IIT/IISc will conduct The GATE 2020 through the online mode. It will be a Computer Based Test. the exam duration for the candidates will be 3 hours. The types of questions in the exam will be – Multiple choice questions 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 Multiple choice questions.

## GATE 2020 Mathematics: Exam Pattern

Table of Contents

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 2020. 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.

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### Marking: Subject base

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

GA | 5 questions of 1 mark each 5 questions of 2 marks each |
15 marks | Multiple-choice questions |

MA- Subject-based | 25 questions of 1 mark each 30 questions 2marks each |
85 marks | Multiple-choice questions and Numerical answer types |

### Obedient Marking**: **Question base

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

Multiple-choice questions | ⅓ for 1mark questions ⅔ for 2marks questions | 1 or 2 marks |

Numerical Answer type | No negative marking | 1 or 2 marks |

## How to learn for GATE 2020 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.

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### Know about the exam:

Candidates should know about the exam. Start with the exam pattern of GATE 2020. 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 2020 preparation. Also, keep time for leisure activities so that the schedule doesn’t get hectic.

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### 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 2020 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 2020 Syllabus: Mathematics

The syllabus of Mathematics subject in GATE 2020 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.

The syllabus for Mathematics in GATE 2020 is accessible to the candidates on this page. Note that the syllabus for all the 25 papers in GATE 2020 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 2020. As for GATE, candidates can check it below.

### Calculus:

Finite, countable and uncountable sets, Real number system as a complete ordered field, Archimedean property; Sequences and series, convergence; Limits, continuity, uniform continuity, differentiability, mean value theorems;

Riemann integration, Improper integrals; Functions of two or three 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; 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, eigenvalues, and eigenvectors, minimal polynomial, Cayley-Hamilton Theorem, diagonalization, Jordan canonical form, symmetric skew-symmetric, Hermitian, skew-Hermitian, orthogonal and unitary matrices;

Finite-dimensional inner product spaces, Gram-Schmidt orthonormalization process, definite forms.

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### Real Analysis:

Metric spaces, connectedness, compactness, completeness; Sequences and series of functions, uniform convergence; Weierstrass approximation theorem; Power series; Functions of several variables:

Differentiation, contraction mapping principle, Inverse, and Implicit function theorems; Lebesgue measure, measurable functions; Lebesgue integral, Fatou’s lemma, monotone convergence theorem, dominated convergence theorem.

### Complex Analysis:

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, the radius of convergence, Taylor’s theorem and Laurent’s theorem;

residue theorem and applications for evaluating real integrals; Rouche’s theorem, Argument principle, Schwarz lemma; conformal mappings, bilinear 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.

### Algebra:

Groups, subgroups, normal subgroups, quotient groups, homomorphisms, automorphisms; cyclic groups, permutation groups, Sylow’s 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.

### Functional Analysis:

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

### Numerical Analysis:

Numerical solutions of algebraic and transcendental equations: bisection, secant method, Newton-Raphson method, fixed-point iteration; Interpolation: error of polynomial interpolation, Lagrange and Newton interpolations; Numerical differentiation; Numerical integration:

Trapezoidal and Simpson’s rules; Numerical solution of a system of linear equations: direct methods (Gauss elimination, LU decomposition), iterative methods (Jacobi and Gauss-Seidel); Numerical solution of initial value problems of ODEs: Euler’s method, Runge-Kutta methods of order 2.

### Partial Differential Equations:

Linear and quasi-linear 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 and wave equations 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 equations mentioned above.

### Topology:

Basic concepts of topology, bases, subbases, subspace

topology, order topology, product topology, metric topology, connectedness,

compactness, countability and separation axioms, Urysohn’s Lemma.

### Linear Programming:

Linear programming problem and its formulation, convex sets and their properties, graphical method, basic feasible solution, simplex method, two-phase methods; infeasible and unbounded LPP’s, alternate optima; Dual problem and duality theorems; Balanced and unbalanced transportation problems, Vogel’s approximation method for solving transportation problems; Hungarian method for solving assignment problems.

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