ITT: Self-Teaching/Stupid Questions Gen.

[Anonymous No.7045990]

Self-Teaching/Stupid Questions/Autodidact General thread

So I have lots of spare time and have pretty much taught myself every math subject after algebra ll/intermediate algebra (I did very well, but public/formal schooling became impossible for me due to circumstances).

However, so much free time has allowed me to not just refine my skills in elementary algebra and geometry that school never entertained, but also explore and enjoy more "advanced" topics like calculus, differential equations (ODE's and PDE's), linear algebra, analysis, topology, algebraic geometry, differential geometry, tensor analysis, and even some differential topology, among other things.

Does anyone else have a similar experience, or interesting things to share? Things I have learned are

>doing well in the majority of mathematics is more about having an open mind, allowing for constant abstractions, and studying constantly along a routine schedule more than having innate intellectual talent.
>having fun with math isn't necessarily better than performing well, but you will always be better off mentally by being able to have fun with math.
>Many subjects and axioms can easily be forgotten if not studied often.

And finally, I have but one stupid question, for now:
>Is Wolfram Alpha or Mathematica good for learning and teaching oneself about mathematics?
Or what programs does /sci/ use or recommend to learn and study mathematical models?

[Anonymous No.7046004]

In the meantime, I will self-bump with good visuals and links that have helped me, for any /sci/ browsers out there that teach themselves things.

>Analysis
https://59clc.files.wordpress.com/2012/08/real-and-functional-analysis-lang.pdf

http://classicalrealanalysis.info/com/documents/TBB-AllChapters-Landscape.pdf

>Engineering Textbooks
http://kisi.deu.edu.tr//ali.sevimlican/Peter_V__O%27Neil-Advanced_Engineering_Mathematics,_7th_Edition__-Cengage%282011%29.pdf

[Anonymous No.7046020]

>Abstract Algebra
http://abstract.ups.edu/download/aata-20120811.pdf

http://www.math.uiuc.edu/~kapovich/417-05/book.pdf

[Anonymous No.7046032]

What good is a bunch of knowledge you cannot apply?

Assuming what you've learned is even correct (no mentor or standards), why not do something more productive with your time?

[Anonymous No.7046069]

>>7046032

Actually, I am working on an independent major at my university, but for now (and because of very low income), I take a few classes at the local community college! All the math I will learn will be to start up a systems theory major at my university, and I plan to research and look into the fields of algebraic topology for things like game theory, mathematics for engineering concepts, the theory of dynamical systems, complexity theory, symbolic systems, etc etc.

[Anonymous No.7046078]

>>7046032

Also, I am pretty sure a good bit of what I have taught myself is pretty accurate; every now and thing I watch those online courses like mit openwave or standford videos and such, and the examples provided in the lectures are examples I work with, and we end up getting the same answers and using very similar methods.

[Anonymous No.7046095]

>>7046069
you sound delusional

[Anonymous No.7046120]

>>7046095

Not entirely so, Stanford's Symbolic Systems Major is something quite similar!

[Anonymous No.7046129]

>>7046120
are you at stanford? no. you are a guy with a very low income taking CC classes and fantasizing to yourself about an independent major that does not exist

[Anonymous No.7046145]

>>7046129
Dude just wants to learn, stop being a dick. This thread isn't about what major he does or doesn't fantasize about, it's about him seeking specific advice, and you're disregarding that, instead doling out your own in an extremely patronizing tone. What else could I expect from this site, though, right?

[Anonymous No.7046146]

>>7046129
Well this guy doesn't get it.
I think it's neat you're working with what you have OP, and while it seems hard to believe that OP should teach math to kids who might be flunking algebra, it's also curious in that something might come from it. My math education is still unformed, but OP gives me hope.

[Anonymous No.7046148]

>>7046129

I am working with a buddy from Standford in the major, though! We both collaborate and work on ideas, and have been since high school, haha

[Anonymous No.7046149]

>>7046145
>>7046146

Thanks guys, I don't talk to people about this very often, but when I do, it always reassures me to have positive feedback as well!

[Anonymous No.7046151]

>>7046149
If you can't teach yourself anything, you'll always be dependent on others for knowledge. Keep working, man. It'll pay off

[Anonymous No.7046169]

>>7046129
>>7046149

Half the battle in the market place is sticking out. If he didn't already have some schooling I was looking for in a candidate I would easily let him know what he's missing. Which might end up being something like some liberal arts or english courses, actually.

I'd hate to think our society has degenerated to the point where they shun independent minded people entirely. But, one thing is for sure, I've never seen good career advice (below 300k starting) here on /sci/ before.

