/sci/ - Science & Math

[Anonymous No.10780917]

ok, let's settle this. If I want to start learning maths, the wiki says that I should start with Calculus (or Precalculus) with Stewart's book.

But now I have pic related and says that I should start learning Logic and then Proof Theory. Isn't Proof Theory something advanced?

Come on, help a bro here.

[Anonymous No.10780926]

>>10780917

[Anonymous No.10780928]

>>10780917
First you need to learn how to write well, so you can take good, pretty notes. Then you need to read “How to Read a Book” so you can read well. Then you need to read books about memory, so you can remember well. Then you need to read books bout logic, so you can think well. Then you need to read intro to math books and math history books, to have a good context of understanding. Then you need to read books on proofs. Then you can start with geometry, then algebra, then calculus, etc.

[Anonymous No.10780962]

>>10780928
>>10780917
But seriously OP I’m in the same boat as you. I don’t know any math. Let’s you and I use the chart and read through the books together, ok? Logic is boring so we can start with the book of proof.

[Anonymous No.10780973]

For set theory, I really liked Munkres chapter 0 on set theory in his book Topology. It has many exercises.

[Anonymous No.10781016]

is there a torrent of useful textbook pdfs and ebooks anywhere? I didn't see anything on /t/

[Anonymous No.10781030]

Start here: https://en.wikipedia.org/wiki/Principia_mathematica

After mastering that book, you can move on to this:https://en.wikipedia.org/wiki/%C3%89l%C3%A9ments_de_math%C3%A9matique

[Anonymous No.10781040]

Khan Academy is pre good to start with desu

[Anonymous No.10781044]

>>10780928
No, no. If he reads "How to Read a Book" before reading about memory, he will forget how to read a book. Perhaps start with "Thinking: the motion picture"

[Anonymous No.10781049]

>>10781044
I think perhaps he should first get a job and save up a lot of money so he can have a private tutor teach him everything he needs to start learning on his own.

[Anonymous No.10781057]

>>10780917
It literally says it takes you from baby logic to bla bla bla. What's the problem OP?

[Anonymous No.10781467]

>>10780917
>Come on, help a bro here.

[Anonymous No.10781616]

>>10780917
I'm similar to op
all I want a math map to start from basics and end with P.hD level

[Anonymous No.10781912]

>>10781467
I also endorse the official /mg/ curriculum.

[Anonymous No.10781973]

BTW, I want to learn math to improve my programming skills.

>>10781057
>>10781467
The problem (like the pic that anon posted) is that one say I have go to calculus, but the other says the Logic and Proofs are better to start with. LIke I said at the beginning, isn't Proof Theory an advanced topic? I think you need a solid math background to start learning proofs.

I am more confused now. If I start with OP pic (with Logic and Proofs), should I need to review my Highschool math or that's enough to keep going? and also, Why should I start like that? isn't "normal" to start doing Calculus in any math related career on college?

[Anonymous No.10781977]

>>10781616
I don't think I could get that far, I will be happy if I can read and understand Knuth's books (Concrete Mathematics and the Art of Programming) without feeling like a brainlet.

Damn I want to read SICP but the math in there is just too much for me right now.

[Anonymous No.10782005]

>>10781977
it's not your fault maybe you lack something try to solve algebra + fractions + decimals...
problems and see where you don't feel easy and study it again

[Anonymous No.10782644]

>>10781977
>SICP
>math
I think you mean TAOCP Anon?

[Anonymous No.10782720]

>>10782644
a lot of SICP material uses calculus. You should at least must be familiarized with it. I am not.

[Anonymous No.10782727]

>>10782720
Actually, the definition of the derivative given in SICP (section 1.3.4) is as good or better than any explanation you'll get in a calculus text. At the level of definition, the derivative just boils down to arithmetic and limits.

[Anonymous No.10782788]

>>10782727
yeah but I am still suck at that. That's the reason why I am reading a precalculus book. The original question was about learning Logic and Proofs before touching calculus like OP pic said..

