This is an introduction to the rigorous treatment of the foundations of real analysis in one variable. It is based entirely on proofs. Students are expected to know what a mathematical proof is and are also expected to be able to read a proof before taking this class. Topics include: properties of the real number system, sequences, continuous functions, topology of the real line, compactness, derivatives, the Riemann integral, sequences of functions, uniform convergence, infinite series and Fourier series. Additional topics may include: Lebesgue measure and integral on the real line, metric spaces, and analysis on metric spaces.

A site for IMA NY Students to find equivalent courses outside of IMA NY

For most students joining IMA in Fall 2022 and beyond, there is a new program structure that affects the categorization of courses on this site:

Any class in any IMA major elective category (ie "Art & Design") refers to the IMA program structure previous to those entering in Fall 2022. If you are in the class of 2026 (most entering Fall 2022 or later), any course in an IMA elective category are generic IMA electives in the new structure.