GATE Mathematics Previous Year Papers pdf download | Mathscare

GATE Mathematics Previous Year Question Papers: With the GATE Exam around the corner, you need to practice the GATE Previous Year Question Paper. GATE exam follows a pattern, and if you want to take over control, you must refer to the questions that have already appeared in the Test. So, after finishing the syllabus, start solving GATE question papers.

Here you can get the latest GATE Mathematics Previous Year Question Papers.

 

GATE Mathematics Previous Year Papers
GATE Mathematics Paper	Question Paper PDF	Answers Key PDF
GATE Mathematics 2022	Download Now	Download Now
GATE Mathematics 2021	Download Now	Download Now
GATE Mathematics 2020	Download Now	Download Now
GATE Mathematics 2019	Download Now	Download Now
GATE Mathematics 2018	Download Now	Download Now
GATE Mathematics 2017	Download Now	Download Now
GATE Mathematics 2016	Download Now	Download Now
GATE Mathematics 2015	Download Now	Download Now
GATE Mathematics 2014	Download Now	Download Now
GATE Mathematics 2013	Download Now	Download Now
GATE Mathematics 2012	Download Now	Download Now
GATE Mathematics 2011	Download Now	Download Now
GATE Mathematics 2010	Download Now	–

MUST WATCH – 

GATE 2023 Mathematics Syllabus

Syllabus for GATE exam

There are 11 chapters in the GATE Mathematics Syllabus. Each chapter has many subtopics. The complete syllabus of Mathematics paper is given below.

Section 1: 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.

Section 2: 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.

Complete playlist – click here

Section 3: 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.

Complete playlist – click here

Section 4: 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.

Complete playlist – click here

Section 5: 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.

Complete playlist – click here

Section 6: 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
• Principal ideal domains, Euclidean domains, polynomial rings, Eisenstein’s irreducibility criterion; Fields, finite fields, field extensions,algebraic extensions, algebraically closed fields.

Complete playlist – click here

Section 7: 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.

Section 8: 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.

Complete playlist – click here

Section 9: 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.

Complete playlist – click here

Section 10: 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.

Complete playlist – click here

Section 11: 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

Complete playlist – click here

 

Study Plan for GATE Mathematics

• The syllabus should be completely understood
• Examine Question Papers from Previous Years
• Understanding the exam pattern
• The Note’s Compilation
• Recognize your advantages and disadvantages
• Making a Proper Study Plan

Thank you for reading, to gain more information about GATE 2023 and learn mathematics and general aptitude from Dr. Gajendra Purohit Sir visit – https://www.youtube.com/c/DrGajendraPurohitMathematics

And for university courses, blogs, quizzes and ask doubts from sir visit – https://www.mathscare.com/