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Real Analysis is one of the most important subjects in BSc Mathematics 3rd Semester. Many students feel scared when they hear this subject name, but with the right explanation and proper preparation, Real Analysis becomes understandable and scoring.
This page explains the BSc Maths 3rd Semester Real Analysis syllabus in a clear and simple way, strictly based on the syllabus of Osmania University, Mahatma Gandhi University, and Kakatiya University.
It is written specially for degree students, using easy language, exam-focused points, and clear explanations.
Real Analysis is the study of real numbers and real-valued functions. Unlike basic calculus, this subject does not focus only on solving problems. Instead, it focuses more on:
Definitions
Theorems
Proofs
Logical understanding
Real Analysis helps students understand why formulas work, not just how to apply them. This subject is very important for future maths papers, competitive exams, and higher studies.
The Real Analysis syllabus for OU, MGU, and KU is almost the same. The subject is divided into units that start from basic concepts and slowly move to advanced ideas.
The syllabus mainly tests:
Concept clarity
Understanding of definitions
Proof-writing skills
Application of theorems
University exams usually include short answer questions, long answer questions, and proof-based questions.
This unit is the foundation of Real Analysis. If this unit is clear, the remaining syllabus becomes easier.
Topics included:
Real number system
Ordered sets
Bounded and unbounded sets
Sequences of real numbers
Convergent and divergent sequences
Monotonic sequences
Series of real numbers
👉 Questions from sequences and convergence are asked very frequently in exams.
This unit explains how a function behaves near a particular point.
Important topics:
Limit of a function
Algebra of limits
Left-hand and right-hand limits
Continuity of a function
Types of discontinuities
👉 Limits and continuity are important for both short questions and theory questions.
This unit is mainly theory and proof-oriented.
Topics covered:
Differentiability of functions
Relation between continuity and differentiability
Rolle’s Theorem
Lagrange’s Mean Value Theorem
Applications of Mean Value Theorems
👉 Proofs from this unit are commonly asked in OU, MGU, and KU exams.
This unit explains integration in a logical and theoretical manner, not just calculations.
Topics included:
Definition of Riemann integral
Upper and lower sums
Integrability of functions
Properties of Riemann integrals
Basic idea of the Fundamental Theorem of Calculus
👉 Students should clearly understand definitions and properties in this unit.
From an exam point of view, the following topics are very important:
Convergence of sequences
Continuity-based problems
Proofs of Mean Value Theorems
Riemann integrability questions
Definitions and short notes
Preparing these topics properly can help students score better marks.
Many students feel Real Analysis is difficult because:
There are many definitions
Proofs look confusing at first
There are fewer numerical problems
But once the basic concepts are clear, the subject becomes much easier. Regular practice and revision make a big difference.
Here are some simple and practical tips:
Start from Unit 01 and move step by step
Understand definitions in simple words
Learn proofs slowly, line by line
Practice previous year question papers
Revise important theorems before exams
👉 Studying regularly is more effective than studying for long hours once in a while.
For better preparation, students should use:
Unit-wise Real Analysis notes
Simple explanation PDFs
Video lectures for concept clarity
Previous year question papers
Using notes along with explanations helps in better understanding and revision.
This page is useful for:
BSc Maths 3rd semester students
OU, MGU, and KU university students
Students preparing for semester exams
Students who want clear concept understanding
What is the syllabus of BSc Maths 3rd Semester?
The syllabus mainly includes Real Analysis topics such as sequences, limits, continuity, differentiability, and Riemann integration.
Is BSc Maths easy to pass?
BSc Maths is manageable if concepts are understood clearly and regular practice is done.
Is Real Analysis compulsory in BSc Maths 3rd Semester?
Yes, Real Analysis is a core subject in most universities including Osmania University and others.
Is the BSc Maths 3rd Semester syllabus same for OU, MGU, and KU?
Yes, the core syllabus is almost the same, with minor differences in exam pattern.
Real Analysis is not about memorizing formulas. It is about understanding concepts clearly. With patience, regular practice, and proper guidance, students can perform well in this subject.
“Built for clarity, not cramming”
“Concept-first, exam-focused”