[not OP No.10783071]

>>10780962
how does one even get into your position? are you an undergraduate? have you even learned single var. calc?

[Anonymous No.10783100]

not op but i just got this from amazon today anons, what am i in for

>t. calc 1 summer student

[Anonymous No.10783104]

>>10780928
needs to learn to read better actually, the wiki doesn't recommend Stewart

[Anonymous No.10783109]

>>10783071
I’m an upcoming sophomore, math major. I don’t really know much about math, but I’ve gotten an A in every class I’ve ever taken. I blame the education system.

[not OP No.10783131]

>>10783109
yup i feel you. the utter shit that is forced down your throat in highschool makes me think there is a sinister reason perhaps to why they teach in such a shitty way in the public system.

regardless, I think if you got A's thus far youll do well down the line. good luck :)

>>10783100
worst fucking book ever. my classes used this (8th edition- literally same thing, just milking for more money) and the who thing is plain and boring. Its: here is the formula, examples, now you plug and chug anon. hip hip hooray now you hate math and your life. Its good for the amount of practice problems it has, but I suggest you supplement with other texts- and for the love of god, dont buy textbooks. I bought stewart and I regret it, learn to just download, its much easier and cheaper.

everyone knows this but just in case: libgen.is

[Anonymous No.10783139]

>>10780917
another option: start with abstract algebra and get to numbers later

[Anonymous No.10783216]

>>10783131
>the utter shit that is forced down your throat in highschool makes me think there is a sinister reason perhaps to why they teach in such a shitty way in the public system.
What can be done? I think that there should be more testing based on explaining some area of math, for example, how the basic calculus formulas are derived, rather than merely trying to follow a process, such as funding the derivative of a formula. Oral exams, proofs, etc should be more emphasized, and nothing should be left out. At my high school calculus was optional, and we only had 6 students in the class. The average day was finding the derivative of expressions for 40 minutes, and chilling out and talking for the next 40 minutes. We ignored all problems that had too much trig, and the most advanced thing we got to was u-substitution. That class was a joke, but the tests required precision and making few mistakes, so I would make high A’s while other kids were failing. Thus it appears as though the class is rigorous, when it is not. We could have learned more, and had better test scores, with a different approach. It’s pathetic.

[Anonymous No.10783355]

>>10783131
is it that bad? fugg
i mostly got it because my class doesn't have a book otherwise and figured it would be better than just learning off of the shitty videos from my uni

[not OP No.10783369]

>>10783216
what should be stressed in class is the concepts. proofs come much later but brief introductions can help you in the long run. (And yes, as OP or whoever said, its a very wise choice to read up on proofs early on to help you later down the line). What is commonplace nowadays when teaching these courses is that your prof (depending on how shit he is) will just give you formulas and you have to follow a robotic plug and chug algorithm. Most students ( i think) have no idea what they are doing or even why. They just follow the steps told to them and they good good grades. But teaching the concepts, proofs, why you are learning said concepts, and the applications are all great ways to make students actually enjoy math.

>>10783355
well its a mistake everyone makes. like I said, even I bought the book first year. no biggie anyway, just save your money in the future because textbooks just are never ever worth the money to buy hardcover. Otherwise, suppliment that book with the single variable calc books above. I personally just learned calc through stewart, back when I wasnt too excited about math - it was boring but did the job- so that could work too.

also, look at the /sci/ sticky- first post on index- it has great resources to learn from.

[Anonymous No.10783574]

The lists are good but I honestly think one could start with Basic Mathematics. If you skim through the first couple chapters you will see why.

