Real Analysis I

Overview

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This is an introductory course on Real Analysis designed for undergraduate students of Mathematics. The only pre-requisite is a knowledge of Calculus at high school level so students of the Sciences or Engineering who want a deeper understanding of Calculus or want to pursue subjects such as Theoretical Physics, Computational Complexity, Statistics, etc. would also benefit from this course.
INTENDED AUDIENCE :UG Students of Mathematics, the Sciences or Engineering
PREREQUISITES :12th Standard Mathematics
INDUSTRIES SUPPORT :Google, DeepMind, Microsoft Research

Syllabus

COURSE LAYOUT

Week 1:Introduction, Set Theory and LogicWeek 2:The Real Numbers as an Ordered FieldWeek 3:Completeness of the Reals and ConsequencesWeek 4:Sequences and Series
Week 5:Sequences and Series continuedWeek 6:A Taste of TopologyWeek 7:Limits and ContinuityWeek 8:Continuity and Topological Properties
Week 9:Differentiation and Basic PropertiesWeek 10:Differentiation Continued and Definition of Riemann IntegralWeek 11:The Fundamental Theorem of CalculusWeek 12:Uniform Convergence, Power Series and Taylor Series