IIT JAM Mathematics Syllabus

IIT JAM MATHEMATICS SYLLABUS
iit jam mathematics syllabus consisting of some different types of major subjects like Linear Algebra, Real Analysis, multivariable Calculus, Differential Calculus, Abstract Algebra.

Every year iit jam conducting the entrance exam of mathematics for the candidate to take admission into postgraduate level.Large number of candidates appears for iit jam mathematics exam because it facilitate to all the undergraduate students. Most of the candidate decided to write the iit jam exam but they should know everything about the iit jam mathematics exam before proceeding to appear in it.
Candidates must be aware of the syllabus of iit jam mathematics and how to complete their syllabus. Because it's syllabus is not much huge but it takes to much time to complete the syllabus. Candidates should try to understand that the their motive is not only the completion of syllabus although clearing the each and every concepts with confidently within the stipulated time.

Iit jam mathematics syllabus is very interesting and easy to learn because it's syllabus is the same as the candidates have studied in their undergraduate level or college level semester exam in mathematics. The semester exam is based on the particular selected topic discussed throughout the whole semester in B.sc undergraduate.
Every year a different institute take participate to conduct the examination for iit jam mathematics exam . They can be iits or iisc . Candidates should be familiarise with the past few years questions paper of iit jam mathematics because it gives the idea about the pattern and structure of the questions discussed till now.
Every candidates can crack their dream iits with AIR. They should follow the strict discipline of the study. Only focused and dedicated candidates can fulfill the aim of doing master through iits. Here we will provide the some tips and way of focused study.

BEFORE PROCEEDING FURTHER...

Before starting the preparation journey for M.sc mathematics course, candidates should be familiar with difficulty of entrance exam.

Iit jam mathematics preparing aspirants will be given the tips, tricks, notes,most important questions, practice question paper and free Lecture course available on the YouTube where you can start watching the lectures. Complete iit jam mathematics free batch for the candidates who want to start self study because candidate can crack the iits with two methods one is by self study and second is if they feel any doubts in their concept clearance then by simply watching the our lectures LECTURES on the youtube.

Let's see the topics of iit jam mathematics syllabus of Linear algebra
1. Matrices: systems of linear equations, rank, nullity, rank-nullity theorem, inverse, determinant,eigenvalues, eigenvectors. Finite Dimensional Vector Spaces: linear independence of vectors, basis, dimension, lineart ransformations, matrix representation, range space, null space, rank-nullity theorem.

Now see the detailed topics to be cover in the first subject as linear algebra

1. what is vectors.

• Vectors in different spaces like Rn and Cn.
• Vector addition and scalar multiplication,

2. All types of Algebra of matrices.

• Introduction of matrices
• Matrix addition and scalar multiplication
• Transpose of a matrix
• All square matrix
• Power of square matrix
• Polynomial in matrix
• Invertible matrix or non singular matrix
• Special types of real square matrix
• Complex matrix
• Special types of complex matrix
• Block matrix

3. System of linear equations

• Introduction to system of linear
• Elementary row operations
• How to convert system into triangular and echelon form
• Gauss elimination method
• System of linear equations as matrix form AX=b
• Consistent system and inconsistent system
• Homogenous system and Non-homogeneous system

4. Vector Space

• Introduction of vector space and their properties
• Linear combination of vectors
• Linear spans
• Spanning set of vectors
• Linearly dependent and linearly independent variables
• Subspaces
• Basis and dimension
• Rank of matrix
• Union of subspace
• Intersection of subspace
• Sums and direct sums
• Relationship between basis and dimension of (w1+w2) and (w1 intersection w2).

5. Linear Transformation (Linear mapping)

• Introduction to linear transformation
• Kernel and image of linear transformation (Null space and Range space)
• Singular and non singular linear transformation
• Operations on linear transformation
• Linear operators
• Linear transformation as matrix form
• Matrix representation of linear transformation
• Change of basis
• Practice questions

6. Determinants

• Introduction of determinants
• Order of determinants
• Minor and cofactor
• Adjoints

7. Diagonalization, Eigenvalues and Eigenvectors

• Introduction of eigenvalues and Eigenvectors
• Characteristics polynomial
• Cayley Hamilton theorem
• Diagonalization
• Diagonalizing real symmetric matrices
• Characteristics and minimal polynomia

Let's see the topics of iit jam mathematics syllabus of Real analysis.

1. Sequences and Series of Real Numbers: convergence of sequences, bounded and monotone
sequences, Cauchy sequences, Bolzano-Weierstrass theorem, absolute convergence, tests of
convergence for series – comparison test, ratio test, root test; Power series (of one real variable), radius
and interval of convergence, term-wise differentiation and integration of power series.

2. Functions of One Real Variable: limit, continuity, intermediate value property, differentiation, Rolle’s
Theorem, mean value theorem, L'Hospital rule, Taylor's theorem, Taylor’s series, maxima and minima,Riemann integration (definite integrals and their properties), fundamental theorem of calculus.

