Exams Prep Master | Updated On - Jan 6, 2021

GATE 2021 Mathematics Syllabus is based on the topics studied at the graduation level. The question asked in paper will be based on formulas, equations, and graphs**. **Major topics that will be covered include Calculus, Linear Algebra, Real Analysis, Algebra, Functional Analysis, Numerical Analysis, etc.

**GATE 2021**will have 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**.**Check GATE 2021 Exam Pattern**- Candidates can sit for a maximum of two papers from the predefined list of combination of papers.
**If you have opted for MA as your first paper then you can select second paper from CS/ PH/ ST.**

GATE is conducted online and candidates need to solve the paper within 3 hours duration. **After qualifying GATE 2021 candidates will be able to get admission in M.Tech courses offered at IITs, NITs, etc. **Other than admission in M.tech courses candidates can also apply for various posts offered by PSUs. Read the article to know more about the syllabus, marking scheme, preparation tips, and much more.

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## GATE 2021 Syllabus of Mathematics

## GATE 2021 Mathematics Syllabus

There are 11 chapters in 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.

### 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.

### 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.

### 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.

### 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
- Principle ideal domains, Euclidean domains, polynomial rings, Eisenstein’s irreducibility criterion; Fields, finite fields, field extensions,algebraic extensions, algebraically closed fields.

### 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.

### 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.

### 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.

### 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.

**Direct link to download GATE Mathematics (MA) Syllabus PDF **

## Weighatge of Important Topics

## Important Topics in GATE 2021 Mathematics Paper

**Sample Question 1:**

**Sample Question 2:**

### Weightage of Important Topics

Important Topics | Weightage of Topics (In %) |
---|---|

Linear Algebra | 10% |

Complex Variables | 10% |

Vector Calculus | 20% |

Calculus | 10% |

Differential Equation | 10% |

Probability & Statistics | 20% |

Numerical Methods | 20% |

## GATE 2021 Exam Pattern of MA

## GATE 2021 Exam Pattern of Mathematics

Every candidate can apply for one stream among all the 25 papers. GATE exam is conducted in online mode (Computer-based). The total weightage of the GATE Exam is 100 marks. **GATE 2021 Exam Pattern** is quite tricky as it varies for different disciplines.

Mode of Examination | Online/ Computer-based Test |

Total no. of questions | 65 |

Question Type | 2 types- Multiple Choice type (MCQ) and Numerical Answer Type (NAT). |

Maximum Marks | 100 |

Duration of Exam | 3 hours |

Sections in paper | Two, i.e. General Aptitude and Subject Specific |

**Note: **There is also Negative marking for every wrong answer. But is no negative marking for **NAT** but it is applicable for **MCQs**. For 1 mark MCQs, 1/3 marks will be deducted for every wrong answer. Likewise, for 2 marks MCQs, 2/3 marks will be deducted.

### Weightage of Sections in Paper

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 |

## Best Books for GATE 2021 MA

## Preparation Books for GATE 2021 Mathematics

**Mathematics section in GATE is considered one of the toughest subjects so the preparation of it should be awesome. **Books are the best option to prepare for any exam. That is why we are providing you soma good books for mathematics preparation. Hence, below is the table represents some important books for mathematics preparation in GATE exam:

Books | Author/Publisher |
---|---|

Chapterwise Solved Papers Mathematics GATE – 2020 | Suraj Singh, Arihant Publication |

GATE Engineering Mathematics for All Streams | Abhinav Goel, Arihant Publication |

GATE 2020: Engineering Mathematics | ME Team, Made Easy Publications |

Wiley Acing the Gate: Engineering Mathematics and General Aptitude | Anil K. Maini, Wiley |

Higher Engineering Mathematics | B.S. Grewal, Khanna Publishers |

**Also Check GATE Recommended Books**

## Preparation Tips for Mathematics

## Preparation Tips for GATE 2021 Mathematics (MA) Paper

**1. Know your Syllabus and Exam Pattern**

- Candidates must have accurate information about the exam pattern. This will help them in understanding the weightage of sections, marking schemes, etc.
- After that, candidates must go through their syllabus again and again so that they won’t miss any topic.
**Candidates are advised to follow the syllabus prescribed by the exam conducting body.**- With the help of the right syllabus, you can easily plan your preparation.

