We recommend starting with the books "Think Like a Mathematician" by Barbara Oakley, "Mathematical Thinking" by Joe Bowler and "Mathematics for Hopeless Humanities" by Nelly Litvak and Alla Kechedzhan.
More books with non-standard and Olympiad problems:
- Living mathematics
- Olympiad mathematics. Arithmetic problems with solutions and instructions. Grades 5-7
- How to solve non-standard problems
- Professor Stuart's mathematical puzzles
- Professor Stuart's mathematical curiosities
- The greatest mathematical problems
Here you can find olympiad problems for different classes with solutions and the necessary theory on different topics, useful articles and lectures:
Free games and simulators for logic, mathematics, memory, attention:
https://play.google.com/store/apps/details?id=ru.allyteam.evrika&hl=ru - application for the development of logic and deduction.
http: / /ru.brainexer.com/ - there is a browser version and an application, no registration, a simple and convenient menu, different categories of tasks.
https://uplift.io/ - free educational games and online simulators, which can be played without restrictions, but registration is required.
https://logiclike.com - a platform for the development of logic and mathematical abilities, bank 3500+ logical problems for different ages. Paid and free functions, registration is required.
Sites for general "brain pumping": not only logic, but also language learning, development of memory, attention and emotional intelligence. Everywhere there is paid and free content, registration is required, it is proposed to take a test to compose workouts.
Entertainment sites with riddles, puzzles, logic tasks and tests:
I advise you to read Simple Obsession (John Derbyshire), the book does not show methods for solving problems, but the way to study in mathematics. Smoothly from the basics of arithmetic, learning why the fractions are inverted during multiplication and where the exponent came from, you will come to complex analysis and integral calculus - a mathematical language of the highest level. You yourself will not notice how to comprehend basic and advanced mathematics.
At the same time, the book is written incredibly understandable for any language. The work will also help specialists to discover something new for themselves, for example, where do the beginnings of calculation methods, functions and specific variables come from (after all, no one usually asks a question, but simply uses them).