IIT JAM Preparation Strategy Subject-wise

Section 1: Real Analysis

Sequences and Series of Real Numbers: Convergence (bounded, monotone, Cauchy), Bolzano–Weierstrass theorem, absolute convergence, comparison/ratio/root tests.
Power Series: Radius & interval of convergence, term-wise differentiation/integration.
Functions of One Real Variable: Limit, continuity, differentiation, Rolle’s theorem, MVT, L’Hospital rule, Taylor’s theorem & series, maxima/minima, Riemann integration, FTC.

Section 2: Multivariable Calculus and Differential Equations
Functions of Two/Three Variables: Limit, continuity, partial derivatives, total derivative, maxima & minima.
Integral Calculus: Double/triple integrals, change of order, surface areas & volumes.
Differential Equations: Bernoulli, exact equations, integrating factors, orthogonal trajectories, homogeneous equations, separation of variables, 2nd order linear ODEs with constant coefficients, variation of parameters, Cauchy–Euler.

Section 3: Linear Algebra and Algebra
Basic Algebra: Permutations & combinations, Binomial theorem.
Matrices: Rank, nullity, inverse, determinant, eigenvalues/eigenvectors, systems of equations, rank–nullity theorem.
Vector Spaces: Basis, dimension, linear transformations, range/null space.
Groups: Cyclic, abelian, non-abelian, permutation groups, normal subgroups, quotient groups, Lagrange’s theorem, homomorphisms.
Subject-wise Preparation Tips
Real Analysis
Master convergence tests (comparison, ratio, root) through repeated practice until selection becomes instinctive.
Memorize standard series results (geometric, harmonic, p-series) and apply them to NAT problems for speed.
Use visual aids to understand limits, continuity, and differentiability deeply.
Revise Taylor’s theorem and apply it to approximation problems regularly.
Solve integration problems systematically, focusing on theorems and their proofs.
Multivariable Calculus
Practice partial derivatives and total derivatives with geometric interpretations.
Work on constrained optimization problems using Lagrange multipliers.
Master double/triple integration techniques and coordinate transformations.
Apply Gauss’s, Green’s, and Stokes’s theorems to real-world scenarios.
Differential Equations
Learn to classify the type of ODE quickly and recall the solving technique instantly.
Automate standard methods (Bernoulli, Cauchy–Euler, exact equations) through repetitive drills.
Focus on applications like heat flow, population dynamics, and oscillations.
Keep a step-by-step approach for integrating factors and orthogonal trajectories.
Linear Algebra
Maintain a dedicated formula sheet for eigenvalues, determinants, and transformation rules.
Practice diagonalization, rank calculation, and inverse finding without shortcuts.
Understand proofs of fundamental theorems like rank–nullity to tackle MSQs.
Apply concepts to solving large systems of equations efficiently.
Algebra & Group Theory
Strengthen combinatorics skills by solving varied-level permutation and combination problems.
Tackle proof-based questions in group theory, especially around Lagrange’s theorem and subgroup properties.
Use abstract algebra problems to connect theory to symmetry in physics/chemistry.