[Anonymous No.7046563]

Question relating to gas cylinders:

I'm confused over the specs of two separate gas cylinders. The tank in [pic] states 9 liters capacity. But reading the specs on a different (slightly smaller) tank claims 420 liters of gas. I keep reading the tank capacity liter number in the hundreds, so I don't understand if the tank in [pic] is a typo, or I'm not understanding something.

[Anonymous No.7046807]

I got another question, that I cant really find the answer to anywhere. If ODE's can be represented visually using slope fields, solution curves, and isoclines, then can partial differential equations be solved visually by using 3 dimensional slope fields, solution surfaces/planes, and isocline surfaces/planes?

And further more, would these 3D solutions model exactlt how a system looks and behaves in real life?

[Anonymous No.7047061]

I'm confused about how much dioxine there is.
In other questions, they use something like "pounds of salt per gallon", and I can work those just fine.
I just don't understand the "parts per billion" bit when used with weight.
Do I have to use the density of water or something?

[Anonymous No.7047204]

Hey guys, I feel pretty embarrassed about this.

I'm a junior studying math. I have no research or internship experience (all I do currently is a job where I type up a professor's notes in LaTeX). I also have no letters of recommendation, but I should have at least one by the end of this quarter. I'll have taken all but two classes needed to graduate by the beginning of next year (grad courses are likely for my senior year). All internships/"research positions/etc. that I've seen require at minimum two letters, and their application deadlines are in the next few weeks. My resume is nothing special.

What do I do over the summer? Is there any sort of position out there that has a really late deadline or requires no letters? In any case, I'll be studying for the basic qualifying exams and the math GRE, but I feel like I've fucked myself over for future job and/or school applications since I've got no field experience. Thanks for any input guys.

[Anonymous No.7047234]

>>7046563
>The tank in [pic] states 9 liters capacity.
Of water volume.
If you fill it with water, you get 9 liters.
>420 blaze it liters of gas.
is at NTP, when let out of the tube.

[Anonymous No.7047475]

shameless self bump for more questions, and more answers

[Anonymous No.7047486]

I am supposed to use the FTOC to find these values. I've looked for examples online but none seem to deal with something quite like this. I think Ive got F'(x) but I'm not too sure. Any help is appreciated.

[Anonymous No.7047493]

>>7047486
Here is the picture oriented the correct way.

[Anonymous No.7047506]

>>7047493
Use complex analysis, evaluating the real part of the Fresnel integrals. Stein and Shakarchi do this in their second volume.
(Alternatively, note that you're dealing with the integral from 1 to 1 and so the answer is 0).

[Anonymous No.7047990]

>>7047234
What does NTP mean?

[Anonymous No.7047994]

>>7047990
It's french for "an ideal gas"

[Anonymous No.7047996]

I have a stupid question. I enjoy Physics but realise in order to get better at it you also need to get good at maths. How do you make yourself enjoy maths?

[Anonymous No.7048226]

I'm revising precalculus.

I have been using Stewart's Precalculus, I'm currently at the end of chapter 7
I thought the first 4 chapters were good, but I'm really hating the trigonometry chapters

The explanations are terrible
I don't like lots of prose
I don't like how he tries to squeeze an explanation into a paragraph and one picture

Look at 6.4 example 7. What was he thinking, using a 3,4,5 triangle, Rather than a triangle with hypotenuse 1? It's an extra layer of complexity that makes the explanation shit. He thinks it's easier but it isn't
The entire book is filled with stuff like this

What should I use instead?
I would like a COMPLETE video series and a text.

Next week I'm revising single variable calculus
I would also like a video series and text recommendation

[Anonymous No.7048228]

>>7047996
relate it to physics

[Anonymous No.7048611]

Are there any good introductory or comprehensive statistics textbooks with an emphasis on implementing solutions in code? Preferably in python, lisp, perl, java or even R?

Posting useful infographs in the spirit of the thread.

[Anonymous No.7048639]

I have roughly a month to learn differential calculus and statics. Any books you recommend?

[Anonymous No.7049475]

>>7048639

Not sure about books, but Khanacademy and others like PatrickJMT have plenty of playlists on those subjects!

[Anonymous No.7049476]

>>7048611
Think Stats
Think Bayes

[Anonymous No.7049477]

>>7047996

Research more advanced math, stuff dealing with infinite dimensions, fractals, set theory, number theory, projective geometry, topology. literally trip and psych yourself, then realize it's aaaaaall related to basic, simple math, and also explains physics and is the only reason physics can work.


Start with stuff like khanacademy, viascience, numberphile, tmpchem, commutant, and many many others.

[Anonymous No.7049482]

>>7048639
>statics
nigga, its just vectors and matrix algebra.

