1. Direct substitution method: directly substitute the known conditions into the sought expression, simplify the calculation, and get the result. This method is suitable for simple algebraic operations and the calculation of elementary functions.

2. Calculus method: Using the basic theorem and formula of calculus, the obtained expression is deduced and integrated, and the result is obtained. This method is suitable for solving the limit, derivative and integral of functions.

3. Matrix method: the problem is transformed into the form of matrix, and the results are obtained by calculating and simplifying the matrix algorithm. This method is suitable for vector sum matrix operation in linear algebra and solving linear equations.

4. Geometric method: the problem is transformed into the form of geometric figures, and the results are obtained by calculation and reasoning using geometric relations and properties. This method is suitable for solving geometric problems and spatial analytic geometric problems.

5. Numerical approximation method: approximate the value of the expression by numerical calculation methods, such as dichotomy and Newton iteration method, and get an approximate solution. This method is suitable for problems that cannot be solved by analytical methods, or when analytical solutions do not exist.

6. Symbol calculation method: use computer software or programming language to perform symbol calculation, and perform symbol operation and derivation on the expression to get the result. This method is suitable for complex algebraic and symbolic operations and can greatly simplify the calculation process.

The above are the common methods to verify the calculation problems of advanced mathematics. According to the characteristics and requirements of specific problems, appropriate methods can be selected for calculation and verification.