[Anonymous No.10783579]

>>10780917
>going through that many books and topics before even basic calculus
Your pic is a meme

[Anonymous No.10783585]

>>10781016
I have seen http://gen.lib.rus.ec recommended on /sci/
I don't know much about it like if the stuff is copyrighted or anything, I just know /sci/ has recommended it for textbook downloads

[Anonymous No.10783587]

>>10783369
>also, look at the /sci/ sticky- first post on index- it has great resources to learn from.

the sticky recommends Stewart's book

-_-

[Anonymous No.10783595]

>>10783587
https://4chan-science.fandom.com/wiki/Mathematics

[not OP No.10783677]

>>10783587
kek yes it does for the practice problem- like i said, stewart is good for its problems. But as a read, its boring, lame and overall a terrible way to learn the course material

[not OP No.10783682]

>>10781016
1.6 GIG:
magnet:?xt=urn:btih:c955ff3e31b334310fd1bcd49fb304df0d0ab7a2&dn=--%20Berkeley%20math&tr=udp%3a%2f%2ftracker.leechers-paradise.org%3a6969&tr=udp%3a%2f%2ftracker.openbittorrent.com%3a80&tr=udp%3a%2f%2fopen.demonii.com%3a1337&tr=udp%3a%2f%2ftracker.coppersurfer.tk%3a6969&tr=udp%3a%2f%2fexodus.desync.com%3a6969

4.6 GIG:
magnet:?xt=urn:btih:923515aaa1bf92da5c91c27722a8c3bb1ccedc7b&dn=Math%20Complete&tr=http%3a%2f%2finferno.demonoid.com%3a3393%2fannounce&tr=http%3a%2f%2ftracker.torrentbox.com%3a2710%2fannounce&tr=http%3a%2f%2fopen.tracker.thepiratebay.org%2fannounce

9 GIG:
magnet:?xt=urn:btih:75b48cad30b9c68a931a60074b61a29d06472c7b&dn=MATH%20MATHEMATICS%20BOOK%20COLLECTION&tr=udp%3a%2f%2ftracker.leechers-paradise.org%3a6969&tr=udp%3a%2f%2ftracker.openbittorrent.com%3a80&tr=udp%3a%2f%2fopen.demonii.com%3a1337&tr=udp%3a%2f%2ftracker.coppersurfer.tk%3a6969&tr=udp%3a%2f%2fexodus.desync.com%3a6969

3 of the best Ive found

[Anonymous No.10783730]

>>10783677
what do you recommend instead? I downl- I mean I bought it for learning precalculus.

[Anonymous No.10783841]

>>10781467
>topology

[Anonymous No.10784172]

>>10783100
literal shit.
>>10783131
oh no anon that is illegal though, you aren't respecting the copyrights :(
also how safe is it ti use this? don't want virus
>>10783139
based
fuck numbers
>>10783585
wtf I don't want to go to jail cuz I want to fuckign learn!?
but I don't have fucking money to waste on books

[not OP No.10784176]

>>10784172
dont be such a boomer. copyrights are a joke. and no, you will never get a virus its a well known site

[Anonymous No.10784178]

>>10783682
kek send you to me
thanks

[Anonymous No.10784180]

>>10784176
im not a gay boomer. im a wide eyed freshman. ;)
but what about jail bro? I don't want to go to jail.

[not OP No.10784204]

>>10784180
kek no you wont to go to jail. thats not how these websites work. your IP will only be seen by the website itself, so the only way a police agency would get your IP is if they took libgen to court. but, libgen is hosted in russia if I recall correctly, also, so many people use it it would be impossible for everyone to be brought to trial lol- its more practical that they try to take down the website.

[Anonymous No.10784227]

>>10781973
>isn't Proof Theory an advanced topic?
Introductory proof books aren't really about Proof Theory. Those introductory books only use the most basic concepts of elementary logic and they are more about APPLYING those concepts in "normal", informal arguments. On the other hand, Proof Theory and Mathematical Logic in general are about studying those logical principles, rather than applying them. So Proof Theory is more about metalogic than logic itself.

>I think you need a solid math background to start learning proofs.
That's very contradictory. Math is all about proofs (when done right), so how are you gonna start math if you don't understand how proofs work?

