Into science? Math, Physics, Chemistry, Biology, I know less than a 5th grader. How and where I start?

into science? Math, Physics, Chemistry, Biology, I know less than a 5th grader. How and where I start?

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It's already too late for you. You should have majored in a STEM field in college.

Begin by watching "Are You Smarter than a 5th Grader"

Why is it too late? I'm 23 btw.

khan academy i guess, then from there you can get into more thorough and deeper stuff

youtube.com/watch?v=au4hbUm4mMo
here is something both science and interesting. Watch this and other videos and google what he talks about that you don't understand.

...

"Golden road or nothing at all" is a Veeky Forums meme. People shitpost about learning only being available to people who roll straight into ivy league at 17 in order to pass their crippling imposter syndrome on to as many people as possible.

For self learning physics, I'd suggest pic related. It's written in a clear, conversational tone and starts extremely basic. I'm sure Veeky Forums knows better books as far as rigorous content goes, but I still think Knight is the right starting point because it goes to great lengths trying to help the student think clearly about the problems presented.

I don't know any good calculus text book for the autodidact at a late HS/early college level. Stewart is basic, but dry garbage. Spivak is lovely but expects a little more going in. Khan Academy might be the best place to start math over desu.

Try KhanAcademy

Hall and Knight - Elementary Algebra for Schools
Lang - Basic Mathematics
Keisler - Elementary Calculus: An Infinitesimal Approach
Young and Freedman - University Physics with Modern Physics
Oxtoby, Gillis, and Nachtrieb - Principles of Modern Chemistry
Reece, Urry, Cain, Wasserman, Minorsky, and Jackson - Campbell Biology

Read the sticky.

>look mom he posted the memelist again

There's an introduction list in the autodidact general here:

>he fell for one of Veeky Forums's memelists so hard that he even reposted it on Veeky Forums
whew the people on this board are gullible

>any attempt to offer suggestions is a meme list
Neck yourself you cynical, useless brainlet.

Calculus: A Modern Approach is a good balance between Stewart and Spivak. And also it's free.

Calculus: A Modern Approach by Jeff Knisley*

>>any attempt to offer suggestions is a meme list
Where did you get that implication? I only referred to the specific list of math books in that Veeky Forums post which is a memelist that gets posted on Veeky Forums every so often. I guess it got copypasted over because someone wanted to make their Veeky Forums list overly comprehensive to point of useless, but didn't actually see if the list was worthwhile

>Neck yourself you cynical, useless brainlet.
zZz

>Where did you get that implication? I only referred to the specific list of math books in that Veeky Forums post which is a memelist that gets posted on Veeky Forums every so often.
Because you accused multiple kinds of lists of being "the meme list" without giving any sort of reason. Seems like you have a neurological condition that prevents you from distinguishing lists from one another.

>I guess it got copypasted over because someone wanted to make their Veeky Forums list overly comprehensive to point of useless, but didn't actually see if the list was worthwhile
Give me 3 reasons why it isn't useful without using the word "meme" or "list". Pro tip: you can't.

He said that it was overly comprehensive to the point of useless, that's a reason to me.

Even the list itself says you can skip around depending on what you need, unless that is too difficult for you. Most of the books cover subjects you'd find in your average math degree, so if you're going to call that book list "too comprehensive to the point being useless" then you might as well throw your math degrees in the trash. I wonder if any of you folks struggle with what to wear in the morning.

>Here's a list to learning advanced mathematics, starting from around high school. This list is comprehensive, but the books don’t have to be done in order if you are looking for specific goals. For example, if you want to do real analysis, you could probably just do Knisley > Velleman > Apostol (optional) > Tao. But if you want to be systematic, I think this is the way to do it by mirroring a typical math curriculum.

What did he mean by this?

I'm not that guy and I'm not criticizing the list. It's just that you said he accused multiple kinds of lists without giving any sort of reason, but he did give one, albeit a, in your opinion, bad one, and I felt the need to point that out. Didn't mean to agitate you, and if I did, I apologize.

