How to teach yourself math?

Question

Mathematics

Hello everyone
I didn’t study at school especially (there was a gymnasium with a mathematical bias), after 9 I had to go to college
There, in my first year, I seemed like a genius, since the training program was like heaven and earth compared to the gymnasium
But in 3 years (now on 3rd year of college) I pretty much missed everything I knew, but I plan to switch to it, and I want to know mathematics myself, because I believe that by understanding mathematics I will succeed in everything else
. I have a lot of free time and I want to learn it myself mat, but there are a couple of questions:
1) How to determine the level of knowledge now?
2) What to decide / teach / take notes? Where to get material?
Thank you
I also do html + css

Answer 1

because I believe that by understanding mathematics I will succeed in everything else

Do not joke so.
Try to solve problems on topics that you can take in __any__ matan textbook, lin. algebra, anal. geometry, discrete, etc.
Previous answer. Plus, the material on the Internet is now a shaft. Lectures from the best universities on YouTube, for example.
Well done.

Answer 2

First, determine why you need mathematics, and do you really need it at all at an ultra-deep level? If you are really engaged in html + css layout, you need mathematics insofar as you know what you knew is enough.
Secondly, if you want to move somewhere in more specific areas, such as programming, data analysis, big data, statistics, and so on, then take any textbook, read the content and try to study each chapter as if from this same textbook, and reading everything that the search engine gives out on this topic. Well, and most importantly, you try to solve, check your decisions and check the answers - you must understand the essence and be able to solve. Then you will come to understand the meaning of mathematics and how to apply it.
Thirdly, in order not to forget what you have already studied, occasionally solve examples on topics that have already been covered much earlier, or rather, arrange tests and tests for yourself. Textbooks, problem books on the Internet in bulk, even Yandex offers a testing service for the exam, repeat this, the school level will also be useful, repeat the basics. And scanned books, methods and programs for teaching mathematics are a dime a dozen.
Set specific goals, determine what you need and why, and go ahead according to your own plan! Good luck to you! Math is always useful! It's a thing!

Answer 3

Serious mathematics is divided into many areas, here, probably, only:
- Algebra.
- Analysis.
- Geometry.
- Discrete.
- Perhaps, the logic, but it is more in terms of preparation for the 1st year.
Algebra is worth reading Shen and Gelfand (google). There is a lot, from column addition to p-adic numbers. This is the school level, then - if you want to know mathematics cool, then Vinberg, if you master the linear algebra of the university - Ilyin-Poznyak (professional mathematicians spit, really)), mathprofi, you can Beklemisheva, but he is unreadable, IMHO. Guide to solving the simplest problems of linal uni - Prosvetov.
Analysis... here, I would probably recommend just reading mathprofi.ru for starters. Standard analysis at school consists of a derivative and an integral at an elementary level, IMHO, it makes sense to teach immediately at a higher level, so first mathprofi, to understand the basic definitions, then Zorich. You can look through Fichtenholtz. Then Laurent Schwartz and Lvovsky's lectures, but this is really a very high level.
It is difficult for me to give advice on geometry. However, if we talk not about the school, but about the higher, then Prasolova-Tikhomirov "Geometry". Then there was some separate geometry of Prasolov, maybe even "Spherical Geometry", but I'm not sure. "Geometries" by Sosinsky, but it's in English. Well, in my humble opinion, I liked Berger, but this is a very, very serious level.
Discrete, probably, Haggarty "Discrete Mathematics for Programmers", you can also Novikov. But here I have less experience in the knowledge of books: with
Logic - Shen, Vereshchagin.
General Mathematics: Courant, Robbins.
You can solve sheets of school 57: www.mccme.ru/~merzon/v14 , there is such a level in a rare university.
If in Moscow, then run into the NMU (google it) for the next year, if not - vk.com/clubium, watch the lectures. NMU is really very serious about the mathematical level.
If there is a task to pass the exam, then reshuege.ru
PS I got acquainted with "Mathematics for Computer Science" from MIT, I liked it very much, if English does not scare, then I highly recommend it. Googled.

Answer 4

material

Answer 5

Try "Nature of Code" ( natureofcode.com/book/introduction ). It is in English, but it can also be useful in IT.

Answer 6

Even if mathematics is no longer useful (although you still have a university ahead of you), it specifically disciplines the brain. Go to the book market and find a couple of old textbooks on algebra, geometry. It is desirable to publish before the 90s.
In general, mathematics is a loose concept. Includes a bunch of sections, from arithmetic to game theory, etc.
Personally, I began to more or less understand diffuses only when their practical application began.
And most importantly, in no case do not get hung up on the exam tests.

Answer 7

I advise textbooks of the Soviet period:
Kaluzhnin L.A. Introduction to general algebra.
Kaluznin L.A. What is mathematical logic?
Manin Yu. I. Mathematics and Physics.
Kaluzhkin L.A. - The ABC of cybernetics.
Poletaev I.A. - Signal. On some concepts of cybernetics.
Pekelis V.D. - Faster thought.
Pekelis V.D. - Possible and impossible in cybernetics.

Answer 8

I really liked the course of mathematics on Coursera. It's the best I've come across! I sometimes use it myself to refresh my knowledge. So, if English is not scary, here is the link:
https://www.coursera.org/learn/calculus1/

Answer 9

mathprofi.ru
on the tower, and not only, everything is chewed to the limit. I myself study at the university for those. specialty and very helpful.

Answer 10

and read more about Fortran and its libraries, you will learn about why all this mathematics is in a computer
and a lot of interesting things about floating point numbers

Answer 11

I heard the assimilation of the material directly depends on the number of incomprehensible words and terms in the text. You can try to start with "Discrete Mathematics" and then fill in the knowledge gaps from other mathematics courses. You can take a book on the topic in which you plan to develop and in which you do not understand anything, and deal with each paragraph, finding the missing information in other books. Although it is a long way, sometimes it takes time to understand and connect with each other anyway. The middle way, it seems to me, is to find a good teacher, a person who will answer those questions that may arise when understanding the material.
Comprehension of mathematics is a path that does not end :) All the same, if there is a specific task, then it is better to look at what sections of mathematics help to solve it and study them. And if for the general development and for the flexibility of the mind, then solve mathematical problems for your pleasure )
euler.jakumo.org/problems.html

Answer 12

Now at the university they teach mathematics (in our country) according to the notes of Pismenny . It contains all the material in a concise form. The topics of vectors and mathematical analysis are a little more complete and understandable than in the school course. Proskuryakov is used as the tasker. Mathematical analysis to help Ter-Krikorov's textbook

Answer 13

I bought these books for myself to repeat and deepen 'Lecture notes 1-2 part ' it describes the main topics that are studied in the 1st course. And then on Coursera there are courses on combinatorics, probability and other things, choose whichever is closer.

Answer 14

Here, higher mathematics is very accessible
www.mathprofi.ru

Answer 15

In the 11th grade, I really enjoyed Knuth's book: Concrete Mathematics.
In the MIPT lecture hall there are very good lectures on discrete mathematics by Raigorodsky
lectoriy.mipt.ru/course/index?category=Maths
In general, in parallel with the additional study of the school mathematics course, I would definitely read:
Kolmogorov was very interested in her translation - he already says a lot.
My recommendation is related to the fact that in the world of modern mathematics it is very easy to get confused and develop only one-sidedly, so you need to be aware of the state of mathematics at least in the 20th century. Well, Courant's book is one of the best, eliminating the semantic gap between elementary and higher mathematics.