IIT JAM AIR 1 Marks :Mathematics

The Mathematics syllabus for IIT JAM is designed to test both theoretical knowledge and practical problem-solving skills. Covering topics ranging from algebra and analysis to calculus and differential equations, this syllabus demands a strong conceptual foundation. Here’s an overview of the updated key topics:
1. Real Analysis
This section focuses on the properties and behavior of real numbers, sequences, and functions. Key topics include:
Sequences and Series of Real Numbers: Convergence of sequences, bounded and monotone sequences, Cauchy sequences, Bolzano-Weierstrass theorem, absolute convergence, and tests of convergence for series (comparison test, ratio test, root test).
Power Series: Radius and interval of convergence, term-wise differentiation, and integration of power series.
Functions of One Real Variable: Limit, continuity, intermediate value property, differentiation, Rolle’s theorem, mean value theorem, L’Hospital’s rule, Taylor’s theorem, Taylor’s series, maxima and minima.
Riemann Integration: Definite integrals and their properties, fundamental theorem of calculus.
2. Multivariable Calculus and Differential Equations
This section emphasizes understanding multi-dimensional systems and dynamic behavior:
Functions of Two or Three Real Variables: Limit, continuity, partial derivatives, total derivative, maxima and minima.
Integral Calculus: Double and triple integrals, change of order of integration, calculating surface areas and volumes using double integrals, calculating volumes using triple integrals.
Differential Equations: Bernoulli’s equation, exact differential equations, integrating factors, orthogonal trajectories, homogeneous differential equations, method of separation of variables, linear differential equations of second order with constant coefficients, method of variation of parameters, Cauchy-Euler equation.
3. Linear Algebra and Algebra
Linear Algebra plays a critical role in modern mathematical applications:
Matrices: Systems of linear equations, rank, nullity, rank-nullity theorem, inverse, determinant, eigenvalues, and eigenvectors.
Finite Dimensional Vector Spaces: Linear independence of vectors, basis, dimension, linear transformations, matrix representation, range space, null space.
Groups: Cyclic groups, abelian groups, non-abelian groups, permutation groups, normal subgroups, quotient groups, Lagrange’s theorem for finite groups, group homomorphisms.
Mastering the above syllabus ensures a strong foundation to tackle both conceptual and application-based problems in the exam.