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GATE 2021 Mathematics Syllabus, Preparation Tips and Books

Exam: 05 Feb `21
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Nikkil Visha

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 sectionCheck 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 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%

Check GATE Paper Analysis

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 

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:

Preparation books for Mathematics
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.

Download GATE Practice Papers

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 

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

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


Ques. Which is the best coaching for GATE or IES in Allahabad?

● Top Answer By Aniket Atul Mahulikar on 15 Jan 21

Ans. GATE and IES both exams have almost the same syllabus. If you are residing in Allahabad and looking for the best coaching institute, then you have limited options. Both the papers are highly competitive and require experienced faculty for mentorship.  A few of the coaching institutes have associated industry experts to help GATE or IES aspirants. The top choices from which you can opt for includes:  Mechasoft AIEFA Mechasoft:  It is a good coaching institute with trusted faculty like Mr. A.K. Tripathi. Tripathi Sir is an expert in Control Systems who also teaches some other electronics subjects.  AIEFA:  AIEFA had a collaboration with Gateforum before. Now it’s a separate coaching center. It has poor management and the class schedule is not fixed. They teach in extremely long hours sometimes.  You can also go for self-studies and take the help of online guides. If you find it essential to opt for a coaching institute, you can opt for Mechasoft because the batches are small, and doubt clearing sessions are effective. For online classes, you can opt for Made easy, Times, or Ace academy.Read more
1 Answer

Ques. Is it good to prepare for the GATE and the IES simultaneously?

● Top Answer By Sandip Pal on 14 Jan 21

Ans. If you are preparing for IES then you can also simultaneously prepare for GATE as well with just a little extra effort. The syllabus of IES is quite vast as compared to the GATE syllabus. If your primary goal is to crack IES, concentrate more on the IES and study for GATE parallelly. If you are more interested in GATE, you need to make some extra effort. However, if you are equally interested in both you can follow the strategy given below for preparation. IES Preparation:  Read class notes and solve the workbook regularly.  Make short notes for each subject containing formulas, facts, and the new concepts you learned while reading. Solve previous year’s questions for IES and GATE. Note down the important questions you come across. During revision, go through the short notes you made and the questions too.  Give online and offline mock tests regularly.  GATE Preparation: If you follow a smart study plan you can complete the GATE preparation in just one and a half months. The syllabus for GATE is just like a subset of the IES syllabus. Both of them have several topics in common. You can follow this strategy to crack the exam: One month before GATE, thoroughly read all the class notes. Solve previous year’s question paper as much as possible. Take as many mock tests as you can. 10-12 days before the exam, revise the short notes daily. You can prepare for IES for the whole year and do the major chunk of preparation for GATE in the last 1-2 months. One of my friends followed this pattern for his preparation and was successful. But you don’t have to follow this plan blindly, you can make up your own strategy too.Read more
1 Answer

Ques. What is the difficulty level of the BITS HD exam compared to the GATE?

● Top Answer By Sahil Sachdeva on 14 Jan 21

Ans. GATE exam focuses on how much the students' concepts are clear and how they can apply them for solving the questions. Most importantly, it contains numerical questions, so it would be better to expect fewer theory questions in the GATE exam. Whereas, BITS HD exam contains the majority of theory questions. You are required to solve more problems in less time. You also have to prepare for aptitude and English. These sections are quite scoring and help to get a better score.  Difficulty Level - Comparison: GATE consists mostly of numerical, while 80 to 90% of the questions in BITS HD are theoretical.  You will hardly find 10 to 15 numerical questions in HD paper out of hundred questions. Numerical questions are not like GATE. These are mostly the formula and solve type. Nevertheless, some numerical may be found very tricky.  You need to have a thorough understanding of your syllabus for BITS HD. Theoretical questions will come from anywhere, and they will test your understanding of the respective topic. BITS HD consists of 15 maths questions that are way more difficult than GATE, 15 general English, and 70 engineering discipline questions. One most important thing to add is that BITS have also started admitting students by accepting their GATE score. If you have a 55+ GATE score, you can get admission to BITS.Read more
1 Answer

Ques. What should be the proper strategy to excel in both GATE and ESE simultaneously?

● Top Answer By Angana Nath on 08 Jan 21

Ans. GATE and ESE (Engineering Service Exam) are almost similar, so preparing for one exam ensures complete preparation of at least one portion of the other. Given below is the strategy of preparing simultaneously for GATE and ESE. ESE: Technical Subjects: Read the theory properly and solve ESE objective questions. Solve all the previous year Gate questions of ECE, EE, IN streams. Solve ESE Test series only, do not start with the GATE test series. Non-Technical Subjects: For these subjects, students must put in the daily effort. Each day 15-20 minutes for this is enough. If you keep up this practice sincerely for 5-6 months, there is a good chance you will be able to score more than 300 in ESE prelims.  GATE: Now that ESE is dealt with, go for the GATE test series. As the theory portion has already been covered, start with solving questions. Give at least 10 full syllabus mock tests for GATE.  How to Attempt GATE questions: Attempt all the 1 mark questions. Go for the aptitude and English section. This will provide a break from all the formula questions which have been solved. For the last 30 questions, attempt which questions are easier so that there is time to get back to questions that could not be solved. After the prelims of GATE, you will have 4-5 months to prepare for Mains. In the meantime attempt the previous years’ question paper of UPSC to get an idea about what is asked in the examination. Read standard books to clear basic concepts. Practice is the key to score well in these exams. So, attempt mack-tests for Main as well.Read more
1 Answer

Ques. What is the minimum score of GATE one should secure to get into PSUs?

● Top Answer By Poorva Chourasia on 08 Jan 21

Ans. The GATE cutoff for PSU recruitment is quite high. Only top rankers in the GATE examination have a chance of getting a call for an Interview. PSUs invite almost 4 times the candidates they actually recruit. As only the top rankers have the privilege of choosing the company they want to work in. PSU Recruitment Details: More than 50 PSUs recruit students based on their scores in GATE. To be recruited, candidates must score above the GATE-cutoff and also the cut-off mentioned by the company of choice. Some companies directly recruit candidates through their GATE scores while some only shortlist. Some PSUs conduct an additional test for recruiting candidates. Some of the companies that accept PSU scores are AAI, BARC, BBNL, BHEL, BPCL, CEL, CIL, DMRC, NBCC, NTPC, HPCL, ONGC, Powergrid, THDC, etc. PSU-Cutoff: Given below are the branch and category-wise cut-offs for some of the major companies, for PSU-GATE. PSU Branch/Post For General Category HPCL Mechanical  68.45 Civil 70.04 Electrical 58.64 Instrumentation 44.33 E&TC 73.05 Chemical 56.67 ONGC(2019) Geologist 557 Chemist 690 AEE Production Petroleum 703 AEE Cementing Mechanical 895 AEE Electronics 868 Surface Geophysicist 621 Programming Officer 840 AEE Production Chemical 689 AEE Cementing Petroleum 873 AEE Electrical 841 Well Geophysicist 697 AEE Mechanical 856 AEE Drilling Mechanical 845 Transport Officer 899 AEE Instrumentation 730 AEE Reservoir 847 AEE Production Mechanical 867 AEE Drilling Petroleum 803 MM Officer 923 AEE Civil 915 The GATE Cutoff for ONGC may vary with each vacancy. Candidates must score a minimum of 65% in their BTech graduation to appear for GATE. The salaries offered are almost the same for PSUs that recruit through GATE, but the salaries offered to people recruited for senior positions may differ.Read more
1 Answer

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