IIT JAM Mathematics Syllabus PDF Download

The official syllabus consists of three major sections, covering Real Analysis, Multivariable Calculus, Differential Equations, Algebra, and Linear Algebra.
SECTION 1: REAL ANALYSIS
Sequences and Series of Real Numbers
Convergence of sequences
Bounded and monotone sequences
Cauchy sequences
Bolzano–Weierstrass theorem
Absolute convergence
Series convergence tests: comparison test, ratio test, root test
Power series: radius/interval of convergence, term-wise differentiation and integration
Functions of One Real Variable
Limit and continuity
Intermediate value property
Differentiation
Rolle’s theorem and Mean Value Theorem
L’Hospital rule
Taylor’s theorem and Taylor series
Maxima and minima
Riemann integration and properties
Fundamental theorem of calculus



SECTION 2: MULTIVARIABLE CALCULUS & DIFFERENTIAL EQUATIONS
Functions of Two or Three Variables
Limit and continuity
Partial derivatives
Total derivative
Maxima and minima
Integral Calculus
Double and triple integrals
Change of order of integration
Surface area and volume using double integrals
Volume using triple integrals
Differential Equations
Bernoulli’s equation
Exact differential equations
Integrating factors
Orthogonal trajectories
Homogeneous differential equations
Separation of variables
Linear differential equations (2nd order with constant coefficients)
Method of variation of parameters
Cauchy–Euler equation



SECTION 3: LINEAR ALGEBRA & ALGEBRA
Basic Algebra
Permutations and combinations
Binomial theorem
Matrices
Systems of linear equations
Rank and nullity
Rank–nullity theorem
Inverse and determinant
Eigenvalues and eigenvectors
Finite Dimensional Vector Spaces
Linear independence
Basis and dimension
Linear transformations
Matrix representation
Range and null space
Rank–nullity theorem
Group Theory
Cyclic, abelian, and non-abelian groups
Permutation groups
Normal subgroups
Quotient groups
Lagrange’s theorem
Group homomorphisms