Foundations of Real Analysis: Sequences and Series for IIT-JAM Prep

To excel in rigorous mathematics examinations like the IIT-JAM, you must develop a deep, intuitive understanding of how sequences and series of real numbers behave. This text-based course guides you step-by-step from foundational definitions to advanced convergence tests, ensuring you can write proofs and solve exam problems with absolute precision. What you will learn: Understand the fundamental definitions of sequences, bounds, and limits of real numbers; Apply key convergence tests, including the Ratio, Root, Comparison, and Integral tests, to complex series; Master the concepts of absolute and conditional convergence, along with alternating series; Analyze sequences of functions, pointwise convergence, and uniform convergence principles; Practice solving rigorous mathematical proofs and typical exam-style problems through structured written exercises. We begin with the core terminology of real analysis before moving into detailed proofs and step-by-step problem-solving strategies. You will read clear explanations of complex theorems and work through written practice scenarios designed to build your mathematical reasoning. This course is designed for undergraduate mathematics students, IIT-JAM aspirants, and anyone looking to build a strong foundation in real analysis, with no prior advanced proof-writing experience required. Start reading today to master sequences and series for your next major mathematics exam.