Mathematics in primary and secondary schools, including Olympic Mathematics, needs appropriate methods in learning. With good methods and ideas, you may get twice the result with half the effort! Thinking in images means that people use thinking in images to understand and solve problems. Its thinking foundation is concrete image, and its thinking process is developed from concrete image.
The main means of thinking in images are objects, figures, tables and typical image materials. Its cognitive feature is that it is average in individual performance and always retains its intuition about things. Its thinking process is represented by representation, analogy, association and imagination.
Commutative algebra:
In abstract algebra, commutative algebra aims to discuss commutative rings and their ideals, as well as modules on commutative rings. Algebraic number theory and algebraic geometry are based on commutative algebra. The most prominent examples of commutative rings include polynomial rings, algebraic integer rings and p- radix rings, as well as their various quotient rings and localization.
Because probability is nothing more than the condensation of commutative ring spectrum, commutative algebra has become the main language to study the local properties of probability.