Are there books for developing really mathematical thinking / not memorizing formulas?

Question

Mathematics

Hello! Please share who was able to really develop mathematical thinking, how did you do it? What books did you read, what problems did you solve? Those who read the "lament of a mathematician" will understand ... Such a training system where they teach to think with their heads, first they give a task, gently lead them to a solution, and then they show how they solve mathematical formulas ... Is there really nothing like this on the Internet?
Z.Y. Please don't pass by. Share sources, resources that you have used from the very beginning of the journey. This will help both me and those who are in the same search ... Thank you.

Answer 1

For example:
Poya D.
How to solve a problem.
Mathematics and plausible reasoning.
mathematical discovery.

Answer 2

There is no magic silver bullet.
Only PRACTICE, only EXERCISES.
And the books that will help you are a book with a good theory and a book with exercises.
Which books they are depends on the SPECIFIC area of ​​mathematics that interests you.
There are many areas in mathematics.
There is no universal simple recipe.
Only the skill to DIGGER, to get to the bottom of things incomprehensible to you, will be universally useful.
But it has nothing to do with mathematics. It's just a character trait

Answer 3

D. Knuth "The Art of Programming"
"Concrete Mathematics" (the same for children)

Answer 4

Only regular training will help, that is, doing exercises in the section of mathematics that interests you.
There are no other "magic" methods.
The only thing that can help in a book is a good presentation to keep you interested.

Answer 5

If you are not interested, then no books will help.
It was necessary to start with Perelman's "Entertaining Mathematics" or the like.

Answer 6

There is a good book by the outstanding Polish mathematician Vaclav Sierpinski 250 Problems in Elementary Number Theory . It is remarkable in that it contains problems, the solution of which does not require knowledge of higher mathematics. At the same time, the problems themselves are quite difficult and have very short formulations and solutions.
The second book I would recommend is the book by the Soviet mathematician Khinchin: 3 pearls of number theory . This book describes solutions to 3 difficult problems for which solutions were found using elementary mathematics (without any diffurations and homotopies!). The solution of one of the described problems was once dealt with by Hilbert himself.
Well, it would be nice to have some book on logic, which actually forms the basis of mathematical thinking. For example, this one: An Introduction to Logic and the Scientific Method .

Answer 7

Reading and analyzing Euclid's "Elements" is very useful for the development of mathematical thinking.

Answer 8

10 years of in-depth study of mathematics with a tutor. Nothing supernatural, no special tasks or resources, just daily practice. In order not to memorize, it is enough to go deep and understand the essence, "work out" the concept under study and that's it.

Answer 9

The main way is to solve many problems. So it’s better to take books with a lot of tasks first.
1. Kanel-Belov, Kovaldzhi - How to solve non-standard tasks
This is if they missed a circle at school. Available here www.mccme.ru/free-books
2. Knuth - Concrete Mathematics
This will cover absenteeism in discrete mathematics in the first year, and more is often not needed.
3. For the soul and motivation, I advise Arnold, you can do everything popular in a row. He was a popularizer of science when it was not yet fashionable! There is something here ilib.mccme.ru and here www.mccme.ru/free-books
4. Poya - Mathematics and plausible reasoning.
This is when the technique has been developed in order to understand how to come to an idea. Reading it before solving problems is like reading about refactoring and clean code without writing a single project.

Answer 10

Of course have.
For those who already fumble a little: Martin Gardner, all books, starting with "mathematical entertainment "
https://ru.wikipedia.org/wiki/Gardner,_Martin
..." (mathematics, physics, geometry, algebra...)
https://ru.wikipedia.org/wiki/Perelman,_Yakov_Isid...
Entire generations of talented mathematicians and physicists were brought up on these books.

Answer 11

As a child, I was very interested in Perelman, especially "Entertaining Algebra".
As an adult, I was impressed by Penrose - "The New Mind of the King" and "The Road to Reality" (the main goal of the books is not a story about mathematics, but mathematics is treated there in an interesting and versatile way).
I also recommend "Gödel, Escher, Bach" by Douglas Hofstadter - ideas from logic, the theory of computability are very clearly explained there.

Answer 12

At one time, the Avanta + encyclopedia in mathematics made a great impression on me

Answer 13

I solved many problems at school. Scanavi's problem book is almost complete.
Without formulas - in any way.

Answer 14

At school, you need to start learning mathematics from the pre-revolutionary Kiselyov.

Answer 15

www.thegreatcourses.com/courses/the-power-of-mathe...