BMTC-133 IGNOU Solved Assignment 2026-27

Real Analysis (BMTC-133) A Rigorous Foundation for Advanced Mathematical Reasoning

BMTC-133: Real Analysis is a core component of the Bachelor of Science (Mathematics) curriculum under IGNOU’s School of Sciences, designed to equip students with a deep understanding of the foundational principles governing real numbers, limits, and function behavior. This course transcends basic arithmetic by systematically exploring the axiomatic structure of the real number system, rigorous proofs of convergence, and the interplay between continuity, differentiability, and integrability. Through its meticulously crafted CBCS modules, students develop critical analytical skills essential for advanced topics in pure and applied mathematics, ensuring a strong theoretical grounding for subsequent specializations.

Core Syllabus Units and Key Topics

• Block-1: The Structure of R: Examines the construction of real numbers via Dedekind cuts and Cauchy sequences, proving completeness and the least upper bound property with formal rigor.
• Block-2: Sequences: Analyzes boundedness, monotonicity, and convergence criteria, including the Bolzano-Weierstrass theorem and characterization of limits via ε-N language.
• Block-3: Infinite Series: Covers convergence tests (ratio, comparison, root), absolute vs. conditional convergence, and applications to power series expansions.
• Block-4: Continuity and Differentiability of Functions: Explores uniform continuity, the Intermediate Value Theorem, and differentiability conditions with applications to Taylor’s theorem.
• Block-5: Integrability of Functions: Develops Lebesgue’s definition of integrability, Riemann-Stieltjes integrals, and connections to area under curves via Darboux sums.

Frequently Asked Questions

Q: How is the TMA for BMTC-133 marked, and what weightage does it hold in the final grade?
A: The Tutor-Marked Assignment carries 30% of the total marks for BMTC-133, with evaluation based on logical coherence, adherence to mathematical notation, and correctness of proofs. Strict adherence to IGNOU’s prescribed word limits (e.g., 500 words for Section A) is mandatory.

Q: Are there specific pass marks or minimum criteria for solving numerical problems in the TMA?
A: While IGNOU does not publish exact pass marks for TMAs, solutions must demonstrate a complete and accurate derivation of results, including intermediate steps. Partial credit is awarded only for well-justified reasoning; unsupported assertions or incomplete proofs will incur deductions.