Mathematical Analysis 2025-26

This course offers a rigorous foundation in real analysis, focusing on the logical structure of the real number system and the fundamental properties of sequences, series, and functions. Key topics include the completeness property of real numbers, convergence of sequences and series, limits and continuity of functions, and essential theorems such as the Bolzano-Weierstrass Theorem and the Cauchy Convergence Criterion. Students will develop critical thinking and problem-solving skills essential for higher-level mathematics.

Course Outcomes (COs):

  • CO1: Understand the structure of the real number system and apply the properties of the real line.

  • CO2: Analyze sequences, determine limits, and apply fundamental convergence theorems like Bolzano-Weierstrass and Cauchy Criterion.

  • CO3: Examine the behavior of infinite series and determine convergence using standard tests.

  • CO4: Apply concepts of limits and continuity to study functions and their properties.