BMTC-133 IGNOU Solved Assignment 2026-27

Course Scope & Syllabus Overview for BMTC-133: Real Analysis (BSCFMT, SOS, IGNOU 2026-27)

BMTC-133: Real Analysis is a core course under IGNOU’s Bachelor of Science (Mathematics) programme, designed to strengthen foundational rigor in mathematical analysis. This course bridges elementary calculus with advanced topics, emphasizing the axiomatic structure of real numbers, rigorous proofs, and deep conceptual understanding. Students explore the formal properties of the real number system, convergence criteria for sequences and series, and the theoretical underpinnings of continuity, differentiability, and integrability. The syllabus aligns with the CBCS framework, ensuring alignment with global academic standards while maintaining relevance to applied mathematical research and problem-solving.

Key Syllabus Units & Topics

• Block-1: The Structure of R: Covers the construction of real numbers via Dedekind cuts and Cauchy sequences, field axioms, order properties, and completeness of ℝ, with rigorous proofs of fundamental theorems like the Least Upper Bound Property.
• Block-2: Sequences: Analyzes boundedness, monotonicity, and convergence of sequences, including the Bolzano-Weierstrass theorem, subsequences, and the Cauchy criterion, with applications to limits and series.
• Block-3: Infinite Series: Examines convergence tests (comparison, ratio, root tests), absolute vs. conditional convergence, and power series, with emphasis on radius of convergence and Taylor/Maclaurin series expansions.
• Block-4: Continuity and Differentiability of Functions: Defines continuity, uniform continuity, and differentiability in ℝ, explores the Intermediate Value Theorem and Mean Value Theorem, and studies higher-order derivatives and Taylor’s theorem.
• Block-6: Sequences and Series of Functions: Investigates pointwise and uniform convergence, Weierstrass M-test, and properties of power series, including term-by-term differentiation and integration.

Frequently Asked Questions

Q: How are marks distributed in the TMA for BMTC-133, and what is the pass criterion?
A: The TMA carries 30 marks (30% of the total grade) and follows IGNOU’s standard weightage: 10 marks for each of the three sections (A, B, C) in the assignment. A minimum of 50% marks in the TMA is required to pass the course, alongside meeting the final examination threshold.

Q: Are there any specific formatting rules for Section B (short-answer questions) in BMTC-133 assignments?
A: Section B requires concise yet precise answers, strictly adhering to the 250-word limit per question. Use mathematical notation accurately, cite theorems explicitly, and avoid redundant explanations—focus on logical flow and proof clarity.