>Because you accused multiple kinds of lists of being "the meme list" without giving any sort of reason. Seems like you have a neurological condition that prevents you from distinguishing lists from one another.
My post () actually says "one of Veeky Forums's memelists". May I recommend you a book on reading comprehension?

>Give me 3 reasons why it isn't useful without using the word "meme" or "list". Pro tip: you can't.
1) It claims to be a "full mathematics track" when there's hardly anything past the 2nd or 3rd year level of study in an average math program. If someone read every book on that list they still wouldn't have actually gotten anywhere
2) It looks more like an attempt at some 'makeshift degree' than actually learning math with any real direction in mind. If you want a degree, get a degree. If you don't, you don't need anywhere near so much fluff.
3) It claims to be "comprehensive" yet is nowhere close, I don't even see a book on complex analysis but there's a book on nonlinear dynamics for some reason? lol. I suspect the person who made the list maybe has a math minor at most (if they have a major that was a serious waste of 4 years)

>Most of the books cover subjects you'd find in your average math degree, so if you're going to call that book list "too comprehensive to the point being useless" then you might as well throw your math degrees in the trash. I wonder if any of you folks struggle with what to wear in the morning.
You only being able to resort to posts like this makes me question your intentions (and self-esteem)

I don't see a point in criticizing a list meant to introduce people to what is mathematics for being comprehensive. Either it is comprehensive and it does its job or it avoids breadth and fails to do its job. Even the list itself gave alternative pathways for those who just want a shortcut to real analysis.

When I originally said comprehensive I meant in terms of the entire Veeky Forums thread. Any list large enough for chemistry, biology, law, reading, math, philosophy, art, music, social skills, and more is certainly not useful

Also to add to 3)

There's literally nothing about number theory, but there's a book on formal logic

>My post () actually says "one of Veeky Forums's memelists". May I recommend you a book on reading comprehension?

First it's "the meme list". Now it's "one of Veeky Forums's meme lists". It sounds like you only became aware of the last list just now, and because of your phobia of lists, you've deemed it a meme.

>1) It claims to be a "full mathematics track" when there's hardly anything past the 2nd or 3rd year level of study in an average math program

It never claims that it'll take you to graduate level mathematics, albeit it will definitely get you mature enough to figure out 1) if that shit is right for you; and 2) how to get through it.

>It someone read every book on that list they still wouldn't have actually gotten anywhere

Being able to tackle pure mathematics is "somewhere".

>2) It looks more like an attempt at some 'makeshift degree' than actually learning math with any real direction in mind. If you want a degree, get a degree. If you don't, you don't need anywhere near so much fluff.

If you want to learn math without going to school, here's how you do it. It's an AUTODIDACT thread for AUTODIDACTS.

>3) It claims to be "comprehensive" yet is nowhere close, I don't even see a book on complex analysis but there's a book on nonlinear dynamics for some reason? lol. I suspect the person who made the list maybe has a math minor at most (if they have a major that was a serious waste of 4 years)

First it's overly comprehensive, now it's not comprehensive at all. Jesus Christ, are you bipolar? Or are you angry that your pet math project wasn't included in the list? Get over yourself.

>You only being able to resort to posts like this makes me question your intentions (and self-esteem)
I have the self-esteem to know what I want to do when I see a list of options instead of getting scared by the number of choices and crying about it. You, apparently, don't.

>There's literally nothing about number theory, but there's a book on formal logic
>Concrete Mathematics - Donald Knuth

You don't even know what you're fucking talking about, you dumb cunt.

>if I combine two good lists into one location, both lists magically stop being useful
Is this what brainlets think? Compile enough useful information together in one place, and it becomes useless? Maybe that's why you have such an aversion to reading.

>It never claims that it'll take you to graduate level mathematics
Then what is "full mathematics track" supposed to imply?

