BMTC-133 IGNOU Handwritten Assignment 2026-27

Course Scope and Syllabus Overview for BMTC-133: Real Analysis

BMTC-133: Real Analysis is a core course under the Bachelor of Science (Mathematics) programme (BSCFMT) offered by IGNOU’s School of Sciences. This course is designed to provide students with a rigorous foundation in the theoretical underpinnings of real analysis, emphasizing logical reasoning, proof techniques, and the formal structure of real numbers. The curriculum is meticulously crafted to bridge the gap between intuitive calculus and abstract mathematical analysis, preparing students for advanced studies in pure mathematics, applied statistics, and related disciplines. Through this course, learners gain proficiency in analyzing sequences, series, continuity, differentiability, and integrability, equipping them with critical skills for problem-solving and theoretical exploration.

Key Syllabus Units and Topics

• The Structure of R: This unit explores the axiomatic construction of real numbers, field properties, order theory, and the completeness axiom, forming the bedrock for subsequent analysis. Students study the least upper bound property and its implications in constructing real numbers rigorously.
• Sequences: Here, the focus shifts to the behavior of sequences, including convergence, divergence, subsequences, and the Bolzano-Weierstrass theorem. The unit delves into monotonic and bounded sequences, establishing foundational tools for analyzing limits and series.
• Infinite Series: This block examines the convergence of series through tests like the comparison, ratio, and root tests, along with absolute and conditional convergence. Students also explore power series and their applications in approximating functions.
• Continuity and Differentiability of Functions: The unit rigorously defines continuity, differentiability, and their geometric interpretations. It covers the Intermediate Value Theorem, Extreme Value Theorem, and the Mean Value Theorem, alongside applications of derivatives in analyzing function behavior.
• Integrability of Functions: Students investigate the Riemann integral, integrability conditions, and the Fundamental Theorem of Calculus. The unit connects differentiability and integrability, emphasizing the theoretical foundations of integration.

Frequently Asked Questions

Q: What is the marking scheme for the BMTC-133 assignment, and how many marks does it carry?
A: The BMTC-133 assignment carries a total of 30 marks, contributing significantly to the overall grade. It is designed to assess understanding of key concepts, problem-solving skills, and the ability to apply theoretical knowledge to practical problems.

Q: What are the pass marks required for BMTC-133, and how is the final examination structured?
A: To pass BMTC-133, students must secure a minimum of 40% marks in the assignment and 50% in the term-end examination. The term-end exam typically consists of theoretical and problem-solving questions, testing both conceptual clarity and analytical ability.