A summary of M396C : analysis and the real line UTeach summers master's course mathematics department at the University of Texas at Austin
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The purpose of this paper is to review and summarize the topics involved in the study of real analysis. Real analysis is a branch of mathematics that studies the field of real numbers including the calculus of real numbers, analytical properties of real functions and sequences. This includes limits of sequences of real numbers, continuity, completeness, and related properties of real functions. While all topics in the course were important and vital to understanding analysis, the goal of this paper is to review, research, and report on a few of the more interesting topics covered in the class.