**2. Prepare a Productive Plan**

Candidates are suggested to prepare a plan as per their capabilities. Do not overburden yourself. You can follow the below-mentioned tips to prepare a plan:

**Long Term Plan:**In long term planning you can divide your syllabus based on the months that are left for preparations.**Short Term Plan:**In short term plan, you can divide the topics that you want to cover in a week. You can also call it a weekly plan.**This plan is more defined in comparison to long term plan because here you would know exactly which topics you have to cover in a particular week.**

**Read Preparation tips from GATE Topper**

**3. Manage your Time Properly**

- Time management is a must in GATE Preparations.
**Candidates need to give 6-8 hours of time for GATE preparations (considering you have 3-4 months left for the exam)**- Take frequent breaks to avoid laziness and to get refreshed.
**Dedicate 1-2 hours especially for revisions.**

**4. Practice Papers**

- Candidates solve the practice papers after completion of the whole syllabus or simultaneously after completion of each topic.
**You can improve the accuracy and speed of solving questions.**- With the help of practice papers, you can judge the level of your performance.
- You can get a better idea about the exam pattern, the difficulty level of questions, type of questions, etc.

**5. Revision from Notes**

- During the time of preparation prepare handwritten notes for each topic.
- These notes should include all the important points, tips, tricks, short cut methods, formulas, etc.
- Revise these notes on a daily basis. This will help you in memorizing important thinks.
- Notes are helpful for a quick look before the exam

## GATE Syllabus of Other Subjects

## GATE 2021 Syllabus of Other Subjects

Other than Mathematics there are other 24 subjects for which GATE 2021 will be conducted. Candidates can check the syllabus of their respective subjects from the links provided below in the table:

## Frequently Asked Questions

## GATE 2021 Mathematics Syllabus FAQs

Ques: What will be the subjects or sections that one needs to cover in GATE 2021 Mathematics paper?

Ans: GATE 2021 Mathematics syllabus includes General Aptitude and core subject i.e. Mathematics. The engineering mathematics sections which are there in various subjects of GATE will not be the part of mathematics. The major sections from mathematics are:

- Chapter 1 – Linear Algebra
- Chapter 2 – Complex Analysis
- Chapter 3 – Real Analysis
- Chapter 4 – Ordinary Differential Equations
- Chapter 5 – Algebra
- Chapter 6 – Functional Analysis
- Chapter 7 – Numerical Analysis
- Chapter 8 – Partial Differential Equations
- Chapter 9 – Topology
- Chapter 10 – Calculus
- Chapter 11 – Linear Programming

Ques: What will be the weightage of topics and marking scheme in GATE 2021 Mathematics paper?

Ans: The weightage and marking scheme is provided below in the table:

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 |

Ques: Will there be any negative marking in GATE 2021 Mathematics paper?

Ans: Yes. For every wrong answer, marks will be deducted depending on the total marks of those questions. Moreover, for attempting wrong NAT questions no marks will be deducted.

Type of question | Negative marking for wrong answer |
---|---|

MCQs | 1/3 for 1 mark questions 2/3 for 2 marks questions |

NATs | No negative marking |

Ques: What are the best books for GATE Mathematics preparation?

Ans: Candidates can refer to the following books:

- Chapterwise Solved Papers Mathematics GATE – 2020 – By Suraj Singh, Arihant Publication
- GATE Engineering Mathematics for All Streams – By Abhinav Goel, Arihant Publication

## GATE 2021 : 37 answered questions

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*The article might have information for the previous academic years, which will be updated soon subject to the notification issued by the University/College.