GATE Mathematics Preparation Tips 2022 | Exclusive Tips To Score AIR 1

GATE Mathematics Preparation Tips: Engineering Mathematics, as a subject, is very much relevant to the GATE exam as the weight-age given to this subject has been consistent over the years in comparison to other subjects. Every year you can find the weight-age of this subject to be 8 to 10 marks. So the key to prepare for such subjects is to keep short notes handy with you or maybe you can have a sort of Formula Sheet so that you can look up to a concept whenever you need it.

Get complete guide on GATE Mathematics Preparation Tips

Table of Contents

Tips and tricks To Get AIR 1 in GATE Mathematics

Get Exclusive GATE Mathematics Preparation Tips :-

Do not panic under any circumstances.
Always Have a Correct Study Plan Ready
Focus On Getting The Basics Right First
Instead of rushing through the whole curriculum and burning yourself out, focus on the important and scoring areas first.
Complete as many exercises and tests as possible.
Practice at least 2030 questions on each topic you prepare so that you can perfect it.
Select which topics to start with first.
Repeat each topic you study so that you remember it, and repeat until you have mastered it.
Try to write down all important concepts and formulas separately.
Spend at least 12 hours doing math alone as part of your preparation.
Take short study times and challenge yourself with some daily goals and try to achieve them.
Be confident and stay engaged and focused on your goal because motivation is the most important thing that continues to inspire you to be committed to your goal.

Gate Mathematics By Dr N K Singh

GATE Mathematics Preparation Tips: Topic wise GATE Mathematics Syllabus

TOPICS	SUB-TOPICS/CONCEPTS
Calculus	Functions of two or more variables, continuity, directional derivatives, partial derivatives, total derivative, maxima and minima, saddle point, method of Lagrange’s multipliers; Double and Triple integrals and their applications to area, volume and surface area; Vector Calculus: gradient, divergence and curl, Line integrals and Surface integrals, Green’s theorem, Stokes’ theorem, and Gauss divergence theorem.
Linear Algebra	Finite dimensional vector spaces over real or complex fields; Linear transformations and their matrix representations, rank and nullity; systems of linear equations, characteristic polynomial, eigenvalues and eigenvectors, diagonalization, minimal polynomial, Cayley-Hamilton Theorem, Finite dimensional inner product spaces, Gram-Schmidt orthonormalization process, symmetric, skew-symmetric, Hermitian, skew-Hermitian, normal, orthogonal and unitary matrices; diagonalization by a unitary matrix, Jordan canonical form; bilinear and quadratic forms.
Real Analysis	Metric spaces, connectedness, compactness, completeness; Sequences and series of functions, uniform convergence, Ascoli-Arzela theorem;Weierstrass approximation theorem; contraction mapping principle, Power series; Differentiation of functions of several variables, Inverse and Implicit function theorems; Lebesgue measure on the real line, measurable functions; Lebesgue integral, Fatou’s lemma, monotone convergence theorem, dominated convergence theorem.
Complex Analysis	Functions of a complex variable: continuity, differentiability, analytic functions, harmonic functions; Complex integration: Cauchy’s integral theorem and formula; Liouville’s theorem, maximum modulus principle, Morera’s theorem; zeros and singularities; Power series, radius of convergence, Taylor’s series and Laurent’s series; Residue theorem and applications for evaluating real integrals; Rouche’s theorem, Argument principle, Schwarz lemma; Conformal mappings, Mobius transformations.
Ordinary Differential Equations	First order ordinary differential equations, existence and uniqueness theorems for initial value problems, linear ordinary differential equations of higher order with constant coefficients; Second order linear ordinary differential equations with variable coefficients; Cauchy-Euler equation, method of Laplace transforms for solving ordinary differential equations, series solutions (power series, Frobenius method); Legendre and Bessel functions and their orthogonal properties; Systems of linear first order ordinary differential equations, Sturm’s oscillation and separation theorems, Sturm-Liouville eigenvalue problems, Planar autonomous systems of ordinary differential equations: Stability of stationary points for linear systems with constant coefficients, Linearized stability, Lyapunov functions.
Algebra	Groups, subgroups, normal subgroups, quotient groups, homomorphisms, automorphisms; cyclic groups, permutation groups,Group action,Sylow’s theorems and their applications; Rings, ideals, prime and maximal ideals, quotient rings, unique factorization domains, Principle ideal domains, Euclidean domains, polynomial rings, Eisenstein’s irreducibility criterion; Fields, finite fields, field extensions,algebraic extensions, algebraically closed fields.
Functional Analysis	Normed linear spaces, Banach spaces, Hahn-Banach theorem, open mapping and closed graph theorems, principle of uniform boundedness; Inner-product spaces, Hilbert spaces, orthonormal bases, projection theorem,Riesz representation theorem, spectral theorem for compact self-adjoint operators.
Numerical Analysis	Systems of linear equations: Direct methods (Gaussian elimination, LU decomposition, Cholesky factorization), Iterative methods (Gauss-Seidel and Jacobi) and their convergence for diagonally dominant coefficient matrices; Numerical solutions of nonlinear equations: bisection method, secant method, Newton-Raphson method, fixed point iteration; Interpolation: Lagrange and Newton forms of interpolating polynomial, Error in polynomial interpolation of a function; Numerical differentiation and error, Numerical integration: Trapezoidal and Simpson rules, Newton-Cotes integration formulas, composite rules, Mathematical errors involved in numerical integration formulae; Numerical solution of initial value problems for ordinary differential equations: Methods of Euler, Runge-Kutta method of order 2.
Partial Differential Equations	Method of characteristics for first order linear and quasilinear partial differential equations; Second order partial differential equations in two independent variables: classification and canonical forms, method of separation of variables for Laplace equation in Cartesian and polar coordinates, heat and wave equations in one space variable; Wave equation: Cauchy problem and d’Alembert formula, domains of dependence and influence, non-homogeneous wave equation; Heat equation: Cauchy problem; Laplace and Fourier transform methods.
Topology	Basic concepts of topology, bases, subbases, subspace topology, order topology, product topology, quotient topology, metric topology, connectedness, compactness, countability and separation axioms, Urysohn’s Lemma.
Linear Programming	Linear programming models, convex sets, extreme points;Basic feasible solution,graphical method, simplex method, two phase methods, revised simplex method ; Infeasible and unbounded linear programming models, alternate optima; Duality theory, weak duality and strong duality; Balanced and unbalanced transportation problems, Initial basic feasible solution of balanced transportation problems (least cost method, north-west corner rule, Vogel’s approximation method); Optimal solution, modified distribution method; Solving assignment problems, Hungarian method.

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FAQ: GATE Mathematics Preparation Tips

Can I skip maths in GATE?

It’s not advisable to skip any subject as Mathematics alone comprises 15-17 marks each year no matter which stream you prepare for.

Can we crack GATE without maths?

Yes, you can crack GATE without maths also.

Are 6 months enough to crack GATE?

It is advised to start preparing early, preferably in the pre-final year of the course so that students have ample time to cover the entire GATE syllabus.

What is the GATE cut-off score?

GATE cutoff is the minimum marks that test-takers need to score to be eligible for admission to MTech, MSc, and Ph.D. courses offered at the participating institutes.

What are GATE Mathematics Preparation Tips?

You can refer to the above article to know about GATE Mathematics Preparation Tips.

How to score AIR 1 in GATE?

You can refer to the above article to know GATE Mathematics Preparation Tips.