### Jamia Millia Islamia Entrance Test(JMIEE)-M.A./M.Sc.(Mathematics) Exam Pattern

#### Exam Pattern

**Test Duration-**105 min.**Total Marks-**100**Total Questions-**100**Marking System–****1 mark**each for the correct answer. There are**0.25 mark**for the wrong answer.

### Syllabus Summary

No. Of Subject | 12 |
---|---|

No. Of Unit | 13 |

No. Of Chapter | 85 |

- Analytic functions
- Complex Integration
- Cauchy’s Integral Theorem and Formula
- Liouville’s Theorem
- Zeros and Singularities
- Taylor and Laurent’s series
- Residue Theorem

- Quotient groups and Homomorphism Theorems
- Automorphisms
- Sylow’s theorems
- Euclidean domains, polynomial rings

- Finite dimensional vector spaces
- Linear transformations and their matrix representations
- Systems of linear equations
- Eigenvalues and Eigenvectors
- Cayley-Hamilton Theorem
- Jordan-canonical form
- Hermitian, Skew- Hermitian and unitary matrices
- Finite dimensional inner product spaces
- Gram-Schmidt Orthonormalization Process

- Linear programming problem and its formulation
- Infeasible and Unbounded LPP’s
- Dual problem and duality Theorems
- Vogel’s approximation method
- Hungarian method

- First order ordinary differential equations
- Initial Value Problems
- Linear ordinary differential equations of Higher Order
- Linear second order ordinary differential equations
- Laplace transforms
- Frobenius method
- Legendre and Bessel Functions

- Bisection, Secant method
- Newton-Raphson method
- Interpolation
- Lagrange, Newton interpolations
- Numerical differentiation
- Numerical integration
- Trapezoidal and Simpson rules
- Gauss elimination, LU decomposition
- Jacobiand Gauss-Seidel
- Ordinary Differential Equations
- Euler’s method
- Runge-Kutta methods of order 2

- Sequences and series of functions
- Fourier series
- Maxima, Minima
- Riemann Integration
- Surface and Volume Integrals
- Theorems of Green, Stokes and Gauss
- Weierstrass approximation theorem
- Lebesgue measure
- Lebesgue integral
- Fatou’s lemma
- Dominated Convergence Theorem

- Linear and quasilinear first order partial differential equations
- Second Order Linear Equations
- Cauchy, Dirichlet and Neumann problems
- Solutions of Laplace
- Interior and exterior Dirichlet problems
- Fourier Series and Fourier Transform and Laplace transform

- Numerical computation
- Numerical Estimation
- Numerical Reasoning
- Data Interpretation

- English grammar
- Sentence Completion
- Verbal Analogies
- Word Groups
- Instructions
- Critical Reasoning
- Verbal Deduction

- Normed linear spaces, Banach spaces
- Hahn-Banach extension theorem
- Inner-product spaces
- Hilbert spaces
- Riesz representation theorem

- Definitions of probability and sampling theorems
- Discrete Random variables
- Continuous random variables
- Descriptive statistics
- Hypothesis testing

- Basic concepts of topology
- Subspace topology, Order topology
- Urysohn’s Lemma

#### How to prepare

**Preparation Strategy**

**Make a proper Time Table**

It is very important that you make a timetable and stick to it and you will have an exact idea of what you are required to study and the time required for it.

**Concept clarity rather than routes learning**

It is essential that you have a clear idea of the formulas and concepts rather than rote learning of things for the papers. While you might require it for memorizing formulas it is important that for other stuff you make sure you clear your basics and concepts before moving on.

**Prepare Notes**

It is very important to make small notes or a comprehensive list of formulas on each covered topic and chapter which will come in handy at the time of revision. This will require you to be regular with your work but will surely make things easy at the time of revision.

**Seek guidance**

It is not possible for you to know everything in your syllabus, at least not at the time of preparation. Sooner or later you will run into a concept or so which will give you trouble and then it is best you seek guidance from an instructor or a teacher. It is necessary that you clear your doubts at regular intervals and don’t prolong things for long. Getting into a good coaching class is nothing to be ashamed off and if anything a regular coaching class will enable you to avoid roadblocks in your preparation.

**Sample Papers**

Even though there may be a complete change in the exam pattern or the expected questions altogether,it is important that you practice on the sample and previous years question papers of Science exams. You will know the existing pattern and have a fair idea of the type of questions to expect in the paper along with the time constraint.

**Mock tests**

The paper pattern, duration of the paper and the number of questions to be attempted in the given amount of time is not something you will be able to pick up on the day of the examination. A Mock Test tests a student’s abilities as it not only provides a similar feel of real exams but also helps in building speed and confident to face the exam. Furthermore, they can improve their performance to get an extra edge in actual exams.

**Time management**

Time management can be learned through thorough practice and regular test taking. So it is important that you practice it and practice it well.

**Negative marking**

Most the entrance examinations will have negative marking and everyone would suggest you stay clear of questions are not sure about. But some experts are of the opinion that you answer the questions in which you are confused between an option or two because there will also be a chance of getting it right.

**Duration :**105 Minutes

#### Important Instructions

All fees are payable in single installment at the time of admission on or before the notified date. Dollars in the form of currency note/ cheque are not acceptable. Security Deposit shall be deposited in cash with the Cashier in the Accounts Office, JMI.