[Anonymous No.7049564]

>>7045990
I want to teach myself how to put LaTex in comments. Disregard this post.
<span class="math">x^2[/spoiler]

[Anonymous No.7049593]

>>7045990
i use wolfram alpha to get a better understanding of what the fuck is going on with my homework.

[Anonymous No.7049769]

G'day. I sucked at maths at school and didn't get really far. It's now biting me in the ass. I'm trying to work out the length of one side of a right-angled triangle. I know the hypotenuse (29") and I know that the other two lengths are a ratio of 21:9. I've tried doing root stuff, but I last did maths at school in a formal context 12 years ago and I'm stuck. Anyone give me some guidance, please?


tl;dr:

(a*a)+(b*b)=(29x29)

Find a.


Thanks in advance.

[Anonymous No.7049774]

>>7049769
a^2+b^2=c^2
a^2=c^2-b^2
a=\sqrt(c^2-b^2)

[Anonymous No.7049777]

>>7049774
How do I enter in the ratio I know (b:a is in a ratio of 21:9)?

[Anonymous No.7049800]

>>7049777
you know that a^2+b^2=29^2 and that a/b=7/3
can you think about how to manipulate one of those equations to isolate a value for one of your variables?

[Anonymous No.7049977]

So, stupid question:
Does <span class="math">r=p + (1-p) \times f^\frac{1}{p}[/spoiler] look like any famous formula ? All variables are in [0;1].
Context is probabilities, perhaps chaos theory.

[Anonymous No.7050035]

>>7049800
I think I almost get it. 'cause 21 can be divided by 3 and 7, and 9 is divisible by 3 as well? That would mean I can simplify the ratio right?

>can you think about how to manipulate one of those equations to isolate a value for one of your variables?

Not without getting confused. Do I work out 29x29 is 841 and then apply that in like this
(Is this factoring?)...?

>21 / 3 = 7
>9 / 3 = 3
> 7 + 3 = 10

> 29 x 29 = 841

> 841 / 10 = 84.1

> a^2 = 3 * 84.1 = 252.3
> b^2 = 7 x 84.1 = 588.7

> 252.3 + 588.7 = 841

Is this the right thinking? Where do I go next?

[Anonymous No.7050083]

Am I doing it right:

<span class="math">2^{log n} = 10^{log 2 \cdot log n} = n^{log 2}[/spoiler]

[Anonymous No.7050500]

>>7050035
you should really never use numbers that large in geometry.. and you know you're doing something wrong when you get an identity (when after solving a problem you get x=x, or in this case, 841 = 841)

the answer to your problem is the means-extreme property
. In geometry, if you lack natutal intuition, always write down, or at least think of, everything you know about a problem. The information they give you, and all the formulas and rules you know about a shape.

[Anonymous No.7050507]

>>7050035
Anyways, the means extremes property tells you all about ratios. In this case, you need to know 3 sides of a triangle; you already know one, but need to know two more. Usually, this would mean you can't solve for the other two sides, because the Pythagorean theorem needs two sides to find the other. However, you do have a ratio telling you how the other two sides are related; this is a clue.


Another useful property here are Pythagorean triples. You should definitely look into them Anon

[None !ELBOWS6FNQ No.7050696]

>>7047994
u wot m8
>>7047990
normal temperature and pressure, google it

[Anonymous No.7051189]

>>7050035
a/b=7/3
3a=7b
a=7/3b

a^2+b^2=29^2
(7/3b)^2+b^2=29^2

[Anonymous No.7051191]

>>7051189
err, let's revise line 3 to
a=((7/3)b)
and line 5 to
((7/3)b)^2+b^2=29^2

[Anonymous No.7051708]

I'm a 2nd year physics major at ICL. I've become disillusioned with physics/the state of science, and the most interesting part of the course has been the two years of python programming. I am considering dropping out and working as a programmer.

1) Are there any immediate harsh truths I should be aware of?
2) What ought I to do, to go from my current situation, to my first programming job?

[Anonymous No.7052005]

I cannot wrap my head around the fact that light is refracted by gravity.

>Pic related

If light always travels straight through space, and space itself is bended, light should just go straight as it went when it's outside of the significant gravitational zone.

[Anonymous No.7052009]

>>7052005
If you ask someone for directions and he tells you to go straight ahead, if the road has a slight turn to the left to avoid a building, would you turn slightly or would you crash into the building?

[Anonymous No.7052011]

>>7050083
>using log as log to the base 10
Cease to exist

[Anonymous No.7052017]

>>7052005
The light actually does travel in a straight line, at least from it's own point of view. The problem is that the space time the light is moving through is distorted. Imagine drawing a straight line on a piece of paper (that is the photon travelling a straight line from it's point of view), now if you say fold that piece of paper in the shape of a cylinder that straight line will appear curved, even though it actually isn't.

It's probably a bad explanation, but hopefully you get the idea.