Now see the detailed topics to be cover in the first subject as Real analysis.

1. Sequence

• Real sequence
• Bounded sequence
• Limit of a sequence
• Convergent sequence
• Limit theorems
• Null sequence
• Divergent sequence
• Some important limits
• Monotone sequence
• Some important sequences
• Subsequence
• Subsequential limit
• Characterisation of a compact set
• Upper limit and lower· limit
• Cauchy criterion
• Cauchy's theorems on limits

2. Infinite series.

• Infinite series
• Series of positive terms
• Tests for convergence
• Series of arbitrary terms
• Conditionally convergent series
• Multiplication of series

3. Limits

• Limit of a function
• One-sided limits
• Infinite limits
• Limits at infinity
• Infinite limits at infinity
• Limits of monotone functions
• Some important' limits4. Continuity
• Continuity
• Continuity of some important functions
• Limit of composite functions
• DiscontinuityProperties of continuous functions
• Monotone functions and continuity
• Uniform continuity
• Continuity on a compact set

5. Differentiation

• Differentiability. Derivative
• Higher order derivatives
• Sign of the derivative
• Properties of the derivative
• Rolle's theorem and Mean value theorems
• The nth order derivatives
• Taylor's theorem and expansion of functions
• Maxima and minima
• Indeterminate forms

6. Riemann integral

• Partition
• Riemann integrability
• Refinement of a partition
• Norm of a partition
• Some Riemann integrable functions
• Properties of Riemann integrable functions
• Inequalities
• Fundamental theorem
• Another definition of integrability
• Integration by substitution
• Integration by parts
• Mean value theorems
• Logarithmic function
• Exponential function

7. Improper integrals

• Introduction
• Definitions
• Tests for convergence (positive integrand)
• Tests for convergence
• Definitions
• Tests for convergence (positive integrand)
• Tests for convergence
• Tests for convergence of the integral of a product
• Some theorems
• Evaluation of some improper integrals
• Beta function and Gamma function
• 8. Series of functions
• Uniform convergence
• Consequences of uniform convergence
• Abel's and Dirichlet's tests

9. Power series

• Introduction
• Determination of radius of convergence
• Properties of a power series

Let's see the topics of iit jam mathematics syllabus of Multivariable Calculus

1. Functions of Two or Three Real Variables: limit, continuity, partial derivatives, total derivative, maxima and minima.
2. Integral Calculus: double and triple integrals, change of order of integration, calculating surface areas and volumes using double integrals, calculating volumes using triple integrals.

Now see the detailed topics to be cover in the first subject as Multivariable Calculus

1. 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.

Let's see the topics of iit jam mathematics syllabus of Ordinary differential equations.

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.

Now see the detailed topics to be cover in the first subject as Ordinary differential equations.
1. 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.

Let's see the topics of iit jam mathematics syllabus of Abstract algebra.

Groups: cyclic groups, abelian groups, non-abelian groups, permutation groups, normal subgroups,
quotient groups, Lagrange's theorem for finite groups, group homomorphisms.

Now see the detailed topics to be cover in the first subject as Abstract algebra.
1. Groups:

• cyclic groups
• abelian groups
• non-abelian groups
• permutation groups
• normal subgroups
• quotient groups
• Lagrange's theorem for finite groups
• group homomorphisms.

There are complete syllabus for the iit jam mathematics. Which we have covered in my youtube channel Candidates you can now watch my youtube channel and start your depression for iit jam mathematics. I have covered detailed concepts in. each topics. I will try to give you the notes, the tips and tricks in my websites as well as Youtube channel.

FAQ

Questions 1. What is IIT JAM Mathematics syllabus?

Answer 1:iit jam mathematics syllabus consisting of some different types of major subjects like Linear Algebra, Real Analysis, multivariable Calculus, Differential Calculus, Abstract Algebra.

Questions 2. How hard is maths at IIT JAM?

Answer 2 : Iit Jam Maths is not hard if you do hard work in your entrance exam And You can get 30 to 40 marks ,then you can qualify easily.

Questions 3. Can I crack IIT JAM in 1 month?

Answer 3 : Candidate can crack the iit jam mathematics in one month, if they follow the strict plan. Only focus important topics, important questions and revision. Then Candidate can qualify the exam with minimum of they need.

Questions 4. Who can give IIT JAM maths?

Answer 4:Candidates who have successfully completed an undergraduate degree or currently studying in the final year of undergraduate are eligible for admission through JAM 2025.

Questions 5.How many marks are required to clear IIT JAM mathematics?

Answer 5: Every year large number of students appear for the iit jam mathematics exam and they qualify the exam with minimum of achieving 30 to 40 marks.

Questions 6. Can an average student crack IIT JAM mathematics?

Answer 6: Yes, Average students crack the iit jam mathematics only with the solution of they do hard work and they practice more and more and keep revising all the concepts.