[Anonymous No.10784234]

>>10781973
>Why should I start like that? isn't "normal" to start doing Calculus in any math related career on college?
You need to be clear about what you want: do you want to be able to do Calculus mindlessly or do you want to undersatnd how math works? Depending on your answer there are different books suited to do the job. If you only want to be able to solve Calculus problems without really understanding what you're doing (like the average engineer), you can read a basic bitch Calculus book without any prerequisite. If you wanna understand how math works, you should learn about logic and proofs; and then move on to rigorous Calculus books, which are usually called "Elementary Analysis" rather than "Calculus".

[Anonymous No.10784244]

>>10784204
PP VERY HARD!!!
holy shit this is fucking based
love russia now

[Anonymous No.10784258]

>>10781977

Bro the maths in sicp is explained in sicp you don't need prior knowledge

>>10780917

That's a ridiculous chart

[Anonymous No.10784265]

Boys I see all these fucking charts posted around here and they're always shit. You only need 3 books for a foundation in Maths.

Book of Proof by Hammack
Engineering Mathematics by K.A Stroud
and then 1 Calculus book by Apostol or Spivak.

Following that, pick up any book on a specialised topic you're interested in. Any maths you need for each topic will usually be described in the book.

Stop obsessing over these dumb charts which recommend you 10 different books you'll never read.

[Anonymous No.10784292]

>>10780928
>>10781030
>>10784265

Is it dumb to power through calculus by Spivak without former proof experience?

I am starting uni soon so I want to Finnish it asap. I start in 2 months and if I can get through 1/2 of it I am happy.

[Anonymous No.10784297]

>>10784292

No it's not dumb at all. You will be taught proofs at university anyway. Though in the same way you're looking to get a head start on the Calculus, getting a head start on proofs will help and it's not that hard to learn really.

You don't even need to be able to write your own proofs, just being able to read and understand the proofs of others alone will help you in learning Calculus.

Wish you the best mate.

[Anonymous No.10784417]

>>10784297
Thank you!

[Anonymous No.10784569]

>>10784172
A virus? From what, retard? Just don't run .exe files you aren't familiar with. How tf are you supposed to get a virus from a .pdf? go away, boomer

[Anonymous No.10784939]

>>10784569
Look it up next time before you, once again, embarrass yourself speaking on a topic which you’re clearly ignorant of, zoomer faggot.

[Anonymous No.10784944]

>>10780917
>the wiki says
>the chart says
Those are suggestions. You can do whatever you want.

[Anonymous No.10785043]

>>10784172
look, I really mock /g/ for being mathlets but you are really computerlets, /sci/

[Anonymous No.10785047]

>>10784258
>Bro the maths in sicp is explained in sicp you don't need prior knowledge
last I remembered, you need some basic knowledge of calculus (freshman year)

>That's a ridiculous chart
but why?

[Anonymous No.10785679]

>>10781467
lmao just finished my 2nd year of Maths at Cambridge and haven't heard of or couldn't explain what at least half of this stuff is. This would be a fucking intense curriculum

[Anonymous No.10785911]

>>10780917
You start with any calculus book and you do all the exercises. Hopefully the calculus book has some proofs. You don't do it to just learn calculus, you do it to learn how to 'do math'. Whatever you don't get you directly research to find out, like say you forgot what to do when you encounter a fractional exponent, you would look that up directly then solve the exercise and repeat for anything else you've forgotten. As you work through the huge calculus book, watch MIT's Open Courseware latest lectures on Calculus as well. They're only a few minutes long for each topic.

The idea is you do enough of these basic elementary calculus exercises that you patch all the holes in your elementary arithmetic game to continue on with whatever other math you wish to do. Something else that helps is looking up youtube lectures of professors, like MIT open courseware (not random shmoes, or 3blue3brown(?) shit) who will show you the geometric interpretation of things. Wildberger is really good for this, despite his hatred for the field of the reals you will absolutely learn by watching him describe geometric field representations like the rational number line, or projective geometry.

tl;dr just do exercises, out of a very large Calc book to start. You'll know what to do after.