>If you want to learn math without going to school, here's how you do it. It's an AUTODIDACT thread for AUTODIDACTS.
So why are you trying so hard to make it look like school? School is for credentials. Most of the list is fluff, quite literally useless for someone who just wants to learn math.

>First it's overly comprehensive, now it's not comprehensive at all. Jesus Christ, are you bipolar? Or are you angry that your pet math project wasn't included in the list? Get over yourself.
see
I don't care about my "pet math project" at all, in fact this list looks far more just like your personal reading list instead of anything curated for anything or anyone in particular. Complex analysis is objectively far more relevant for most people in mathematics than nonlinear dynamics

>I have the self-esteem to know what I want to do when I see a list of options instead of getting scared by the number of choices and crying about it. You, apparently, don't.
I know exactly what I want to do when I see such a useless list: ignore it.

>You don't even know what you're fucking talking about, you dumb cunt.
If you think Knuth is at all a useful introduction to number theory this just tells me you literally don't know any number theory beyond what's in that book. More to suggest whoever made the list has a math minor at most.

>Compile enough useful information together in one place, and it becomes useless?
You're perhaps the only person who would make the claim that this information is useful for anyone.

There is no need to get so upset mate.

I'm not surprised he spams a memelist so hard on Veeky Forums, with that much anger he probably doesn't much attention in real life, this probably gives him some sense of validation.

Not a good list. You start good with tao, hk and pinter, but then theres stuff all over the place, nonlinear dynamics for physicists without an ode book, no complex analysis or geomrtry, etc

Is the stuff recommended in the Veeky Forums wiki any good? Will I be able to learn math by reading a book or two from each of the topics listed? I'm reading Elementary Calculus An Infinitesimal Approach right now.

Thats not number theory mate. Thats combinatorics. Try ireland & rosen

>Then what is "full mathematics track" supposed to imply?
That it gets you to doing serious mathematics.

>So why are you trying so hard to make it look like school? School is for credentials. Most of the list is fluff, quite literally useless for someone who just wants to learn math.
TIL pre-calculus, calculus, linear algebra, differential equations, proofing, real analysis, and beyond are "totally useless for learning math"

>I don't care about my "pet math project" at all, in fact this list looks far more just like your personal reading list instead of anything curated for anything or anyone in particular. Complex analysis is objectively far more relevant for most people in mathematics than nonlinear dynamics
If I had to be totally honest, it was a list that tried to incorporate those interests in pure mathematics for its own sake and those interested in pure mathematics for the sake of understanding its use in applications without simply regurgitating how they're taught to use it.

>I know exactly what I want to do when I see such a useless list: ignore it.
If you don't need to learn anything from the list, then feel free to ignore it. I have yet to see any real indications that you are offering critique and alternatives instead of sperging over your hatred of lists.

>If you think Knuth is at all a useful introduction to number theory this just tells me you literally don't know any number theory beyond what's in that book. More to suggest whoever made the list has a math minor at most.
"If I don't start out learning about the Goldbach conjecture, you're literally not getting an introduction." Sounds like another one of those aspergers-addled nerds suggesting readers to begin their math studies with Rudin.

>You're perhaps the only person who would make the claim that this information is useful for anyone.
Plenty of people have found one book or a series of books in this list to be useful.

The sticky is shit, the wiki is ok-ish. Best is to ask whenever in doubt of what to do next.

It's infuriating dealing with people who are only interested in massaging their own ego instead of contributing to, I don't know, a decent reference guide to others. Most of the choices in that list are well justified.

>Not a good list. You start good with tao, hk and pinter, but then theres stuff all over the place, nonlinear dynamics for physicists without an ode book, no complex analysis or geomrtry, etc
They're not meant to be done in order at that point, only if you have some sort of preference towards one topic or another. Real analysis is supposed to be the point where stop for reflection and decide what purpose math should have for you.

