MAA 5216: Advanced Calculus

University of Central Florida

This course provides a rigorous, axiomatic introduction to the fundamental concepts of calculus in one real variable, framed within the broader context of mathematical analysis. Topics include the construction and properties of the real number system, convergence of sequences and series, basic notions of topology, continuity, differentiability, the Riemann integral, and sequences and series of functions. As a proof-based course, it emphasizes developing the skills necessary for constructing, analyzing, and presenting mathematical proofs. Students will gain extensive practice in recognizing valid arguments, crafting complete and logically sound proofs, and refining their mathematical writing style.