This repository contains my lecture notes and exercise solutions from Kenneth A. Ross: Elementary Analysis, The Theory of Calculus (Second Edition). The focus is on understanding Real Analysis to support advanced topics in Probability, Statistical Inference, and Machine Learning.
- Introduction: The Set Natural numbers, Rational numbers, Real numbers, Completeness Axiom, and symbols (+∞, −∞).
- Sequences: Limit Theorems, Monotone and Cauchy sequences, Subsequences, lim sup's and lim inf's, Series, and Topological concepts.
- Continuity: Properties of Continuous functions, Uniform Continuity, and Limits of Functions.
- Sequences and Series of Functions: Uniform Convergence of Seq of Functions.
- Lecture Notes: Summaries of key concepts.
- Exercise Solutions: Solved exercises (some skipped or deferred due to time constraints).
These notes and solutions reflect my effort to strengthen my understanding of Real Analysis, a critical mathematical discipline that forms the foundation for Probability, Statistical Inference, and Machine Learning.
Real Analysis provides the rigorous mathematical foundation for understanding key concepts in Statistics (such as the Law of Large Numbers, Central Limit Theorem), Convex Optimization, and the Fourier Transform, enabling precise formulation and solution of problems in Machine Learning, AI, and Robotics.
Whenever possible, I aim to document my work in LaTeX for clarity and professional presentation.
Not all problems from the textbook are solved—some are skipped or deferred to be completed later.
Feel free to connect with me:
- Email: [email protected]
- LinkedIn: www.linkedin.com/in/sai-sampath-kedari