# GATE Mathematics (MA)

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#### GATE Mathematics (MA) Online Study Material

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#### GATE Mathematics (MA) Online Test Series

Check Scholarship Coupon Details and Course Duration before purchase. Best GATE Mathematics Engg Test Series in India. 75 Mathematics, 50 Aptitude Tests. 5 Mocks held in Dec and Jan.

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Each of us requires a different kind of study program based upon our style/preference of studying. Normally, all students take our study material and test series. Many also take video lectures as it helps them clear concepts. A lot depends upon time available to prepare, current stage of preparation, etc. If you are still unsure, please contact us.

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Typically 5-6 months are required, but some students need a longer time frame based on other commitments. College students start preparation 12-18 months before GATE to have more time to practise questions as they may have semester exams as well.

We suggest about 800 to 1200 hours of preparation time overall. This can be divided into 3-4 months or 12-18 months, based on your schedule.

A Good Score For GATE Mathematics (MA) is considered to be: 50

**Steps And Strategy To Prepare For GATE Mathematics (MA) Exam**

- Take a diagnostic test โ best diagnostic test is a GATE paper of any of the previous 3 years.
- Note down what you have scored and what was the actual GATE qualifying score cut-off. Note that qualification does not help you much. What you need is a good score. So note the good score mentioned above and measure the gap between your score and a good score.
- Note the GATE syllabus and mark your topics that you are good at. First try to master subjects that you are good at.
- However, some subjects like Probability and Statistics, Partial Differential Equations and Numerical Analysis have a high weightage. So you should definitely prepare these.
- General Aptitude does not require preparation. It requires practice. So just practice solving Aptitude questions every day for 30 minutes.
- Take lots of section tests and Mocks. Career Avenues provides an excellent test series for GATE Mathematics (MA).ย
- In case you require focused GATE study material and books, you should take Career Avenues GATE Mathematics (MA) study material which has been made by IIT alumni and is focused towards GATE.

- Being a GATE aspirant, it is very important that you first know what is the syllabus for GATE Mathematics (MA) Examination before you start preparation.
- Keep handy the updated copy of GATE Mathematics (MA) Examination syllabus.
- Go through the complete and updated syllabus, highlight important subjects and topics based on Past GATE Mathematics (MA) Papers and Weightage plus your understanding of particular subject or topic.
- Keep tracking and prioritising your preparation-to-do list and the syllabus for the GATE Mathematics (MA) examination.

**Section I: Linear Algebra**

**Topics:**

Finite dimensional vector spaces; Linear transformations and their matrix representations, rank; systems of linear equations, eigenvalues and eigenvectors, minimal polynomial, Cayley-Hamilton Theorem, diagonalization, Jordan-canonical form, Hermitian, Skew-Hermitian and unitary matrices; Finite dimensional inner product spaces, Gram-Schmidt orthonormalization process, self-adjoint operators, definite forms.

**Section II: Complex Analysis**

**Topics:**

Analytic functions, conformal mappings, bilinear transformations; complex integration: Cauchys integral theorem and formula; Liouvilles theorem, maximum modulus principle; Zeros and singularities; Taylor and Laurents series; residue theorem and applications for evaluating real integrals.

**Section III: Real Analysis**

**Topics:**

Sequences and series of functions, uniform convergence, power series, Fourier series, functions of several variables, maxima, minima; Riemann integration, multiple integrals, line, surface and volume integrals, theorems of Green, Stokes and Gauss; metric spaces, compactness, completeness, Weierstrass approximation theorem; Lebesgue measure, measurable functions; Lebesgue integral, Fatous lemma, dominated convergence theorem

**Section IV: Ordinary Differential Equations**

**Topics:**

First order ordinary differential equations, existence and uniqueness theorems for initial value problems, systems of linear first order ordinary differential equations, linear ordinary differential equations of higher order with constant coefficients; linear second order ordinary differential equations with variable coefficients; method of Laplace transforms for solving ordinary differential equations, series solutions (power series, Frobenius method); Legendre and Bessel functions and their orthogonal properties.

**Section V: Algebra**

**Topics:**

Groups, subgroups, normal subgroups, quotient groups and homomorphism theorems, automorphisms; cyclic groups and permutation groups, Sylows theorems and their applications; Rings, ideals, prime and maximal ideals, quotient rings, unique factorization domains, Principle ideal domains, Euclidean domains, polynomial rings and irreducibility criteria; Fields, finite fields, field extensions.

