How does university-level math differ from high school math?
In high school, mathematics courses usually emphasize computational techniques-factoring polynomials, solving equations, and the like. At the university level, there is a much greater emphasis on ideas, and proof plays a greater role. Calculations still matter but it no longer suffices to “get the right answer” by applying a recipe in mechanical fashion. At heart, mathematics concerns the search for underlying patterns and the precise communication of meaning. *Mathematics as a science The science of mathematics differs from empirical sciences such as biology, chemistry, and physics. Theories in these fields are supported by bodies of observation and remain true until invalidated or refined by new information. Mathematical theories are supported by deductive proof and remain true forever. For example, the geometry of the ancient Greeks is still valid and useful even though Euclid wrote his famous Elements more than two thousand years ago! *Mathematics-the golden age Mathematics is a wo
