Whether a qualitative self-study of math?

Good evening.
Studying for a year of school math 3 times a week( a week for 4 hours).
Thinking at the expense of self, caught 1 quote from the book "be your own MBA":
A self-taught easily tucked in his belt PhDs, masters and bachelors from the best universities.

Ludwig von Mizen
Australian economist.

The idea is the following: cannot do the learning for best results.
But to take this step, you need to be sure that I will be able to learn mathematics without a tutor.

Are there any books for self study?
And can books replace a tutor?
July 2nd 19 at 13:15
5 answers
July 2nd 19 at 13:17
Any textbook involves self-study. School teacher - a luxury that can afford a modern society.
July 2nd 19 at 13:19
But... How would... No, I am in no way trying to deprive You of motivation, just... Why? It you in good stead? Can be in programming? Or You go through school course? Then Yes, any tutorial. However, Mizen meant that the necessary practice, then, of course, plugged any doctor. When I was studying programming (sorry, there is some programmers just), duck really, I'm no book gave as much as gave practice. I started to create a large project on it to sharpen the knowledge that I acquired. And you can just read a stack of books - but without the use of these acquired knowledge in practice, it would be a waste of time. Or more close to life example from foreign languages: for anybody not a secret that you can pass at least a dozen famous courses, but without practice, conversation on it, this knowledge will be forgotten completely in six months. Unfortunately I can't say what might be practice within mathematics, but You get the gist, I think.
Your message made me ponder a little deeper into your question.
As if I didn't answer, all boils down to is desire, and how much of a bunch. - norene29 commented on July 2nd 19 at 13:22
But can books replace a tutor? - norene29 commented on July 2nd 19 at 13:25
: Oh, it certainly is) But now just remember how was my training in mathematics in school, and I remember that just this is practice - this was the task of physics and mathematics. Yes, they are not applicable in real life and the artificial, they are great help to learn these knowledge into practice. Therefore, in this situation, if we want to get from school to some knowledge, it is necessary to stay on top of the problem books, otherwise the pants will sit. The main plus in the exact Sciences is that they are great to put brains into place, and then You have no more work will not make to start to study what You really need in your life, and where the need is a mathematical mind, it is Humanities then harder, obviously)

PS But let me tell You a little secret: in programming (if You think to connect it with his life. You will not be disappointed, I assure You)) ) do not need much mathematics as such, but more a Boolean algebra, and discrete mathematics as a bonus. This somewhat different areas of mathematics. That is, if in Russian-not the dry numbers and the ability to count anything in mind (you won't need it), and the logic and ability to solve practical problems. Mathematics and computer science - is a completely different discipline, so I recommend You to decide on which pull is stronger. In computer science You will have the opportunity to become world-class and well-known programmer. For math, well... I honestly don't know who You can be, excuse me for being blunt :/ - wilfred_Ebe commented on July 2nd 19 at 13:28
: above colleague just said Your question short and to the point: "Any textbook involves learning". That is, again, only under the condition of independent practice, can replace completely, if You have enough motivation and understanding. And if it's not enough for this and there are tutorials. The school course of mathematics, it explains everything you need. Need a tutor just in case if you want a purely human help and it is chewed, when some aspects of the textbook can not help. Just in perfect conditions great school teacher. It is assumed that the students are so conscious that all the knowledge learn in their own practice, but if necessary they can ask the teacher. Here it can replace the tutor, Yes. - wilfred_Ebe commented on July 2nd 19 at 13:31
: Nuuuu, I'll start with the fact that everything I do makes sense to me.
For example, I consider mathematics to further the transition to the development of machine learning(AI), and by the way in programming I fortunately already more than semi-years(html5, css3, javascirpt, nodejs(in learning)), starting to learn C++ directly for the further development of machine learning.
I really like math, but unfortunately, the school had graduated 9 classes(and there was a good teacher), now in College, and then the teacher really does not know Russian.
Therefore, tutoring is trying to recover in level:
1 - At the moment the most important thing - getting into a good University.
2 - As I wrote above, for the development of AI( one thought dominates :D ).
3 - As you wrote, for the right mindset.

And in General there is no limit! - norene29 commented on July 2nd 19 at 13:34
: as the thoughts go - and in the course of writing... More the area in which you may need a tutor is a lack of motivation: if You have difficulty with self-education, if You are doing the subject because you just have, and not because-because-like - he at least will help You to engage in such a program, You will be forced to put for the table. But if the object You like - You most looking in, what sort of Tutors?) It's like programming to have a tutor. They're not there for the same reason that people do it, because I really like him. But if you just "have to", you should choose another region :/ - wilfred_Ebe commented on July 2nd 19 at 13:37
Oh yeah, the AI is really awesome, I agree) There really need math. Although only in the framework of robotics and space exploration. That is, at the level of machine code in fact. The same Board, it's just programming. - wilfred_Ebe commented on July 2nd 19 at 13:40
: And what is your level of mathematics?
Whom you work(area in programming)?
How can you help the knowledge of mathematics? - norene29 commented on July 2nd 19 at 13:43
: As far as I know, functions, variables and loops - all this and more went from mathematics.
So we can safely say that programming is math from a different angle. - norene29 commented on July 2nd 19 at 13:46
: Allow-from, "functions, variables and loops" - how is that math?

Proiluction for example:


str_sum function (num) {
return num +2;

echo str_sum (3); // 5


output = 0;
for (i = 1; i <= 5; ++i) output += i;
echo output; // 5


output = 2; // We assigned a value of 2 to variable "output".