Then why bother posting anything else? Let your list be what it is:

>Veeky Forums guide for beginning in math
Linear Algebra - Hoffman & Kunze
A book of Algebra - Charles Pinter
Analysis I&II - Terrence Tao
(Before this you should know calculus, try X by so and so)

Clean, simple, to the point

>Is the stuff recommended in the Veeky Forums wiki any good? Will I be able to learn math by reading a book or two from each of the topics listed?
Well they're math books, so unless you have any more focused direction in mind I don't see the problem.

>TIL pre-calculus, calculus, linear algebra, differential equations, proofing, real analysis, and beyond are "totally useless for learning math"
Ah so you're from reddit, now this makes more sense. Anyway, any list that has both PDEs and Khan academy on it is clearly too unfocused to be useful.

>If you don't need to learn anything from the list, then feel free to ignore it. I have yet to see any real indications that you are offering critique and alternatives instead of sperging over your hatred of lists.
see >"If I don't start out learning about the Goldbach conjecture, you're literally not getting an introduction." Sounds like another one of those aspergers-addled nerds suggesting readers to begin their math studies with Rudin.
The list is completely uneven, it takes differential equations all the way to PDEs but doesn't even take number theory to something as basic as quadratic reciprocity.

>Plenty of people have found one book or a series of books in this list to be useful.
[citation needed]

>It's infuriating dealing with people who are only interested in massaging their own ego
Oh the irony, as he posts his personal reading list to be ignored for the 100th time

>They're not meant to be done in order at that point, only if you have some sort of preference towards one topic or another. Real analysis is supposed to be the point where stop for reflection and decide what purpose math should have for you.
What is your educational background even? I can't tell if you're an undergrad or did a major in something other than math

See, I don't mind these kinds of suggestions. I have been considering re-organizing the list to take a lot of "remedial" and "general problem-solving troubleshooting" material out of the core for presentation purposes.

>Ah so you're from reddit, now this makes more sense.
Did you pull that from your ass?

>Anyway, any list that has both PDEs and Khan academy on it is clearly too unfocused to be useful.
[citation needed]

>see
Where's the alternatives? Where is any indication that you'd want to see an improved list?

>The list is completely uneven, it takes differential equations all the way to PDEs but doesn't even take number theory to something as basic as quadratic reciprocity.

So the list is immediately fixed by adding Hardy or Rosen to 5. Further Reading. Address complex analysis by adding Needham. Simple.

>[citation needed]
I never thought I would have to argue that Apostol or Tao were found to be useful by people studying mathematics. But I guess anything is possible with Veeky Forums.

It's not my even list. And I'm getting all of these (You)s so I'm clearly not getting ignored.

It's not a list meant for people who are majoring in mathematics. It's a list for people who want to learn mathematics on their own. If you were doing a degree in mathematics, then you don't really have a choice in learning about abstract algebra, complex analysis, etc., because you need to know it if you want to get modern math. You're free to jump off the ride any time you want once you feel satisfied or once you know it's not for you. I don't get why that concept is so hard for people to get.

>Did you pull that from your ass?
No, the TIL was the giveaway.

>[citation needed]
If you're anywhere near PDE level, the top half of the list is useless, if you're anywhere near Khan academy, the bottom 90% of the list is useless.

>Where's the alternatives? Where is any indication that you'd want to see an improved list?
The alternative is to scrap the whole list. Have you still not gotten the implication that I don't think your list is adequate for anything? I'd think that 10 posts in you'd be able to see I think your list is very sub-optimal

>It's not my even list. And I'm getting all of these (You)s so I'm clearly not getting ignored.
So you're just reposting someone else's book list over and over... have you even read any of them?

>It's not a list meant for people who are majoring in mathematics. It's a list for people who want to learn mathematics on their own. If you were doing a degree in mathematics, then you don't really have a choice in learning about abstract algebra, complex analysis, etc., because you need to know it if you want to get modern math. You're free to jump off the ride any time you want once you feel satisfied or once you know it's not for you. I don't get why that concept is so hard for people to get.
Why did you dodge the question? What's your educational background? It gives more context into why the list is as flawed as it is.