[Anonymous No.10785935]

>>10781977
Then do the alternative to SICP from Brown University (PAPL) https://functionalcs.github.io/curriculum/#sec-2-2 while you fix your math.
You can also just start with Concrete Math and then directly look up on Khan Academy or Expii.com whatever notation you don't get, like limits notation whenever you see it in Concrete Math, there's not much Calculus in there a motivated highschool student could finish it. 'Motivated' means, you refuse to not learn a subject, try a little everyday and if you can't figure something out you just keep working at it until you eventually do using well established techniques of problem solving from Polya's book about it. You print out the wikipedia page and just go through the list "Have I seen this problem before... yes I have in the previous Chapter... Ok now let's break down this problem by changing all the variables to 0 or 1 and see what happens"

[Anonymous No.10785949]

>>10785043
I can watch an hour long youtube video to figure it out, you cannot do that for math.

[Anonymous No.10785967]

>>10785949
>1hour youtube video to learn about cryptography

lol, good luck with that

[Anonymous No.10785997]

Can someone explain to me how they teach math in the US? it just doesn't make sense to me. How would you even understand anything substantial about calculus or linear algebra if you could not understand at least simple proofs? And what kinds of exercises do you do, just calculating stuff? isn't that extremely boring and a waste of time?

[Anonymous No.10786031]

>>10785997
where are you from? I hear americans do it like you said. My country do it like that too.

[Anonymous No.10786070]

>>10786031
I'm from germany. The first thing we teach freshmen here is how to prove simple stuff. In the first semester they learn basic analysis and linear algebra, by seeing proofs for every statement that is in the lecture and by having to come up with their own proofs for simple problems each week. Its the same in at least some other countries in europe.

[Anonymous No.10786145]

>>10786070
so OP's pic is not so bad after all?

[Anonymous No.10786203]

>>10786145
No, it's bullshit. Reading a book on proof theory is not necesary at all. You just need to know very basic elementary logic, you could probaply watch a few youtube videos and be fine. I think the best way to start is to learn some introductory material and to just prove simple statements about the topic for yourself (i.e. just get a suitable beginner book and do the exercises) that way you get better at writing proofs naturally as you learn. Proving something is just making a very rigerous argument for why it's true, it's not magic.

[Anonymous No.10786314]

libgen.io

[Anonymous No.10786808]

>>10785047

SICP isn't about maths. The maths in it is not hard and most of the time is explained within the book. Watch the lectures on YouTube by the author if you can't handle it. They're even more accessible.

[Anonymous No.10786810]

>>10785935

You're better off downloading a lecture series on computing maths to be honest. Concrete Maths is big because of knuth fanboys who all own TAOCP but haven't read more than 2 pages.

[Anonymous No.10786835]

For people who are afraid of calculus and wants something even easier and concrete than Spivak, I usually recommend Richard Hamming's book. The explanations are remarkably clear and concise, but fully detailed and have very good concrete explanations that also generalize very well. He also talks about cool topics like Fourier series and probability, which is cool considering that the author worked with John Tukey himself (he also shared an office with Claude Shannon once, according to wiki).

https://books.google.com/books?id=WLIbeA1aWvUC&lpg=PP1&dq=hamming%20calculus&pg=PP1#v=onepage&q&f=false

[Anonymous No.10786914]

>>10786314

God what an awful person

[Anonymous No.10787033]

What are the best books for self learning high school level algebra and trigonometry? I know Gelfand has covered both but I don't think those books are as rigorous in exercises as they should be. Or are they enough? Any recommendations?

[Anonymous No.10787279]

>>10787033
organic chemistry tutor
khan academy

[Anonymous No.10787284]

>>10787279
I said books.

[Anonymous No.10787289]

>>10787284
oh my bad
calculus for dummies
and stop being anime nignog

[Anonymous No.10787299]

>>10787289
>calculus for dummies
For learning algebra and trigonometry? Forget it honestly, I'll just use Gelfand. Besides, I hate the "for dummies" series. It treats you like an idiot.