[Anonymous No.7052027]

>>7052005
if you travel in a straight line, you're really travelling in a giant circle because the earth is curved

[Anonymous No.7052029]

>>7052017
Your comment helps, but I'm still not entirely sure. It's most likely my idea that light is "clung" to the space it flies through.

The reason I adopted this mindset is probably because light has no mass and therefore isn't affected by gravity. If there is no force on an object, it shouldn't change direction/velocity (the latter isn't even possible with light).
So why, is what I'm thinking, can the curvature of spacetime adjust the direction of an object without applying force?

I probably should just accept it to be true, though. Perhaps the explanation as to why I'm wrong is a little to be complicated if you're not neck deep into relativity theory.

[Anonymous No.7052031]

>>7052017
>at least from it's own point of view

I've given it a little more thought, and this (and same goes for what other people said) is moving something within me. You're saying light moves the way it does because it should go straight according to its own perspective. Spacetime can have curvatures, and light will move through it as if it goes straightly. However for an outsider it's easy to see that the path of the photon actually curves.

Is there some physical law, theory or an otherwise explanation as for why the path of an object is determined from the perspective of the objective itself, instead of from an "outsider" perspective (i.e. the perspective that my mind is set on)?

[Anonymous No.7052048]

>>7052031
Here's another analogy (I will try to answer your question directly later):
Imagine you have two bugs on an apple (which we assume as a perfect sphere in ol' physicist fashion). The bugs are really tiny and they can't tell whether the apple they are moving on it curved or not, it appears like a flat surface to them (just like earth does to us on first glance). So they decide to do the following: They face each other, turn around 90° so they face a parallel direction and just move that way. They notice of course, that are getting closer and closer. Their interpretation is that there's an attracting force between them, because they have no perception of the third dimension. Pic related, an illustration I just made.

The "law" is that space time is thought to be a pseudo-riemannian space (four dimensional). Now, that sounds complicated, but the point is that it can be distorted without being a subspace of a higher dimensional space, plus it looks like undistorted minkowski space time at every point. The best analogy to this is earth, which locally looks flat, but is actually curved. The reason is a different one though, earth doesn't appear curved because the curvature is so big.

[Anonymous No.7052068]

>>7052048
Yes, thanks for the image, it does clear it up somewhat more. Comparing it to the coordinate system of Earth, it is as if the spacetime grid follows the latitude lines, whereas objects' tracing patterns follow the longitude lines, am I right?

[Anonymous No.7052079]

>>7052068
Sort of, in the mathematics used in GR there's actually two strictly distinct geometrical objects, called contravariant and covariant tensors
<span class="math">x^\mu[/spoiler](contravariant)
<span class="math">x_\mu = g_{\mu\nu}x^\nu[/spoiler](covariant)
connected with the metric tensor <span class="math">g_{\mu\nu}[/spoiler] which is basically an object describing the intrinsic geometry of space time.

Now, I know this may sound like gibberish, but the point is, those two objects <span class="math">x^\mu[/spoiler] and <span class="math">x_\mu[/spoiler] are not the same; Compared to earth one describes the position in longitude/lattitude coordinates, and the other one in real three dimensional cartesian coordinates (although the analogy doesn't really work, because as I mentioned before, pseudo-riemannian spaces are not thought to be a subspace of a higher dimensional space).

[Anonymous No.7052082]

>>7052079
Okay. All in all I'll just remember that light travels straightly from its own point of view, not from that of an outsider, or according to the Cartesian coordinate system.

[Anonymous No.7052085]

>>7052079
I should mention that many physical laws only rely on one of the two objects, meaning that stuff like bending light paths can happen, because the physical law doesn't "see the big picture". There are things that are depending on both objects, so that they are not depending on the "point of view". We call these things "lorentz invariant". An example for a lorentz invariant quantity is mass:<div class="math">m^2 = p_\mu p^\mu</div> It depends on a covariant and contravariant vector, so it's independent on the frame of reference, because it can see the "big picture".

Damn, I'm really bad at explaining stuff, I'm sorry.

[Anonymous No.7052089]

>>7046004
>real-and-functional-analysis-lang.pdf
bretty gud

thank u based OP

[Anonymous No.7052092]

>>7052085
>Lorentz invariance
I think that's the magic word, the thing that I wasn't aware of and bugged me to no end.
If all of this is true and I do get it the way you want me to get it (you can't see into my mind but I feel I've got it now), thank you so much.

[Anonymous No.7052574]

Real shitty question here

A patient takes 0.25 mg of Digoxin every day and has plasma levels of 2.4 ng/ml. then it asks me what dosage should use to get the plasma levels to 1.6 ng/ml

is it just 0.25 *1.6/2.4?