>No, the TIL was the giveaway.
I don't even go on Reddit. As far as I can tell, you're more familiar with Reddit than I am.

>If you're anywhere near PDE level, the top half of the list is useless, if you're anywhere near Khan academy, the bottom 90% of the list is useless.
And? This is the most pedantic criticism of what is supposed to be a list that takes you from the top to the bottom. Every list does that. If you start at the top of a list, the bottom is going to be useless. If you've already read some of the topics in the beginning of the list, then only the bottom is useful.

Again, it just sounds like you're terribly afraid of lists.

>The alternative is to scrap the whole list. Have you still not gotten the implication that I don't think your list is adequate for anything? I'd think that 10 posts in you'd be able to see I think your list is very sub-optimal
What I've gotten is that the presentation needs to be improved and that people felt like complex analysis and number theory couldn't be ignored, which I think is right, and I'll change by adding Hardy and Needham if I repost it.

I thought it was a good idea given my personal experiences with several books in the list. No, I haven't fully read a good 75% of them, but I did take a peek at each book to see if they'd be useful. I actually like good criticism because it makes me figure out how to improve it in the future.

You've got me. I'm a physics major with a math minor.

>And? This is the most pedantic criticism of what is supposed to be a list that takes you from the top to the bottom. Every list does that. If you start at the top of a list, the bottom is going to be useless. If you've already read some of the topics in the beginning of the list, then only the bottom is useful.
Why not just put some coloring books and "learning to write the alphabet" books at the top and some arithmetic geometry books at the bottom then? Might at well keep making it bigger. Do you have no concept of scope?

>Again, it just sounds like you're terribly afraid of lists.
What gives you this implication? I haven't made any criticism about lists in general, just this memelist.

>What I've gotten is that the presentation needs to be improved and that people felt like complex analysis and number theory couldn't be ignored, which I think is right, and I'll change by adding Hardy and Needham if I repost it.
Why not just give recommendations about things you actually know, instead of books you've never read? You don't need to give advice about every thing in existence, it's okay to offset that to others

>I thought it was a good idea given my personal experiences with several books in the list. No, I haven't fully read a good 75% of them, but I did take a peek at each book to see if they'd be useful. I actually like good criticism because it makes me figure out how to improve it in the future.
You sound more focused on lists of books that's the things actually inside the books

>that's
than*

>You've got me. I'm a physics major with a math minor.
So why not make a physics list? It's very clear you don't have enough experience with the math literature based on the recommendations

>Why not just put some coloring books and "learning to write the alphabet" books at the top and some arithmetic geometry books at the bottom then? Might at well keep making it bigger. Do you have no concept of scope?
Scope is easily addressed by presentation and formatting. It is meant to take somebody with a high school education and get them into doing pure mathematics, and if that is too unwieldy of a scope, then your average mathematics degree is "useless".

The problem is that if you're trying to beeline to pure mathematics, you're generally forced to take a lot of classes that aren't really helpful for developing the proofing skills that you'll need later on but are still critical for doing quantitative work in the sciences. And a lot of great books have been written in light of that problem, i.e., Axler's and Hoffman/Kunze's books are written for your second pass at linear algebra after you finish an intro class that often won't have much proofing if any at all.

I get that the list hasn't done a good job of presentation by including too much "fluff" in terms of books like "How to Prove It" and "

>What gives you this implication? I haven't made any criticism about lists in general, just this memelist.
Because of your comment about the phenomenology of lists. Seriously, if you're supposed to go through a list to learn something, then obviously the more advanced stuff in the bottom is going to be useless to the beginner at first. But what kind of criticism is that? All lists would have that "flaw".

