An investigation into the mathematical foundations of calculus.  Through lectures and exercises, visit fundamental concepts of mathematical analysis including logic, basic set theory, functions, number systems, order completeness of the real numbers and its consequences, sequences and series, topology of R^n, continuous functions, uniform convergence, compactness, and theory of differentiation and integration.  Expand mathematical proof and writing skills through ample practice with LaTex to communicate mathematics effectively and demonstrate rigorous math thinking in preparation for more advanced courses.