[Anonymous No.10787305]

>>10787299
>high school
>algebra
>trigonometry
brainlet school

[Anonymous No.10787343]

>>10787305
I'm not in school though, which is why I said SELF LEARNING.

[Anonymous No.10787374]

>>10787343
I'm trolling don't worry

[Anonymous No.10787434]

>>10780928
Yeah and by the time then you are 80 years old you can finally start actually learning math.

[Anonymous No.10787443]

>>10787434
lmao!

[Anonymous No.10787460]

I picked Apostol's Calculus? Should I have chosen Spivak?

[Anonymous No.10787522]

>>10787460
I read Spivak and I think it's decent, but not really as good as some people make it out to be. His way of defining trigonometric functions is pants-on-head retarded.

Never read Apostol, but I hear he covers both single-variable and multi-variable calculus (and also some linear algebra that you need for multi-variable), unlike Spivak that only covers single-variable. So Apostol sounds like a better one-stop solution.

>>10787299
Why do you want to learn high-school algebra in the first place? It's retarded and not rigorous at all (so you might as well read a For Dummies book at that point). If you aren't a kid anymore, you should just learn some logic and set theory (just the basics) and then study abstract algebra (or just linear algebra if you don't care much for algebra itself and just want to use it for calculus and other shit). By doing that you'll pick up everything that high-school algebra could teach you and much more. Gelfand books are a waste of time, not much better than Calculus For Dummies.

[Anonymous No.10787957]

>>10786070
I'm from a third world south american shithole and it's done the same way, in highschool just mindlessly computing shit and in uni introductory analysis with proofs, so I don't think that in America should be any different

[Anonymous No.10788052]

>>10787033
OP here, just do what I am doing. Precalculus - Stewart.

[Anonymous No.10788061]

>>10787957
hey I am from Peru, the same but I think in university is different (I never got in thought). Where are you from? I thought it was a "peruvian thing" the way they teach mathematics at school.

[Anonymous No.10788173]

>>10787033

Gelfand is not good for self-teaching. There are better methods of teaching that modern books use based on research. Get a book like foundation mathematics by ka stroud.

[Anonymous No.10788265]

>>10788173
>foundation mathematics by ka stroud
Not available on libgen.io. Any other recommendations?

[Anonymous No.10788456]

Non meme answer:

1. Learn Proofs, it's nothing complicated and if you know programming you're basically halfway there. It can be done by high schoolers, and it can be like solving a fun puzzle, because it doesn't feel arbitrary.

I recommend Hammack's "Book of Proof" and Velleman's "How to Prove it".

2. Get your precalculus foundations rock solid. Just get a book like "Precalculus in a Nutshell" or "Precalculus for Dummies", do a bunch of excercises and hone in on the problems and sections you don't understand. It's important to have a good understanding of this so you can do everything else faster.

3. Learn Calculus (single and multivariable) with the average textbook (Stewart or Larson) + a supplement like "Calculus Lifesaver" or "Calculus for Dummies". Just read the explanations and do all/most of the excercises and you'll develop the so-called "Mathematical Maturity" and intuition to tackle more advanced math.

Don't listen to the memers who say "pick up Spivak/Apostol", they already have math degrees and thus think these books are better for beginners; They are not.

4. Learn Ordinary Differential Equations. Tenenbaum and Simmons are the only good books, in my opinion.

5. Learn Linear Algebra. You can technically do this at the same time as Calculus but it's easier after because of the aforementioned "Mathematical Maturity".

Again, favor introductory books like "Introduction to Linear Algebra" by Strang over rigurous ones like Axler or Hoffman and Kunze.

6. Now you're actually ready to learn. You can go straight into Real Analysis, or you can actually start on the more advanced books /sci/ recommends like Axler, Spivak or Apostol.