>Why not just give recommendations about things you actually know, instead of books you've never read? You don't need to give advice about every thing in existence, it's okay to offset that to others
I'm still recommending books that I've read. And I generally see more people on Veeky Forums bashing other people and shitposting instead of offering recommendations. I figured I would put some effort into making a digestible list.

>How and where I start?
youtube.com/watch?v=91c5Ti6Ddio

*I cut myself off prematurely

I get that the list hasn't done a good job of presentation by including too much "fluff" in terms of books like "How to Prove It" and "The Art and Craft of Problem Solving", but I personally found them helpful in dealing with a particular area of mathematics. The former helped me get Apostol, the latter helped me qualify for the AIME back in high school and otherwise do well in quantitative problem-solving. Kolmogorov confirmed my desire to pursue pure mathematics in my own time.

The original list had great books that I knew from experience, but it also had pointless or stupid recommendations like books you couldn't libgen or books that didn't cover appropriate topics for progressing in the list. If I knew a book would be good, I kept it. If I knew a book would be trash after looking at the table of contents and checking out samples, I tossed it. I also relied on recommendations from people like you here for the last part of the list, but you'd be right to say that that's my "personal reading list", though I'd wager that anybody else with my goals in mind would have parts of in common in their reading list as well.

I have enough experience to give advice to someone about what mathematics they'll need for physics and how to get a more in-depth understanding instead of just embracing "shut up and calculate". Some of the fluff books like How to Prove It I'd appreciate all of the input into making a better list because it'd help me out extensively too.

>It is meant to take somebody with a high school education and get them into doing pure mathematics
So why the books on applied mathematics?

>and if that is too unwieldy of a scope, then your average mathematics degree is "useless".
This list is not at all comparable to the average degree, your physics background is clouding you here. There isn't even any geometry on the entire list lmao

>Seriously, if you're supposed to go through a list to learn something, then obviously the more advanced stuff in the bottom is going to be useless to the beginner at first.
But what is the 'something' for this list? There's no focus at all.

>But what kind of criticism is that? All lists would have that "flaw".
No, only 'vertical' lists that are too long and unfocused like this memelist have this flaw. 'Horizontal' lists don't have this problem, neither do better curated vertical lists.

>I'm still recommending books that I've read.
How can you say that after saying
>No, I haven't fully read a good 75% of them

>I have enough experience to give advice to someone about what mathematics they'll need for physics and how to get a more in-depth understanding instead of just embracing "shut up and calculate"
Why not say it's a list for physicists then? Full mathematics track is misleading

>but it also had pointless or stupid recommendations like books you couldn't libgen
Bad reason for leaving a book off a list.

>If I knew a book would be trash after looking at the table of contents and checking out samples, I tossed it.
Ever heard of 'don't judge a book by its cover'? Try actually reading a book for calling a book "trash".

>though I'd wager that anybody else with my goals in mind would have parts of in common in their reading list as well.
You'd lose that wager, a lot.

>So why the books on applied mathematics?
Not all pure mathematics has real world applications, but the ones that have real world applications serve as the basis of applied mathematics. I'm not a fan of "shut up and calculate".

>This list is not at all comparable to the average degree, your physics background is clouding you here. There isn't even any geometry on the entire list lmao
You're right, it doesn't get beyond the 3rd year. Lacking introductions to algebraic geometry and differential geometry is a big oversight.

>But what is the 'something' for this list? There's no focus at all.
I've told you the "something", serving as a resource for autodidacts who want to develop mathematical maturity, either for pure or applied purposes.

>>No, I haven't fully read a good 75% of them
I'm referring to the "Further Readings" list which is basically me regurgitating recommendations (that I'd imagine would be held in high regard) from others. That's my "personal reading list".

Because there are books on that list I would have never read if I were interested in only as much mathematics as I needed to "shut up and calculate".

