/sci/ - Science & Math

[Anonymous No.11896167]

Why are memecharts meme? What do I risk by following each of them, and simply skipping chapters on stuff I already know?

[Anonymous No.11896179]

why don’t you try it and find out

[Anonymous No.11896192]

>>11896167
Skipping chapters on what you know takes away the entire meme part of them.

[Anonymous No.11896207]

>>11896179
I am, and people are telling me to stop

[Anonymous No.11896211]

It's a lot better to learn from a flawed source like these memecharts than to sit home wondering which is the best place to learn from while doing nothing.
Just read them, you're bound to learn something.

[Anonymous No.11896217]

>>11896207
>oh no! some anonymous stranger online told me not to do it! What am I gonna do?
Get a brain, loser.

[Anonymous No.11896223]

>>11896167
This list is repetitious and frankly many of these books are mediocre to study from.
Do you really want to listen to a list that has you do a basic proof book before calculus? Do you want to listen to a list that has you do fucking Lang and Landau but take a detour through more set theory? Do you really want to follow a list that lists "How to solve it" by poly about 3 books after your intro to proofs books?

Is it not obvious how much of a meme this list is?

[Anonymous No.11896228]

>>11896223
>Is it not obvious how much of a meme this list is?
To someone that doesn't already know math, no, it's not obvious.

[Anonymous No.11896237]

>>11896167
>>11896223
Adding onto this, here are some good books in a loose order
>calculus
pick your favorite book, go with what's standard in universities
>intro linear
just skim through basic exercises on some standard book, paying a bit more attention to eigenvalues and diagonalization. you will study this properly later
>intro to proofs and foundations
book of proof
concrete mathematics
>linear algebra
Hoffman and Kunze
Friedman's alright too
>analysis
Understanding Analysis by Abbott
baby rudin
folland
>algebra
(all of) artin, D+F
cross reference with aluffi's algebra: chapter 0
>combinatorics
van lint
>graph theory
diestel
bollobas

This is a rough outline, but it's the "core" of most undergrad programs.

[Anonymous No.11896239]

>>11896167
To be honest, everything up to and including calculus and linear algebra should be learned from applied textbooks - not necessarily even math-specific texts - and they can be learned much earlier. Only once you've done them, then one who's particularly interested in math (or maybe theoretical physics) should bother with a more formal framework starting with linear algebra, abstract algebra and analysis. You don't need a rigorous understanding early on in math.

[Anonymous No.11896280]

>>11896207
Don’t do proof books, they’re for brainlets, philosofaggots and CSniggers who can’t into abstract reasoning. Retards in math programs shill out money for intro to proofs classes bc we don’t teach formal math in hs anymore. Its completely unnecessary. Set theory is totally vacuous, uninteresting, a waste of brain power and fucking gay. Don’t read set theory books. Read Basic Mathematics if you don’t know trig and how functions work. Pick up Spivak, Apostol, or Courant, these are your only options, and finish at least the first volume of Apostol or Courant. Then you do Rudin, Tao, or Zorich. For Linear Algebra, Lax, Roman, or Hoffman&Kunze. If you download Strang you should kill yourself. After that do whatever the fuck you want.
>>11896237
absolutely brainlet, incredible showing of raw undistilled stupidity and tastelessness. If I didn’t want to cave your skull in I’d keep you in an a lab for further study, faggot.

[Anonymous No.11896282]

>>11896237
>algebra
> (all of) artin, D+F
cross reference with aluffi's algebra: chapter 0

What do you mean by all-of artin? As in wholly finish his 'Algebra'?

[Anonymous No.11896306]

>>11896280
please elaborate, methinks as if following your example wholly would be far more entertaining than following the same path everyone does, considering the fact that they are restricted by the intellect of their classmates.

[Anonymous No.11896380]

>>11896167
Under no circumstances should you consider any infographic with anime present the least bit credible.

[Anonymous No.11896383]

>>11896380
Nah bro, pic related is legit.

[Anonymous No.11897169]

>>11896280
>Roman
>Hoffman&Kunze
Why are you comparing graduate math with freshman math?

[Anonymous No.11897319]

>>11896383
Are any of those coping books good? I need someone to tell me I'm not a failure

[Anonymous No.11897351]

>>11896280
>If I didn’t want to cave your skull in I’d keep you in an a lab for further study, faggot.
>grrr me tough guy grrrr
OP's starting from very little and not in school. If he feels like he can skip it, then he should skip it.
>pretending concrete mathematics doesn't have good analysis problems anyway
you're also a dumbfuck who doesn't know what they're talking about, either.

