/sci/ - Science & Math

Try reading it. find out yourself loser.

Can someone post the other meme lists?

Just start reading Spivak.

>>12333102
When I was your age I used stewart's precalculus. Don't worry about rigor right now, if you want a challenge then you can axlers precalc or basic mathematics.

Spivak is fun but if you are a ninth grader its way too ambitious.

>>12333102
Here's my foundational mathematics list:

Book of Proof by Hammock -> Naive Set Theory by Halmos -> Matrix Analysis and Applied Linear Algebra by Myer -> Understanding Analysis by Abbott -> Real Mathematical Analysis by Pugh -> Baby Rudin -> Papa Rudin -> Abstract Algebra by Dummit & Foote

>>12333108
>meme list
This is a good list though, it outlines a suggested path in order of difficulty, but also signposts what you can expect to gain from reading each book (including the supplementary ones), so that the user can plan their own itinerary according to how much they already know.
Compare with the list in >>12333102 which railroads you into doing formal logic before basic algebra, and then says of the individual books that most of the material is "repeated" or "already covered" in earlier ones, with an occasional sprinkle of empty upvote words like "best","great", "nice" etc.

>>12333151
I guess your right, that must be why I saved it the first place.

Dude this is the third time you've made essentially the same thread. Some making excuses and start learning math. Of course people criticized the books. There's literally nothing you could post that people aren't going to criticize. You could spend forever trying to figure out the perfect book list without ever learning anything. You're better off just getting started and course-correcting as you go.

As for the other book images they're all linked in the OP of this thread >>12332227

Maths is a pretty broad subject. Would recommend zoning in on a particular domain or goal that you're interested in, helps keep up the interest. Is there some particular topic or thing that you want to understand? Then search up everything you need to read to get to understanding that thing.

By the way, why not check out some videos like 3blue1brown. Intuitive understanding is far more interesting to start off with than slogging through a book. Although, you need to do exercises and problems to prove that you understand the topic.

I haven't read all the books in the list, but the problem with it is that it is "foundational" in the literal sense of seeking to lay out the set theory and axiomatic systems of logic in a concrete way before moving to more familiar topics like calculus and algebra. It does not mean "foundational" in the sense that it is for beginners.

I would take Feynman's advice and set your ground truth at basic laws of algebra, and not get into the nitty gritty of set theory and logics (the exception is if you are interested in those topics independent of anything else).

>>12333229
Thanks, I found my favorite list.

Op, here is the list you should use for now.

I can't speak for everybody, but I did Khan Academy, Apostol's Calculus, The Book of Proof and Tao's Analysis and that shit was a bit too redundant for me

>>12333310
>I would take Feynman's advice and set your ground truth at basic laws of algebra
It's good advice, especially for the beginner, but I'd quibble with calling this a "ground truth". Is AB-BA=0 a basic law of algebra? In what sense is it "true"? If you encounter a situation where it fails, on what grounds can it be dismissed as being mathematically refuted?

>>12333102
I'm convinced that nobody has ever actually gone through one of these lists in a rigorous way. unless you're going to uni you're not going to learn pure maths, sorry.

>>12334387
False. You can learn pure maths by yourself.

Don't pick a book at a time. Open them all at the same time so you can have a broader perspective, skip redundant content and dive in the easiest chapters of the easiest books first, without overlooking the other books i. e. keeping and eye on them. Start making your own notes of what you wish you'd find together in the same book.

>>12333102
Just pick something and stick to it. After spending years procrastinating with book lists and finding the right book I realized it is an absolute waste of time. There is no perfect sequence of books to read, just get your feet wet and work from there. What you want to focus on instead is specific topics and skills. Usually I found it useful to read multiple books at the same time. Often one explanation would make more sense to me than another, so I would alternate between two or three different books. The method doesn’t matter as long as you can get tangible results.

>>12333116
This.
Spivak starts from zero. After Spivak read Hubbard's Vector Calculus and Linear Algebra.
If you are having some trouble with spivak read Lang's Basic Mathematics.
The "How to think" books in these lists are stupid. You will pick up and find your own ways to understand and do proofs. This is only possible by actually attempting the math problems you will find in Spivak, for example.

>>12335130
I agree but Spivak moves way to fast for a 9th grader.

>>12333537
The underlying idea here is that for any proposition theorem, etc, that thing depends on some choice of axioms that you decide to accept as true without proof.

The point of different set and axiomatic theories tends to be to find the simplest set of such axioms that are sufficient to create some first order logic. However, you still have to decide those axioms are true without cause, besides their simplicity.

Feynman's point is that the axioms at this level tend to be entirely disconnected from higher level structures in math that we are used to, algebra and calculus. Rather than choosing axioms to maximise simplicity, he suggests something like this as a practical principle: admit the set of propositions that are most mutually consistent with each other that do not contradict themselves. The measure of "truthiness" in this case is the volume of other basic propositions the proposition you wish to admit agrees with. I say basic to emphasise that the choice of such propositions still matters, but such a framework allows you to choose basic as "laws of algebra" rather than ZFC.

So yeah, I think perhaps ground truth is the wrong phrase. My point is you can choose your entry point, your axioms somewhat more flexibly in practical thinking of mathematics, and observing that those axioms you chose for topic A are consistent with some axioms that you chose in topic B is a much more useful measure of truth as opposed to some set theory axioms.

>>12335922
I've found the video of the lecture where Feynman discusses this 'choice of axioms' idea.

https://youtu.be/kd0xTfdt6qw?t=1368

Feynman is a physicist, so a lot of context is drawn from his ideas about the structure of natural laws, but he was also an excellent mathematician, and makes reference to the foundations of mathematics from the viewpoint of the mathematician alone as well.

>>12336060
Timestamp 22:48

>>12335922 (You)
I've found the video of the lecture where Feynman discusses this 'choice of axioms' idea.

[YouTube] Richard Feynman - The.Character.of.Physical.Law - Part 2 (full version) (embed)

Timestamp 22:48


Feynman is a physicist, so a lot of context is drawn from his ideas about the structure of natural laws, but he was also an excellent mathematician, and makes reference to the foundations of mathematics from the viewpoint of the mathematician alone as well.

>>12334992
Of course it’s possible and math basically has to be self taught anyway. I just feel like without the structure and external motivation of school it’s incredibly unlikely that one would do the 3-4 years of consistent study that are necessary to reach a basic understanding. Almost nobody has that amount of free time and without a degree it’s not as if you can do anything with the knowledge anyway

>>12334387
No one has ever taught me mathematics. I learned it all myself the hard way; basically, by being a retard and struggling with all the concepts and being wrong 90% of the time. I don't think I learned anything, I just became familiar with the concepts.
What is a kick in the balls is that I used to be very proficient and trigonometry and calculus but I stupidly got into a business job that doesn't require any skill other than sucking DICK so I forgot a lot of it. It's like learning a language in that you constantly need to be exposed to the subject or you forget.

>>12336580
So where did you begin?

>>12333102
Lists are retarded. Just learn 1-2 subjects at a time, and focus on finding the most suitable literature for those.

It's 100% shit. Imagine if you spent the first two years of little league sitting in a chair learning about the theory of baseball?