>Ever heard of 'don't judge a book by its cover'? Try actually reading a book for calling a book "trash".
That's a ridiculous characterization of what I did. If you can clearly tell that book is inadequate from looking at what it says it'll cover in the table of contents, then you can say it won't be useful. Maybe it'll be useful for something else, but not the pace and integration that I'm striving for. Reading a sample chapter is also an effective way of telling if a book is suitable or not. You get to see the content, rigor, style, and exercises. If I find that other advanced people have recommended a book after I've deemed it to be useful, then I kept it.

>You'd lose that wager, a lot.
Nobody has ever wanted to read Hoffman/Kunze, C.C. Pinter, and/or Donald Knuth? No, I think this is a safe bet.

Alright, I've been humbled enough to realize that the original list tries to do too much and carries too many concerns with not enough experience to balance anything out effectively.

Here is a re-ordered list:

>0. Remedial High School Mathematics
Khan Academy
Pre-Calculus - Carl Stitz & Jeff Zeager

>1. Introduction to University Mathematics (No Proofs)
Calculus: A Modern Approach - Jeff Knisley & Kevin Shirley
Linear Algebra and Its Applications - David C. Lay
Calculus of Several Variables - Serge Lang
Differential Equations - Shepley Ross

>2. Introduction to Pure Mathematics (With Proofs)
How to Prove It - D. J. Velleman
Calculus Vol. I & II - T. M. Apostol
Principles of Topology - Fred H. Croom
Analysis I & II - Terence Tao

Is this any better? I can vouch for every resource here.

>Linear Algebra and Its Applications - David C. Lay
>No Proofs
You really haven't read any of these books have you?

Do you consider David Lay to be a rigorous book in presentation and in the exercises? It has proofs but it doesn't make you prove much at all.

I never said that the books were "devoid" of proofs, but rather that there was no proofing emphasis in the exercises for students. Every good book will have at least some proofs of crucial theorems, but not all books will have the same scope. Some books are meant for students seeking to understand quantitative problems in, let's say, the sciences. Other books are meant for students to understand the theoretical basis for such and such mathematics. Once you get to the last section of the list, you're going to need to solidify your proofing skills, hence Velleman.

You should have called me out on the Lang recommendation, because that actually has some proofing involved. I wish I had a better book for the topic though, given the scope I want to keep.

lang is good for a textbook. i'd actually throw away apostol if you're already doing lang, also Analysis II and topology may be out of scope here

>lang is good for a textbook. i'd actually throw away apostol if you're already doing lang,
Lang's Multivariable Calculus is halfway between Stewart's multivariable calculus and Spivak's calculus on manifolds, between calculating for applications and rigorously proving foundations It's kind of an odd "middle way" recommendation and I don't know how to situate it in my list.

You're right that Apostol and Lang would overlap too much, so I'd go for one or the other. I like Apostol though, so I'm looking for a replacement for Lang that isn't quite Stewart for the purposes of that list.

>Analysis II and topology may be out of scope here
Croom is an introduction to topology, goes into point-set topology as preparation for real analysis. You only need experience with proofs and a solid foundation in calculus for it. And once you're done, real analysis becomes much more bearable.

>I never said that the books were "devoid" of proofs
That's the obvious interpreation of "no proofs" in my humble opinion

I'll update to include (no proofing) for clarity while I find a better replacement for Lang. Thanks for letting me know, I see where that could be an issue.

that's not how people use that phrase

Even Stewart has proofs by your definition.

you mean by your definition? we don't say stewart has proofs, but it literally has sections which start as "Proof" and give an argument for something

Which are cursory and definitely not based on the student proving basic principles but rather the textbook's authors showing you that they're not pulling things out of their ass.

First, Math because it gives you the tools to understand not only the "natural" sciences but also statistics to understand social sciences.

Afer that, whatever you like.

What you're looking for to replace Lang is a "Vector Calculus" by Susan Colley. But to be honest, it still has small "proofing" exercises, though nothing really like you'll find in Apostol. Consider it as a little primer. Or maybe you should just stick to Stewart if you're going to stay with the no proofing focus and instead remain focused on computations. I see what you mean in "mirroring" how an average mathematics degree will begin first with computational stuff for the rest of STEM then segue into proofing based mathematics, but a good list sidesteps the problem.

