3 credits
Fall 2026 Lecture HonorsUpper Division
Real analysis in one and n-dimensional Euclidean spaces. Topics include the completeness property of real numbers, topology of Euclidean spaces, Heine-Borel theorem, convergence of sequences and series in Euclidean spaces, limit superior and limit inferior, Bolzano-Weierstrass theorem, continuity, uniform continuity, limits and uniform convergence of functions, Riemann or Riemann-Stieltjes integrals.
Learning Outcomes1Perform rigorous proofs using the definitions of open sets, closed sets, connected sets, compact sets, interior points, boundary points, cluster points, finite sets, infinite sets, and denumerable sets in Euclidean spaces.
2Perform rigorous proofs of convergence or divergence for sequences or series in Euclidean spaces.
3Determine points of continuity and existence of limits using rigorous proofs for functions whose domain and range are in Euclidean spaces.
4Perform rigorous proofs that a sequence of functions converges uniformly or does not converge uniformly on a subset of a Euclidean space.
5Know and be able to apply the definition and related theorems on the existence of Riemann or Riemann-Stieltjes integrals.
Prerequisites
GPA by professor
made by Purdue students.