[Anonymous No.11897352]

>>11896282
Yes. His chapters on Algebraic Geometry is lacking, but all in all he's a good baseline. His exercises border on tedious at first, but he does regularly ask really good questions.
It's important to look at a classification for a small finite group and be able to intuitively tell what it should be.

[Anonymous No.11897527]

>>11896280
>>11896306
A good intro to proofs class is actually a good course to introduce challenging problems that take only a little background to solve. If you’ve never had really good combinatorics problems in your intro to proofs class, then you’re missing out on good intuition.

[Anonymous No.11897547]

>>11897527
What would you consider a good combinatorics problem ?

[Anonymous No.11897953]

>>11897527
>>11897547
????

[Anonymous No.11898183]

>>11897319
No just read the greeks instead, self help is a meme for dumb consooomers

[Anonymous No.11898381]

>>11897953
Here are a few from my intro to proofs class:
1. Consider the infinite sequence of integers
[eqn] A_n = 6^{4^n} + 1, n \geq 1[/eqn]
Prove that any two elements [math] A_k, A_j, 1 \leq k < j < \infty [/math] are relatively prime.

2. Consider the sum of the reciprocals of the first [math] n [/math] integers
[eqn] S_n = \sum_{k = 1}^n \frac{1}{k} [\eqn]
Prove that [math] S_n [/math] is not an integer for any [math] n \geq 2 [/math].

3. You have six colors of paint. Each face of a cube must be painted a different color. How many distinct ways can we color the entire surface of the cube with the understanding that two colorings are the same if one can be obtained by the other by rotation?

4. Enumerate the numbers from 1 to [math] 10^8 [/math] in the usual decimal form. How many zeroes show up in the list?

[Anonymous No.11898387]

>>11898381
Huh, question 2 didn't render. Let's try it again:
2. Consider the sum of the reciprocals of the first n integers
[eqn] S_n = \sum_{k = 1}^n \frac{1}{k} [\eqn]
Prove that [math] S_n [/math] is not an integer for any [math] n \geq 2 [/math].

[Anonymous No.11898399]

>>11898381
Deleting my original posts
>>11898381
>>11898387
Updated:
Here are a few from my intro to proofs class:
1. Consider the infinite sequence of integers
[eqn]A_n = 6^{4^n} + 1, n \geq 1[/eqn]
Prove that any two elements [math]A_k, A_j, 1 \leq k < j < \infty [/math] are relatively prime.

2. Consider the sum of the reciprocals of the first n integers
[eqn] S_n = \sum_{k = 1}^n \frac{1}{k} [/eqn]
Prove that [math] S_n [/math] is not an integer for any [math] n \geq 2 [/math].

3. You have six colors of paint. Each face of a cube must be painted a different color. How many distinct ways can we color the entire surface of the cube with the understanding that two colorings are the same if one can be obtained by the other by rotation?

4. Enumerate the numbers from 1 to [math] 10^8 [/math] in the usual decimal form. How many zeroes show up in the list?

[Anonymous No.11898414]

>>11898399
meant for >>11897547

[Anonymous No.11898420]

>>11898399
Yup, these are challenging, alright !

[Anonymous No.11898564]

>>11898399
Ok, i have no idea what to do with the upper 2, and i contemplated the last 2 for about an hour and have no idea how to solve them. Just give me the answers.

[Anonymous No.11899195]

>>11898399
Very challenging indeed.

[Anonymous No.11899314]

>>11899195
I think 4 is manageable, it's like a nested loop deal. but the rest i have no idea how to tackle. How do the first 2 questions even relate to combinatorics ?

[Anonymous No.11899348]

>>11898399
If thread archives before you see this, make sure to make a thread and post solutions.

[Anonymous No.11899491]

>>11898399

[math]S_n = \sum \frac{1}{2} + \frac{1}{3} + \frac{1}{4}+....\frac{1}{n} < \sum \frac{1}{2} + \frac{1}{2} + \frac{1}{4}+....\frac{1}{2^{\lfloor log_2(n)\rfloor}} [/math]

[Anonymous No.11899937]

>>11898399
The first question(SPOILERS):
In fact I can prove that the sequences of integers
B_n = 6^(2^n)) + 1 are relatively prime for different n's.
Proof:
Assume d divides B_n and B_m and n>m.
then
6^2^m = -1 mod d
but then
6^2^n = (6^2^m)^(2^(n-m)) = (-1)^(2^(n-m)) = 1 mod d, contradicting the fact that 6^2^n = -1 mod d. QED

[Anonymous No.11900143]

good list... however, did you read the greeks first?