If it is mathematics - the level of the first class. So I say, there is an important logic. For example, you want to store data in any form, to process them in any way and presenting them to the user according to his criteria. There really brain-dead sometimes. The whole process of implementation of this task and from is development.

Java. Write for Android. - wilfred_Ebe commented on July 2nd 19 at 13:49
: You have not understood correctly. What I wrote is found in higher mathematics. - norene29 commented on July 2nd 19 at 13:52
: Yes, found, myself remember from mathematics (though the Institute), but to be specific, I will say that the programming from these phenomena one name, and the principles of action, although General, they have nothing. It has, for example, iron with the possibility of steam Ironing of linen, and an industrial steam generator, it does not mean that iron and steam - the same thing, although the name and the principle they have one - they both just evaporate water, but to use the iron where you want a industrial steam generator, at least strange. - wilfred_Ebe commented on July 2nd 19 at 13:55
July 2nd 19 at 13:21
I too wanted to do the AI, entered and graduated from the faculty of applied mathematics and Informatics (thought there is more programming, but rather 80% in mathematics).

School mathematics is essentially "kindergarten" compared to out there that studied even in the first year. Not always of how much depth of understanding. For example, at school they say that the axioms must "believe" forced to learn the proofs of the theorems roots of negative numbers do not exist, the quadratic equations may have 0, 1 or 2 solutions, etc. In the University say that the axioms you can collect and build their algebra and the theory, are forced to invent their own proofs of theorems (based on axioms), talk about the roots of negative numbers (a complex number) that the quadratic equation always has 2 solutions (the cubic - 3, etc.). Plus, matrices, logic, probability, game theory (pure math, if that), graphs, cryptography...

In the end, the knowledge obtained is very extensive but not very deep and need specifically to me. Most of them are forgotten shortly after the exam)

But when doing your own project, starts a completely different story. Have questions, look for answers, in the process of studying these responses can occur even in unexpected subjects, grades "magically" begin to grow. But most importantly, found the answer to my own question was much more memorable, than a learned response to yet not asked question)

Therefore, self-learning through the development of its own project and the result is a much more effective "stupid study". About your quote about "bachelors and masters". But practicing Professor is unlikely that someone will plug in their skills and knowledge) for Example, the module Assembly of spherical panoramas from single images just some Professor written, and based on it have already made a program (in fact, the graphic interfaces in it), many even pay) while the complex mathematical core was developed by a completely separate person.

About AI because most of the learning was math, the bulk of the so-called "AI" was formulated in the form of formulas, often not very sophisticated. Machine learning was taught superficially, "for cases where you cannot compile formula process". For example, a dreamer builds a robot with arms and legs, so he could protect the citizens from the falling asteroid) Most of his work, he will spend on making it human functions, the ability to move, aim, analyze what is happening. The potential range of tasks can become much wider than originally conceived, but the development speed will be very low and, for the most part, not related to the task. A "Soviet engineer" will be the formula of motion of the asteroid, equations of motion of the rocket, shoot down the asteroid, calculate the point of intersection, the area where this point is invalid (villages, strategic objects) from these data construct the mesh the location of the radars and launchers (some mine), in the end, the problem is solved, artificial intelligence in popular understanding is missing, but the whole system operates automatically without human intervention (in "pure mathematics"), as if that makes it intelligent :)
Thanks for the reply. Very informative. - norene29 commented on July 2nd 19 at 13:24
July 2nd 19 at 13:23
I can't prolangirovat Your purpose for studying mathematics (including trust level of proficiency and depth of learning), but here's what I can offer:
https://toster.ru/answer?answer_id=925815 (see Links in my answer)
Think I'm still too early.
Algebra I topic: "Evidence of inequalities",
geometry: Polygons finished and start the circle as such have already studied( i.e., the circumference treug-ke, square, rectangular and-ke, trapezoid, etc. has passed).

I think we should start already?
Post Scriptum: like that Tried the book of Hiekel, the neural networks start reading, so I do not understand. - norene29 commented on July 2nd 19 at 13:26
Maybe until derivative or even before, the integrals reach, will begin to think about neural network books. - norene29 commented on July 2nd 19 at 13:29
There was one more question: since what moment it is already possible to go on learning "machine learning"? Mean after what themes from elementary mathematics, you can head towards AI.
Or should first undergo a full course of elementary mathematics? - wilfred_Ebe commented on July 2nd 19 at 13:32
first, please UNDERSTAND! all at a basic level (as You said correctly), after a full course of elementary mathematics, and then the same course of logic.
It "understand", not walk or read.
Prior to that, - no complicated things! - wilfred_Ebe commented on July 2nd 19 at 13:35
and you start learning "machine learning", and then understand what knowledge is not enough) if anything is not clear, then keep studying your math course) - norene29 commented on July 2nd 19 at 13:38
July 2nd 19 at 13:25
Machine learning rests on 3 pillars: linear algebra, mathematical statistics and mathematical analysis. They, in turn, lie on higher algebra, probability theory, combinatorics and the study of functions. Below is elementary mathematics. You need to know all of these items at the level of understanding.

It is possible for simplicity to focus on this program: https://cache-mskm902.cdn.yandex.net/download.cdn....
Thanks for the reply. Understand that until they have mastered all basic math can't go any further. - norene29 commented on July 2nd 19 at 13:28

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