[Anonymous No.10788460]

>>10788456
Some pointers for the last step:
-All Lang books are memes.
-Abstract Algebra can be done early and only strictly requires precalc and proofs, but you're better off learning it after you develop the aforementioned mathematical maturity. Pinter is the easiest introduction.
-Baby Rudin is not a meme, you will literally feel your brain growing as you solve the exercises, but it's dogshit for self-study and without a good instructor.
I recommend Abbott's "Understanding Analysis" and "Real Analysis" by Jay Cummings.
-Topology is weird.
-Probability is it's own thing. There are 4 books that I recommend and that are intuitive (ie. Not proof-jerking or overly verbose):
**"Introduction to Probability" by Bertsekas
**"A First Course in Probability" by Ross
**"Introduction to Probability" by Hossein
**"Statistical Inference" by Casella and Berger
And from there you can decide which subjects you want/need to pick up.
-You will have to learn coding at some point; It makes things easier, and actually ties in very well with subjects like Proofs and Probability. Learn Python and then R or Matlab.
-Anyone can do math but you have to be persistent and learn from your errors.
Don't fall for the IQ or "genius math people" myths, if you're lazy it doesn't matter how big brained you are because you will hit a wall at some point or another.
Converserly, anyone can learn math (at very least undergraduate math) like anyone can learn a language. Millions have done it, it's not really an otherwordly thing.

[Anonymous No.10788561]

>>10788456
>>10788460
Thank you, thank you, anon! I am already reading precalculus, I guess I will try baby first proofs after I finish it.

If I wanted to go more into computation and CS, should I go full Discrete Math after Calculus? instead, can I jump directly to statistics after Calculus?

[Anonymous No.10788805]

>>10788561
You can get started with discrete maths as soon as you know how to do proofs if you're in a hurry to learn, really. Many hobbyist programmers already know the fundamentals. But it's easier if you have mathematical maturity.

And you can learn Probability and Statistics after Calculus, but if you want to do a lot of fun stuff (ie. Data science and programming) you should learn linear algebra. You can get your feet wet with Hossein and Bertsekas since the first chapters are very gentle introductions.

[Anonymous No.10788834]

>>10788805
Great, I will check it out.

[Anonymous No.10788854]

Ok, after apostol and spivak... what?

[Anonymous No.10788858]

[Anonymous No.10789626]

>>10788854
Number theory and combinatorics. Linear algebra. Differential equations. Coding and math sofware. Physics 1 to 3. Probability theory. Abstract algebra, real and complex analysis, topology, vector analysis, differential geometry, functional analysis, measure theory...

[Anonymous No.10789650]

>>10786070
>>10787957
Epsilon-delta proofs? Of course not compactness proofs for example. Well that is not mindless computation. And Linear Algebra, as taught by algebraists, is completely proof based.

[Anonymous No.10789663]

>>10786835
>Nice! Thank you

[Anonymous No.10789665]

wait, so you are telling me that mathematics teaching in most parts of the world are taught completely wrong and/or in reverse?

why aren't we changing it?

[Anonymous No.10789721]

>>10789665
((()))

[Anonymous No.10789726]

>>10789721
kek, clown world

HONK HONK

[Anonymous No.10789958]

>>10789665
Many people wouldn't be able to keep up.

[Anonymous No.10790082]

>>10788460
>Pinter is the easiest introduction
>Learn Python
If it weren't for these two things, I would've fallen for your bait.

Pinter relegates a lot of important proofs to the exercises. It's not a good idea to have a beginner prove the bulk of Galois theory as an "exercise". And if you're in math why would you learn a meme language like Python? Just learn C, Lisp, and Fortran.

[Anonymous No.10790219]

>>10785679
I’m sure many working mathematicians (basically anyone not working in complex geometry/mathematical physics) would not either. This list is a meme

[Anonymous No.10791507]

>>10790082
>calls Python a meme language
>includes Lisp and Fortran
Lmao

[Anonymous No.10791530]

>>10791507
i know get a load of this old man here

[Anonymous No.10791709]

>>10787434
if reading 4 books takes you about 60 years then you ain't smart enough for math pal, try again in another life

[Anonymous No.10792624]

What do I have to read and in how much time I would be able to understand InterUniversal Teichmuller Theory?

