MATH 4014 - Real Analysis I

Description

This course provides a rigorous study of the principles of real analysis. Topics include the real number system, sequences and series, limits, continuity, uniform continuity, differentiation, and an introduction to point-set topology. Additional topics may include uniform convergence, integration, and selected applications of analysis. Proof-writing and problem-solving are integral components of the course.

Learning Objectives

• Explain the structure of the real number system, including the completeness axiom and its consequences.
• Prove results concerning sequences, subsequences, monotone sequences, Cauchy sequences, and series.
• Calculate limits using appropriate definitions.
• Analyze properties of functions using the definitions and theorems of limits, continuity, and uniform continuity.
• Apply major results in differentiation, including the Mean Value Theorem, Cauchy’s Mean Value Theorem, and related consequences.
• Construct clear, rigorous mathematical proofs related to the core topics of real analysis.