Core Module: Modern Algebra + Real Analysis
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Mode of Learning: Online
Why is this Module a Game-Changer?
Modern Algebra and Real Analysis are not just topics; they are the foundation and the super-scoring pillars of the Mathematics Optional syllabus. Mastering them is the key to a top rank.
High Weightage: Together, they form the core of Paper-I and a significant portion of Paper-II.
Conceptual Clarity: Strong fundamentals here simplify other areas like Calculus and Linear Algebra.
Defined Syllabus: Finite and well-bound topics mean focused preparation and maximum marks ROI.
Module Breakdown: What You Will Learn
1. Modern Algebra (The Logical Framework)
We will deconstruct abstract concepts into intuitive, easy-to-understand modules.
Group Theory: Groups, subgroups, cyclic groups, cosets, Lagrange's Theorem, normal subgroups, quotient groups, homomorphisms, and isomorphism theorems.
Ring Theory: Rings, integral domains, fields, ideals, ring homomorphisms, quotient rings, polynomial rings, and unique factorization domains.
Field Theory: Field extensions, finite fields, and an introduction to Galois Theory.
Linear Algebra: Vector spaces, linear transformations, matrices, determinants, eigenvalues, eigenvectors, Cayley-Hamilton Theorem, and inner product spaces.
2. Real Analysis (The Bedrock of Rigour)
We build your analytical thinking from the ground up, focusing on proof-based learning.
The Real Number System: Order, completeness, supremum, infimum, and Archimedean property.
Sequences & Series: Convergence, limits, Cauchy sequences, tests for convergence of series, absolute and conditional convergence.
Continuity: Limits of functions, continuous functions, uniform continuity, and the properties of continuous functions on closed intervals.
Differentiation: Mean Value Theorems (Rolle, Lagrange, Cauchy), Taylor's Theorem, and L'Hôpital's Rule.
Riemann Integration: Definition, integrability conditions, fundamental theorems of calculus, and improper integrals.
Specialized Features for This Module
PYQ-Centric Approach: Every lecture integrates and deconstructs Previous Year Questions (PYQs) to align your preparation with UPSC's pattern.
Theorems & Proofs Bank: Exclusive access to a compiled repository of all important theorems and their proofs, a must for scoring high marks.
Problem-Solving Sessions: Dedicated live classes focused solely on solving complex problems from these topics.
Handwritten Notes & Crux: Concise, visually appealing notes that highlight definitions, theorems, and key takeaways for quick revision.
Doubt Clearing: Priority doubt-resolution sessions for these core subjects to ensure 100% conceptual clarity.
Your Pathway to Success
This module is part of our comprehensive Platinum Course, which includes:
One-to-One Mentorship from Mathematics experts.
Regular Answer Writing Sessions with detailed evaluation.
Mains Test Series (Sectional & Full-Length) focused on application.
Optional Gyan Bhandar - a treasure trove of resources.
Weekly Doubt Clearing Sessions with faculty.
Build an unshakable foundation. Enroll today!
- 2025
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- English (UK)
