MA 371

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.