[Anonymous No.10793080]

>>10792624
You only need to know that Teichmuller was a nazi and died fighting the russians

[Anonymous No.10793135]

>>10793080
so it's good math?

[Anonymous No.10794052]

>>10780917
>let's settle this
110 posts later and nothing is settled

[Anonymous No.10794056]

You should definitely start with precalculus

[Anonymous No.10794063]

>>10794056
Oh yes, he should also do exercises too, that will help him.

[Anonymous No.10794064]

>>10794052
its already been explained thousands of times, the wiki has a comprehensive list of textbooks on most undergraduate topics in mathematics along with brief, concise explanations for different approaches to learning the various subjects. If someone is too stupid to understand how to access that page they don't deserve help.

[Anonymous No.10794100]

>>10794063
are you being unironically ironic?

[Anonymous No.10794445]

On the topic of the anime boy above; is algebra needed for many of the books mentioned here? As of now, I'm going through Gelfands Algebra book. This was done as I tried Langs Basic Mathematics, but felt my lack of basic Algebra stopped me from really understanding what he was doing. Should I really just learn proofs/logic, and jump into abstract algebra then calculus? What if I know jack shit about geometry? Should I go and learn that first? View me as someone with only knowledge of arithmetic. If I would ask, "I want to learn higher math"; what would you recommended me?

[Anonymous No.10794461]

>>10780928
>Not learning Sanskrit to read the original mathematical sutras

Do Americans REALLY??

[Anonymous No.10794488]

>>10794445
I don't know how anyone can claim with a straight face that learn abstract algebra and skip middle school tier math. Literally no one does this, you are getting facetious answers from people who went through the normal math circuit themselves before going to uni

Unironically use Khan Academy to get you up to precalculus level at least before tackling these meme books.

[Anonymous No.10794512]

>>10794488
Thank you for clearing it up for me. Is their any advantage from learning from Gelfand, versus Khan Academy? I started with Khan, then when I was done with Arithmetic I jumped to Gelfands Algebra. I really enjoy studying mathematics; but questioning if I'm on the right study path makes me scared I'm not advancing how I really should be.

[Anonymous No.10794536]

>>10794512
You aren't going to poison the well by going on Khan Academy to practice the basics. I see no reason why you can jump back and forth between both?

[Anonymous No.10794567]

>>10794536
Ture. Thank you for the help. I hope the other anon asking about his studys with Gelfands Algebra is a little less bit confused as I was now.

[Anonymous No.10794742]

>>10789721
>>10789726
>>>/pol/

[Anonymous No.10794761]

>>10794742
mathematics is racist

[Anonymous No.10794784]

>>10794742
Imagine putting in the effort to make such an empty, clichéd post. Very NPC-like. Many such cases

[Anonymous No.10794818]

>>10780917
it doesn't matter there are many approaches.
Just proceed to have fun ;)

[Anonymous No.10794820]

>>10788460
false abstract algebra has zero requirements (except perhaps functions and set theory but those always come included in introductory chapters to abstract algebra already)

[Anonymous No.10795151]

>>10794742
>thinking only pol knows clownworld

how new are you friend?

*honk honk*

[Anonymous No.10795174]

>>10785047

There's only calculus for one problem which you can skip without any fear of missing something.

SICP isn't a maths book. It uses maths to teach programming but it typically explains the maths.

If you don't like the approach use HTDP instead.

[Anonymous No.10796768]

ah fuck this gay, I will just use these for precalc and calculus

http://www.stitz-zeager.com/

https://activecalculus.org/

fuck Stewart, fuck Spivak, fuck Apostol

[Anonymous No.10798376]

>>10794512

> I really enjoy studying mathematics

You're already 90% there