Course Description:
This course offers a rigorous introduction to the foundational concepts of real analysis, focusing on the structure of the real number system and the formal underpinnings of calculus. Topics include the completeness property of the real numbers, sequences and series, limits, continuity, differentiation, and an introduction to the Riemann integral. Emphasis is placed on mathematical proof, logical reasoning, and precise definitions. This course builds the analytical tools necessary for higher-level mathematics, including topology, measure theory, and functional analysis.
Prerequisites: A solid background in calculus and familiarity with elementary set theory and basic proof techniques.
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