm too brainlet for that, bye

>>8531954
It's pretty overkill to spend a whole book just learning proofs. Your introductory textbooks will go slow enough that you can learn it through those.
If you understand what a contrapositive is (most undergraduates fucking hate contrapositives for some reason) and how proofs by negation/contradiction work (on the other hand most undergrads try to do everything by contradiction) you're ahead.

Abbott's understanding analysis is a pretty nice book that takes great care in explaining the basic mechanics of analysis at a fairly handhold-y level (which is what you want).

Another helpful thing to look at is Counterexamples in Analysis, which is not a text but rather just a long list of counterexamples to things that might seem true. Doing lots of counterexamples helps stuff feel a lot less arbitrary because you can see what goes wrong when you change assumptions or aren't careful.

General advice: know and understand your definitions precisely. You will fall on your face otherwise.
Try to engage with (think about) the material on your own. Pisses the hell out of me seeing students so dedicated to being a sponge that they can't come up with f(x) = 0 as a counterexample to something.

>>8531963
downloaded, will check it out
>>8531988
not to worry, my brainlet bail out plan is actuarial science
>>8531996
that's some solid advice. I've taken discrete structures, so I'm not unprepared in terms of basic proofs. However, intro to analysis is known as a landmine course at my uni for math majors/minors, I just want to give myself a real fighting chance. I'll have to check those books out

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>>8531954
I'm in the same position buddy. I read this then started rudin and googling lecture notes when needed. But seriously this is the book that fills in the holes in between a calculation based curriculum to a proof based one.

>>8531996
Proof by contradiction and contrapositives are basic logic topics. Do people really make it to analysis coursis not knowing these things?

>>8532071
in the united states, we sure do. undergraduate curricula and course progression are barely given a second thought. Basically, your only hope is to latch on to a competent adviser/mentor early in your undergrad career

>>8532071
yeah see >>8532088
Calc 1-3, maybe only 2 semesters if you're school is pretty gud. Then Linear algebra and differential equations for engineers then boom fucking intro to analysis.

A lot of US schools I think don't take the time to 'design' math curriculum for freshmen so the first two years of you being a math major you're pretty much an engineer unless you; test out of classes, take a math pre-req in the summer, or get into some type of honors program. Which is doable but even more US high schools are shit so then you have to prep again on your own for doing any of the above if you lost the geographical/economical lottery.

>>8532113
*your
Jesus I'm horrible.

>>8531954
I learned from bartle!

It's a good intro to analysis. complete, but gentle, unlike the obnoxiously impossible rudin.

i think it uses gauges for riemann integrals which we did a different way in class. but that isn't a bad thing, it's just a matter of taste

do the exercises

>>8532071
I had to take an intro to proofs course before being able to take any upper level math course. It was really helpful.

>>8532113
>Calc 1-3, maybe only 2 semesters if you're school is pretty gud. Then Linear algebra and differential equations for engineers then boom fucking intro to analysis.

>i'm just gonna let them spoonfeed me without ever researching on my own or critically considering what i have been taught in theses courses and how it might be approached from an analytical perspective. thinking is literally too much to ask of me. i am literally shaking.

>>8533544
kek approves.

/sci/ is your friend. /sci/ pushes you to be a better student.

>>8531954
Based on what I can gleam by skimming it, I'd look at Calculus by Spivak (or possibly some other rigorous calculus book, but I like Spivak).

My general advice is just work hard and do your best to understand everything. The key is sustained effort, not attempting to learn things at the last minute. You can only understand so many new things a day, so as long as you put in meaningful effort consistently, you'll be able to keep up without issue. It will be hard, and you won't be able to learn things as quickly as you'd like at first. But so long as you continue to put in effort, you will get better and do well.

Sets proof and logic by Marvin bittinger is what I use to self study and I like it because it suits the style of math I prefer: straightforward and lots of easy exercises. Same goes for book of proof which you can download for free, although it doesn't cover real analysis just modern proof terminology and techniques. I recommend going to the stacks of your library and getting out all the intro texts on real analysis and proof writing and comparing them so you can figure out which one you like the most. That's what I did. Remember its more important to find a writing style that you can understand and even better if you like it. For example I really like reading george polya but I can't stand reading pinders book on set theory. They're both very popular though! Contrary to what sci might tell you there are actually a lot of different ways of thinking and writing about math. Don't starve yourself to be cool. Read what you like and what works. But do the work and find it!

>>8531954
Used this book. It was absolutely terrible. The professor was horrible as well. He would spend an hour and fifteen minutes speed writing proofs on the board. He didn't care whether you understood the proofs or definitions, he assumed you did as he was writing.

If someone asked a question in a very demeaning way he'd respond so snappy once he asked as a follow up "do you understand?" The student would automatically say "yes" to stop the harassment.

I never learned analysis and unfortunately couldn't give t the time it deserve because I was required to take other classes I was much worst in that semester.

Once I find the time I'll revisit analysis and learn it from scratch.