/sci/ - Science & Math

>>10471795
Welcome to the world of math, enjoy your journey

>>10471833
>implying his journey goes further than this

>>10471850
>>10471795
I hope OP doesn't get scared off by this book, to elaborate OP,

The difference between somebody who is good at math and somebody who isn't is the person who is good said "this shit doesn't make any sense" and then had the patience to sit there until it did make sense

>>10471795
"Yeah
I know sometimes things may not
Always make sense to you right now
But hey
What daddy always tell you?
Straighten up little soldier
Stiffen up that upper lip
What you crying about?"
- Eminem

>>10471864
Real shit

>>10471795
Lang is a meme.

>>10471795
>he fell for the biggest meme anons in /sci/ push to newfags who want to "start again in mathematics"

>>10472579
I have no idea what you're talking about and I'm capable of doing 3D integrals.

Flipped through the Amazon Look Inside...what's so difficult about this?

>>10472579
it's a good book im learning a lot from it

>>10472579
what are you saying? that list was a meme?

>>10471795
>t. cs major

>>10472584
>3D integrals
????

>>10471859
Basically this.
When confused you seek secondary sources, you refuse not to be able to do all the material. At the end of each chapter, you go through all the concepts, and teach an invisible class out loud to test your own learning. If at anytime you fuck up/fumble your words or have to think to remember go back and review the material again. Keep doing this until you can effortlessly explain every chapter. This just takes a few extra minutes after you complete a chapter and the exercises.

When you do an exercise, think 'how can I prove my answer if correct'. If there's an exercise you can't figure out, systematically attack it with tests like replacing all the variables with 0 or 1 to see what happens. Input corner cases like -1 or the square root of 2, see what happens when you try to solve it. See if some kind of pattern is revealing itself. At this point you are now /sci/, operating on a massive dome level than just injesting the material passively and not really ever knowing what's going on.

You learned math in school to do calculations. Lang teaches you how to "do mathematics". Brainlets need not apply

>>10473490
Is it the best pre-calc book?

>>10471795
That book is easy and I never got why people had issues with it. Did every exercise.

On the other hand, Gelfand's problems are MUCH harder.

>>10473548
In my opinion the best precalc book is just going through some site, like this one https://www.expii.com/ and spending the bulk of your time solving problems, because you probably know more than you think and don't have to review so much, if you get stuck each module has short lectures/tutorials. It's run by this guy: http://www.math.cmu.edu/~ploh/

Or, just jump straight to the calculus module and try to complete it https://www.expii.com/t/calculus-1

>>10473490
Good advice. I do something very similar. Teaching friends who also work on this helps a lot.

>>10474322
>Don't buy books
Should be replaced with
>Don't buy books brand new

If you can find a book that interests you for $1 at a library sale then buy it, alongside your libgen PDF version. Physical books are always nice.

>>10474322
Using Khan Academy is a sure-fire way of ruining your mathematical education forever.

>>10474322
who cares what some random says

>>10475761
elaborate

These are the fundamental concepts of math:
substitution
>substitute variables or formulas with other variables or formulas, expressions, functions, operators, numbers and so on
Proof methods
>given axioms, use substitution, induction, contradictions, cases, construction, logic, generality, etc to prove a theorem
Bounding
>As you place further constraints on your problem, it may get easier
Permutation
>if all else fails, make a list of all possible permutations, all possible cases, all possible truth tables... usually requires writing a computer program for something with even a little substance, since the order of magnitude of your problem done this way usually increases by n! or 2^n. So use this as a last resort.
Abstraction
>very difficult to wrap your head around. Given a very deep question, it can often be near impossible to construct a specific model. Separates pure math from applied math. Requires complete knowledge and understanding of every theorem and technique used up to this point, and finding something common and relevant to solve the problem. Easy examples: using group theory to solve questions in number theory, is there (irrational x)^(irrational y) = rational?

>>10475761
...why

>>10473563
Which Gelfand do you suggest?

Why does the deeper math get it feels like a language?

>>10476031
meme-loving fuck

>>10476054
notice how the >>10476031 poster never says anything in his posts. Memes have completely consumed him, he no longer has a personality or a face. He is destined to keep posting it everywhere he can because either he's delusional and thinks it's actually funny or he's just too fucked up psychologically to have an opinion of his own.

>>10471795
>All elementary math in just one post
Basic math, just look at the axioms (sometimes called rules) of whatever field you're working in.

A good start is the nine field axioms of Q, which you can lookup anywhere. The axiom a*a^-1 = 1 gives us fractions. The nine field axioms encapsulate the arithmetic of numbers, high school algebra, and many other algebraic systems. (Axiom systems also exist for geometry, number theory, and for mathematics as a whole, though they aren't totally complete, you can still get a solid overview by looking at them.) A system satisfying the nine field axioms has the structure of a field. The first field that we all meet is the system Q of rational numbers, or fractions, but there are many more fields. If we drop the axiom about a^−1, we get eight axioms for a more general structure called a ring. The first ring that we all meet is the system Z of integers. Learn the axioms, now go practice solving some equations in that field, using said axioms. Not very hard is it? There's also an algebraic number field Q(α) to deal with irrationals, it has it's own field axioms. In Geometry, you can use vector spaces over fields to construct new ones. Q(α) is a vector space over Q whose dimension equals the degree of α. See how this is all fitting together? Moving on to more axioms, we also have the theory of finite sets, or axiom of foundation. Finite set theory provides objects like graphs. Finally, Zermelo-Fraenkel axioms (ZF) gives us infinity. When we include the Infinity axiom we get the set N of natural numbers, and its power set P(N), which is effectively the set R of real numbers. From R we can build the concepts of geometry and analysis, and virtually all of classical mathematics. Thus, ZF encapsulates a vast amount of mathematics. This can all be learned in any analysis intro text, like Tao's books, how to build fields (structures), their axioms and how to can derive proofs in that field using the axioms, ect.

My favorite /sci/ meme-list to troll newfags is the one that tells you to read two proof books that are basically the same.

>>10476155
how is that trolling in any way? When the anon downloads the second book it will be clear that it's the same content and just won't read it. Seems more like retardation to me than trolling

>>10472584
it's called multivariable calculus, anon. not "3D integrals."

>>10476031
say a lie enough, and people will believe it

>>10475610
> Physical books are always nice.
I think building a library with stuff you 've read is pretty cool and one of my long term life goals.

>>10476155
> scitards
Omg lulz we trolled this guy into reading 100 books.
> guy who got trolled
pic related

>>10477367
way to reveal you're a pseud and don't read a lot of books lol

>>10477372
I don't read any books. Haven't read one in decades.
Just thought it would be a nice idea IF I started.
Probably gonna go back to playing video games tho.

>>10476031
Schemes over ring, class field theory, Teichmuller space, AND Ergodic theory. at Junior.
https://www.youtube.com/watch?v=_NDl0M9Tf1o