**Section VI: Functional Analysis**

**Topics:**

Normed linear spaces, Banach spaces, Hahn-Banach extension theorem, open mapping and closed graph theorems, principle of uniform boundedness; Inner-product spaces, Hilbert spaces, orthonormal bases, Riesz representation theorem, bounded linear operators.

**Section VII: Numerical Analysis**

**Topics:**

Numerical solution of algebraic and transcendental equations: bisection, secant method, Newton-Raphson method, fixed point iteration; interpolation: error of polynomial interpolation, Lagrange, Newton interpolations; numerical differentiation; numerical integration: Trapezoidal and Simpson rules; numerical solution of systems of linear equations: direct methods (Gauss elimination, LU decomposition); iterative methods (Jacobi and Gauss-Seidel); numerical solution of ordinary differential equations: initial value problems: Eulers method, Runge-Kutta methods of order 2.

**Section VIII: Partial Differential Equations**

**Topics:**

Linear and quasilinear first order partial differential equations, method of characteristics; second order linear equations in two variables and their classification; Cauchy, Dirichlet and Neumann problems; solutions of Laplace, wave in two dimensional Cartesian coordinates, Interior and exterior Dirichlet problems in polar coordinates; Separation of variables method for solving wave and diffusion equations in one space variable; Fourier series and Fourier transform and Laplace transform methods of solutions for the above equations.

**Section IX: Topology**

**Topics:**

Basic concepts of topology, bases, subbases, subspace topology, order topology, product topology, connectedness, compactness, countability and separation axioms, Urysohns Lemma.

**Section X: Probability and Statistics**

**Topics:**

Probability space, conditional probability, Bayes theorem, independence, Random variables, joint and conditional distributions, standard probability distributions and their properties (Discrete uniform, Binomial, Poisson, Geometric, Negative binomial, Normal, Exponential, Gamma, Continuous uniform, Bivariate normal, Multinomial), expectation, conditional expectation, moments; Weak and strong law of large numbers, central limit theorem; Sampling distributions, UMVU estimators, maximum likelihood estimators; Interval estimation; Testing of hypotheses, standard parametric tests based on normal, X^2, t, F distributions; Simple linear regression.

**Section XI: Linear programming**

**Topics:**

Linear programming problem and its formulation, convex sets and their properties, graphical method, basic feasible solution, simplex method, big-M and two phase methods; infeasible and unbounded LPPs, alternate optima; Dual problem and duality theorems, dual simplex method and its application in post optimality analysis; Balanced and unbalanced transportation problems, Vogels approximation method for solving transportation problems; Hungarian method for solving assignment problems.

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Here are some recommended books for GATE Mathematics (MA) preparation:

**Linear Algebra:**- “Linear Algebra” by Seymour Lipschutz, Marc Lipson
- “Linear Algebra and Its Applications” by Gilbert Strang

**Complex Analysis:**- “Complex Analysis” by Gamelin
- “Complex Analysis for Mathematics and Engineering” by J. H. Mathews

**Real Analysis:**- “Real Analysis” by Royden H.L., Fitzpatrick P. M
- “Introduction to Real Analysis” by Donald R. Sherbert, Robert G. Bartle

**Ordinary Differential Equations:**- “Ordinary and Partial Differential Equations” by M. D. Raisinghania
- “Elements of Partial Differential Equations” by Ian N. Sneddon

**Algebra:**- “Topics in Algebra” by I. N. Herstein
- “Linear Algebra” by Ian N. Sneddon, Seymour Lipschutz, Marc Lipson

**Functional Analysis:**- “Functional Analysis” by Rudin
- “Introductory Functional Analysis with Applications” by Erwin Kreyszig

**Numerical Analysis:**- “Numerical Analysis” by Francis Scheid
- “Introductory Methods of Numerical Analysis” by S. S. Sastry

**Mechanics:**- “Classical Mechanics” by Herbert Goldstein, John Safko, Charles P. Poole
- “Engineering Mechanics” by S S Bhavikatti

**Topology:**- “Topology” by James R. Munkres
- “Introduction to Topology and Modern Analysis” by S S Bhavikatti

**Probability and Statistics:**- “Probability and Statistics” by John J. Schiller
- “Introduction to Probability and Statistics for Engineers and Scientists” by Sheldon M. Ross

*Please note that while these books are recommended, you can also consider using focused GATE Mathematics (MA) study material that covers all the concepts and practice questions specifically tailored for the exam.*