👉 Accurately explaining the mathematics involves breaking down complex concepts into clear, logical steps using precise definitions and formulas. For example, when discussing calculus, one might start by defining derivatives as limits of ratios of changes in function values, then apply the limit definition to show how derivatives measure instantaneous rates of change. In linear algebra, accurately explaining vector spaces involves defining operations like addition and scalar multiplication, then using these definitions to prove properties such as distributivity and associativity. For differential equations, one would start by defining the equation in terms of derivatives, then apply methods like separation of variables or integrating factors to solve it, ensuring each step adheres strictly to the underlying mathematical principles and theorems. Throughout, maintaining clarity and rigor is key to conveying the accuracy of the mathematical reasoning.
