MATH421

Identify algebraic and topological properties of the real number system.

Write correct mathematical proofs about algebraic and topological properties of the real number system.

Identify open sets, closed sets, and limit points.

Write correct mathematical proofs about various properties of functions and sets.

Use limits to differentiate functions.

Distinguish between differentiable and non-differentiable functions, integrable and non-integrable functions, and convergent and divergent sequences and series.

Explain how concepts of real analysis are applied in science and engineering.