MA 371 - Real Analysis

1. Fundamental Concepts
   a) Set Theory
      i) Basic notions
      ii) Relations and functions
   b) The Real Number System
      i) Ordered fields
      ii) The rational numbers as an ordered field
      iii) The real numbers as a complete ordered field
      iv) Sequences of real numbers and their properties
      v) The Cauchy criterion
    
2. Functions of a Real Variable
   a) Continuity
      i) Limits and continuity
      ii) Continuous functions and sequences
      iii) Properties of continuous functions
      iv) Intermediate Value Theorem
      v) Theorem of Bolzano-Weierstrass
      vi) Extreme Vaule Theorem
   b) Differentiation
      i) Properties of derivatives
      ii) Rolle's Theorem
      iii) Mean Value Theorem
   c) Integration
      i) Review of the Riemann integral

Learning Outcome 1: The student will demonstrate a rigorous understanding of the complete ordered field of real numbers.

Learning Outcome 2: The student will demonstrate a rigorous understanding of convergence.

Learning Outcome 3: The student will demonstrate a rigorous understanding of continuity and differentiability.