GATE Mathematics Syllabus 2023 (Released) - Check here
GATE Mathematics Syllabus 2023 - IIT Kanpur has released the GATE 2023 Mathematics syllabus at gate.iitk.ac.in. The Mathematics syllabus of GATE 2023 is available in the official notification. The GATE 2023 Mathematics syllabus includes the topics from which questions will be asked in the Graduate Aptitude Test in Engineering.
Latest Updates for GATE
- 5 days ago:
GATE 2023 Result declared on March 16.
- 6 days ago:
GATE 2023 Result will be declared on March 16 after 4:00 pm in the candidate application portal.
- 22 Feb 2023:
GATE 2023 answer key released by IIT Kanpur on February 21.
Stay up-to date with GATE News
Students can also check here the GATE Mathematics syllabus for the previous year here. The GATE Mathematics syllabus 2023 has been updated on this page as per the GATE syllabus. Along with the GATE syllabus for Mathematics 2023, students can also check the previous year’s Maths GATE question papers for better preparation. GATE 2023 exam date is February 4, 5 11 & 12. Read the complete article to know more about the GATE Mathematics syllabus 2023.
GATE 2023 Mathematics Syllabus
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.
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.
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
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; CauchyEuler 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.
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
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
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.
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 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.
Previous Year GATE Mathematics Question Paper
Candidates can below check the GATE Maths paper for previous years. Using the GATE question papers, candidates can get an idea of the topics that have high weightage in the entrance exam.
Previous Year GATE Maths Question Paper
Maths question paper
Frequently Asked Question (FAQs) - GATE Mathematics Syllabus 2023 (Released) - Check here
Question: Is calculus included in the GATE Mathematics syllabus?
Yes, Calculus is one of the topics included in the GATE syllabus for Mathematics.
Question: Can I download the GATE Maths syllabus in pdf format?
Yes, the GATE Maths syllabus 2023 is available in pdf format.
Question: When will the authorities release GATE 2023 syllabus Mathematics?
The GATE Mathematics syllabus 2023 has been released along with the official brochure.
GATE 2023 - Dates, Result & Scorecard (Out), Cutoff, Merit Lis...
GATE 2023 exam - IIT Kanpur has declared the GATE result 2023 ...
GATE Score Card 2023 (Out) - Direct Link, Download Scorecard a...
GATE Score Card 2023 - IIT Kanpur has released the score card ...
MP M.Tech Admission 2023: Dates, Application Form, Fees, Eligi...
MP M.Tech Admission 2023 - Directorate of Technical Education ...
Sastra M.Tech Admission 2023: Dates, Application Form, Eligibi...
Shastra M.Tech Admission 2023 – Sastra Deemed to be University...
GATE 2023 Topper Interview - Mayukh Banerjee, AIR 7 in Sociology
Team careers360 conducted GATE 2023 Topper Interview - Mayukh ...
Questions related to GATE
Which branch is best for GATE?
The best field is Computer Science and Engineering (CSE). However, the best branch of engineering in GATE is the one that you believe is the best for you.
Is GATE difficult?
The second question that is likely to be asked is, "How difficult is GATE?"As previously said, while many students assume GATE is a tough exam, it is not. Many students have scored on the exams throughout the decades. Students that work hard will be able to successfully complete the GATE exam. Furthermore, a GATE aspirant can take the GATE test as many times as they desire, and there is no age limit to take the examinations, which might be advantageous to applicants. GATE hopefuls should also tackle questions they are confident in and avoid giving incorrect responses, which may result in a negative grade. The greater the candidate's GATE score, the more right answers they can provide. Avoiding negative marking ensures that the candidate's grades are not diminished. As a result, we can readily infer that the answer to the question "Is GATE Tough?" is that GATE exams, while frequently regarded as difficult, are not insurmountable. It is feasible to do well in these tests. And, depending on the exam preparations, "how difficult is GATE?" can also be answered.
What is the maximum number of attempts in GATE?
Exam scores are normally valid for three years from the day the results are released. As a result, if a candidate performs well in the test, they should avoid taking the GATE for the next three years. Aside from that, let us check how many GATE exam tries a candidate may get. There is no restriction on the number of GATE exam attempts. How many GATE attempts a candidate can make is entirely up to him or her. While some PSUs may say that the age limit is 28 or 30, the number of GATE exam tries for admission to research and post-graduate seats is totally dependent on the institution. Even though a score is only valid for three years after it is released, there is no age limit or limit on the number of attempts for GATE tests. A candidate may take the GATE examinations an unlimited number of times.
What is the difference between GATE and JEE?
The Graduate Aptitude Test in Engineering (GATE) is the entrance exam for postgraduate studies at prestigious institutes like the IITs, IISc, and NIT. The Joint Entrance Examination (JEE), on the other hand, is the entry point to graduation. Both tests serve various goals.
Who is eligible for the GATE exam?
A candidate who has finished any government-approved degree program in engineering, technology, architecture, science, commerce, or the arts is qualified to take the GATE test. Candidates who have certification from any of the professional societies, however, must ensure that the examinations administered by the societies are recognized by the MoE/AICTE/UGC/UPSC as equal to B.E., B.Tech., B.Arch., B.Planning, etc. Candidates who have achieved or are pursuing their qualifying degree outside of India must be in their third or higher year of study or have obtained a bachelor's degree (duration: at least three years) in engineering, science, the arts, or commerce.