**GATE 2021 Mathematics Syllabus: **The syllabus for Mathematics in GATE 2021 is accessible to the candidates on this page. Note that the syllabus for all the papers in GATE 2021 will be different. In the exam, there will be a total of 65 questions. Out of these total questions, 55 questions will be based on Mathematics and the remaining questions will be based on the General Aptitude section. The syllabus for all the papers is available on the official website of GATE 2021. As for GATE, candidates can check it below.

## GATE 2021 Mathematics Syllabus

The syllabus of Mathematics subject in GATE 2021 consists of various topics. These topics are Calculus, Linear Algebra, Real Analysis, Ordinary Differential Equations, Algebra, Functional Analysis, Numerical Analysis, Partial Differential Equations, Topology, and Linear Programming. Under these topics are subtopics.

**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, a 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, homomorphism, 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, accountability 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.

### GATE 2021 General Aptitude Syllabus

Candidates must note that the General Aptitude section is common in all the papers of GATE 2021. The syllabus for this section also remains the same in all the GATE subjects. The section is divided into Verbal Ability and Numerical Ability. There will be a total of 10 questions in this section. 5 out of 10 questions will carry 1-mark each and the other 5 questions will carry-marks each. Candidates can check the syllabus for GA below.

**Verbal Ability- **In VA, there will be topics like English grammar, Sentence completion, Instructions, Verbal analogies, Word groups, Critical Reasoning, and Verbal deduction. **Numerical Ability- **In NA, there will be topics like** **Numerical computation, Numerical reasoning, Numerical estimation, and Data interpretation.

### GATE 2021 Mathematics Mock Test

Before you begin your practice, keep in mind that you must solve mock tests throughout your preparation. Mathematics is a quantitative exam. You need a lot of practice to score in this exam which is possible through solving the mock tests.

### GATE 2021 Mathematics Exam Pattern

The exam pattern and the marking scheme should be carefully analyzed by the candidates. This will help them in getting a better understanding of GATE 2021. Candidates must be aware of the information related to the exam such as types of questions that will be asked in the exam, how will be the marking done in the exam, what will be the exam duration, etc.

Section | Distribution of Marks | Total Marks | Types of questions |

GA | 5 questions of 1 mark each 5 questions of 2 marks each | 15 marks | MCQs |

MA- Subject-Based | 25 questions of 1 mark each 30 questions of 2 marks each | 85 marks | MCQs and NATs |

The GATE 2021 will be conducted through the online mode. It will be a Computer Based Test (CBT). the exam duration for the candidates will be 3 hours. The types of questions in the exam will be – MCQs and NATs. There will be 2 sections in GATE, General Aptitude and Mathematics. The total number of questions in the exam will be 65 and the total marks in the exam will be 100. There will be negative marking in the exam but only for MCQs.

**Marking scheme**

Type of question | Negative marking for wrong answer | Marking for correct answer |

MCQs | ⅓ for 1 mark questions⅔ for 2 marks questions | 1 or 2 marks |

NATs | No negative marking | 1 or 2 marks |

### How to Prepare for GATE 2021 Mathematics?

Preparation for Mathematics looks difficult, especially if the subject isn’t exactly your favorite one. But one good thing about mathematics is that you know that the only way to secure marks is extensive practice. There is no shortcut or any other source that will help you ace this exam, but only practice and more practice. This solves our biggest dilemma of creating an exam strategy. You know your only strategy is practicing. Besides this, there are a few tips that will help you in preparing better.

**Know the exam**

Candidates should know the exam. Start with the exam pattern of GATE 2021. We have already discussed that above. Don’t forget to go through the marking scheme of the exam. This will help you in preparing accordingly. Next, you must know the syllabus as it is the most important part of the exam. You should be aware of what you will have to prepare for the exam. Get yourself familiar with each and every topic and go through them carefully.

**Study Plan**

Irrespective of you having discipline issues or not, you must create a study plan. It is an important step towards successfully securing good marks. A single study plan will not be enough. You should make a daily study plan, weekly study plan and lastly, monthly study plans.

Allot at least 6-8 hours every day for your GATE 2021 preparation. Also, keep time for leisure activities so that the schedule doesn’t get hectic.

**Practice papers**

Mathematics is one such subject that requires extensive practice without any doubt. We have already discussed above how important practice is. It is the only mantra that will help you score in this exam. What you should practice though is the big question. We all know about preparing the standard topics through standard books. But candidates must try other sources of preparation. The most common is the mock tests and previous years’ question papers. Solve as many question papers as you can. This will help you prepare better and from a variety of questions and exam papers. You can also join online test series. They are really effective in preparing you for time management.

**Revision**

The last step of your GATE 2021 preparation is your revision. Revision must be done in a couple of ways. First, make a habit of revising every day. This way you’ll memorize better. The last month is kept solely for revision. You must revise the entire syllabus in small parts. Take the help of your notes that you made during your preparation. They will come in handy now. The last month’s revision is crucial. It helps you in remembering all the topics and if in case you have missed or forgotten something, then you can prepare it while there is still time.

### GATE 2021 Mathematics Books for Preparation

Candidates must be careful while selecting their study material for the preparation of GATE 2021. Your study material should be only from the best authors and publications.

Title of the book | Name of the Author/ Publication | Link to buy |

1. Engineering Mathematics for GATE 2021 & ESE 2021, Theory and Solved Papers | ME Editorial Board | LINK |

2. Chapterwise Solved Papers Mathematics GATE 2021 | Suraj Singh | LINK |

3. GATE 2021: Engineering Mathematics | Umesh Dande | LINK |

4. GATE General Aptitude & Engineering Mathematics | GATE 2021 | by Pearson | Pearson | LINK |

### GATE 2021 Preparation FAQs

**Q1. What type of questions will be asked in the Mathematics section in GATE 2021?****Ans.** There will be two types of questions in the Mathematics section – Multiple Choice Questions (MCQs) and Numerical Answer Type (NATs).

**Q2. What should I practice more – mock tests or previous year papers?****Ans. **You should practice both of them. Practice as many mock tests as you can. Solve at least the last 10 years’ question papers.

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