What I would do is just introduce proofing early with How to Prove It or Book of Proof, and then go straight into Apostol, then Croom, then Tao. If you already finished computational calculus, then I would skip Apostol and use Croom as a primer for real analysis. I understand that you want to practice proofing before real analysis, but if you do Apostol & Croom for preparation, then you're wasting your time, especially if you have already covered calculus before.

-- --

Here let me edit this list for the demanding idealist in you:

>0. Remedial Mathematics
Khan Academy

>1. The Prerequisites of University Mathematics
Pre-Calculus - Carl Stitz & Jeff Zeager
Calculus: A Modern Approach - Jeff Knisley & Kevin Shirley
How to Prove It - D. J. Velleman

2a. Introduction to University Mathematics (Some Proofs)
Linear Algebra and Its Applications - David C. Lay
Vector Calculus - Susan Colley
Differential Equations - Shepley Ross

>2b. Introduction to Pure Mathematics (Lots of Proofs)
Calculus Vol. I & II - T. M. Apostol
Principles of Topology - Fred H. Croom
Analysis I & II - Terence Tao


>2c. The Efficient "Mixed" Approach
Linear Algebra and Its Applications - David C. Lay
Vector Calculus - Susan Colley
Differential Equations - Shepley Ross
Principles of Topology - Fred H. Croom
Analysis I & II - Terence Tao

>"Vector Calculus" by Susan Colley
maybe I just had a bad professor for a class using that book, but I don't remember it being a fun read

To be honest, I don't think any of those books are going to be a fun read. I suggested Colley because proofing is probably maybe like 10-20% of the exercises and the book can be done without going through it much. You might as well return to Lang, which has more proofing and is generally well-regarded.

That's the problem with textbooks. It's hard to balance accessibility, insight, rigor, understanding, and application. Usually you get to pick 3, maybe 4 in an outstanding book. That's what upper division books are so great, because they don't have to worry about getting a mathematician's skills up to par. It's also a reason why lower division books suck, because it's hard to be intuitive and rigorous without going into proofs and building upon other fields. I think Thomas and Knisley do a good job of this. Same for Strang, Lay, Ross, etc., for their fields.

>0. Remedial Mathematics
Khan Academy

-- --

>1. The Prerequisites of University Mathematics
Pre-Calculus - Carl Stitz & Jeff Zeager
Calculus: A Modern Approach - Jeff Knisley & Kevin Shirley
How to Prove It - D. J. Velleman

-- --

Pick One:

>2a. Introduction to University Mathematics (Some Proofs)
Linear Algebra and Its Applications - David C. Lay
Calculus of Several Variables - Serge Lang
Differential Equations - Shepley Ross


>2b. Introduction to Pure Mathematics (Lots of Proofs)
Calculus Vol. I & II - T. M. Apostol
Principles of Topology - Fred H. Croom
Analysis I & II - Terence Tao


>2c. The Efficient "Mixed" Approach
Linear Algebra and Its Applications - David C. Lay
Calculus of Several Variables - Serge Lang
Differential Equations - Shepley Ross
Principles of Topology - Fred H. Croom
Analysis I & II - Terence Tao


-- --

Good list.

bump

bump

You fellas missed your chance. The unemployed mathematicians went out to get their NEETbux. Sounds like the 300k yearly meme is a myth.

bawmp

bump for the meme list

bumper

Try this

Science is dumb leave it to the autists

bump

Good list

bumps for chumps

Bump.

Gimme more nice lists & meme lists.

All of those lists suck.

...

OP here, so based on your replies, I should first start with Math no matter what I decide to study after. Also bump

Yes. Because math will be essential. Also you should use this list for whatever track you want to take: .

> op asks what he should start learning
> autistic retards start a 200 post argument about a book list.