Advanced Calculus

Course Description

A look at sets, functions and the real numbers. Topics include the Completeness axiom, cardinality and Cantor’s Theorem, LimSup and LimInf; the topology of R1 and R2, open sets, limit points, compactness and the Heine-Borel Theorem, continuous functions properties, uniform continuity, the Mean-Value theorem; the Riemann integral and the Lebesgue Measure.

Learning Outcomes

  • Demonstrate proficiency in correct formulation and proving theorems covered in the class.
  • Be able to show different ways to disprove incorrect mathematical statements on concrete examples.
  • Have clear understanding and strong awareness of mathematical concepts covered in this course and be able to solve problems formulated in terms of these concepts.

Prerequisites

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Class of 2014, Military Veteran