/sci/ - Science & Math

>>12186326
>I'll start
>Doesn't start
Fine. I'll start then.

>>12149279
Pugh is really good. It's got similar content to Rudin but is a lot more fun and visual and has better descriptions.

holy fuck this topology discussion is moronic
A METRIC SPACE IS A SPACE WHERE YOU CAN FIND OUT HOW FAR APART TWO POINTS ARE
IT IS A SET WITH DISTANCES

A TOPOLOGICAL SPACE IS A SPACE WHERE I CAN TELL YOU WHICH POINTS ARE CLOSEISH TO A GIVEN POINT
IT IS A SET WITH A MORE GENERAL NOTION OF CLOSENESS

A METRIC SPACE IS A TOPOLOGICAL SPACE BECAUSE NUMERICAL DISTANCES GIVE YOU A NOTION OF CLOSENESS

A MEASURE SPACE IS TOTALLY UNRELATED. A MEASURE SPACE IS A SET WITH A NOTION OF SIZE. IN A MEASURE SPACE ONE CAN THINK ABOUT LENGTH, AREA, OR VOLUME, ETC, BUT NEVER DISTANCE.

MANY TIMES ONE DEALS WITH TOPOLOGICAL MEASURE SPACES. BUT THE MEASURE AND TOPOLOGY RARELY INTERACT VERY WELL, IF AT ALL.

Please.
Stop spreading misinformation.

>>10725928
>pugh
holy fucking BASED!

>>10719863
just press the "unfollow" button on the top right. but fill out the survey first about why you're leaving! we'll be sad to see you go :(
>>10719865
stop ruining people's lives
>>10719862
watch gilbert strang's linear algebra lectures on MIT OCW to get a good linear algebra foundation which is part computational and part theoretical.
if you like that and want more, read axler's Linear Algebra Done Right.
if you want something different and liked calculus, read pugh's analysis and do exercises.

>>10659826
Occular deltrons?

http://realityshifters.com/pages/articles/williamtillervacuum.html

that's right, it's him...

>>10553084
>not understanding the most basic mathematics textbook available
>implying rudin is in any way "opaque"
blunt != opaque, rather, it is essential for clarity.
>>10553104
oh, you buy textbooks? yeah, that explains it. never gonna make it.
try pugh (pdfs on fucking line) if you need something that's more comprehensible and readable but on the level of rudin in content.

lol imagine liking any textbook besides pugh and rudin

just use pugh, it has the rigor of rudin with the character and soul of a book like strang, axler, or artin.
you can tell the person who wrote it absolutely adores what they're teaching you. and it's a very visual book for first time learners. at the same time, it doesn't hand hold like fucking bartle or ross, and it has incredible exercises.
plenty of pdfs online!

No, the best book on real analysis is written in English.

>>10285799
>>10285811
imagine liking ross, god damn
rudin is a classic but I prefer pugh. it's far more readable and has great images, but it's not a book for literal children like ross. it's also got amazing exercises (better than rudin imo)

for me its

>>10248141
>his style of writing and useless diagrams
those are the best part idiot

>>10246951
I'd very much recommend going back over linear algebra wiith a proof based approach, say with Axler. You may also want to check out Pugh's Real Analysis book (pdfs online) because it's more visually oriented and is more readable as opposed to memes like Apostol, Rudin, and Spivak. Can't imagine why people here are so intent on suggesting garbage instead of Pugh.

>>10207499
spivak is a meme, don't bother with "calculus"

>>10187860
for me, it's pugh. the best undergraduate real analysis text.

for me, it's pugh. the best undergraduate analysis textbook.