BMTC-133 IGNOU Guess Paper 2026-27

Course Scope & Syllabus Overview: BMTC-133 Real Analysis

BMTC-133: Real Analysis is a core course under the Bachelor of Science (Mathematics) programme, designed to equip students with rigorous foundations in real number theory and advanced mathematical analysis. This course, aligned with IGNOU’s CBCS curriculum, delves into the axiomatic structure of real numbers, sequences, series, and function behavior—critical for understanding higher mathematics. Students gain proficiency in proving theorems, analyzing limits, and mastering continuity, differentiability, and integrability, all essential for research and applied statistical modeling.

Key Syllabus Units & Topics

• Block-1 The Structure of R: Covers the field axioms of real numbers, order properties, completeness, and the least upper bound principle, forming the bedrock for subsequent analysis.
• Block-2 Sequences: Explores convergence/divergence of sequences, subsequences, and the Cauchy criterion, with applications in defining limits rigorously.
• Block-3 Infinite Series: Examines convergence tests (comparison, ratio, root), absolute/conditional convergence, and power series expansions with radius of convergence.
• Block-4 Continuity and Differentiability of Functions: Analyzes uniform continuity, differentiability conditions, and the Mean Value Theorem, linking algebraic properties to graphical behavior.
• Block-6 Sequences and Series of Functions: Introduces uniform convergence, term-by-term differentiation/integration, and applications to Fourier series and approximation theory.

Frequently Asked Questions

Q: How are marks distributed in the BMTC-133 TEE, and what weightage does each unit carry?
A: The Term-End Examination (TEE) for BMTC-133 carries 100 marks, with questions typically spanning all six blocks; past papers show ~15-20% weightage per unit, with emphasis on theorems (Blocks 1, 2) and applications (Blocks 4-6).

Q: Are assignments mandatory for BMTC-133, and how do they impact the final grade?
A: Assignments contribute 30 marks to the final grade (70% TEE), requiring submission within deadlines; focus on solving problems from Blocks 3-5 to maximize scores, as these often appear in TEE questions.