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Table of Contents
GATE Mathematics (MA) Syllabus 2023: Important Topics, Weightage, Question Paper, and Preparation Books
GATE Mathematics (MA) Syllabus 2023 is going to be released on the official website. No changes have been made to the syllabus this year. GATE 2023 Mathematics Paper 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. The candidates who opted for Mathematics as their first paper in GATE 2023 can appear for Computer Science and Information Technology (CS), Geomatics Engineering (GE), Physics (PH), or (ST) as their second paper. Check GATE 2023 Exam Pattern
Major topics that are covered in GATE Mathematics Syllabus 2023 include Calculus, Linear Algebra, Real Analysis, Algebra, Functional Analysis, Numerical Analysis, etc. The students are advised to attempt as many previous year question papers as possible and analyze their mistakes. This would enable them to gain confidence and form a better judgment regarding GATE Mathematics Syllabus 2023. CheckGATE Paper Analysis.
Quick Links:
| How to use GATE 2023 Virtual Calculator? | What will be the Validity of GATE 2023 Score? | Online Coaching for GATE 2023 |
GATE Mathematics Syllabus 2023
There are 11 chapters in the 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
- Principal 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.
GATE 2023 Exam Pattern of Mathematics
GATE 2023 Exam Pattern varies for different disciplines. Given below is the examination pattern for GATE Mathematics.
- Mode of Examination: Online
- Duration of Exam: 3 hours
- Types of Questions: MCQs and NAT
- Sections: 2 sections – General Aptitude and Subject-based
- Total Questions: 65 questions
- Total Marks: 100 marks
- Negative Marking: For MCQs only
Weightage of Sections in GATE Mathematics 2023
GATE Mathematics Syllabus 2023 is divided into two sections. The below table describes the distribution of marks in each section.
| 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 |
GATE Mathematics Marking Scheme 2023
| Type of question | Negative marking for wrong answer |
|---|---|
| MCQs |
|
| NATs | No negative marking |
GATE Mathematics Syllabus 2023: Weightage of Topics
The students are advised to commence their GATE Preparation after going through the weightage of each topic mentioned. This will save them a lot of trouble and effort.
| 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 Preparation 2023 for Mathematics
To assist in the GATE Mathematics Preparation 2023, the following sections have been curated. The students are advised to check out the following and avail of the benefits.
Best Books for GATE Mathematics (MA) 2023
Given below are the recommended books for GATE Mathematics 2023 that would be beneficial for the students.
| Books | Author/Publisher |
|---|---|
| Chapterwise Solved Papers Mathematics GATE | Suraj Singh, Arihant Publication |
| GATE Engineering Mathematics for All Streams | Abhinav Goel, Arihant Publication |
| GATE: 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
GATE MA Previous Year Question Paper
Given below are the links for GATE MA Previous Year Question Papers along with their answer key.
| Year | Link for GATE MA Question Paper | Link for GATE MA Answer Key |
|---|---|---|
| 2021 | Check Here | Check Here |
| 2020 | Check Here | Check Here |
| 2019 | Check Here | Check Here |
| 2018 | Check Here | Check Here |
| 2017 | Check Here | Check Here |
GATE Mathematics Sample Questions
Sample Question 1:
Sample Question 2:
GATE Syllabus 2023 of Other Subjects
Other than Mathematics there are other 24 subjects for which GATE 2023 will be conducted. Candidates can check the syllabus of their respective subjects from the links provided below in the table:
GATE Mathematics Syllabus 2023 FAQs
Ques. What will be the subjects or sections that one needs to cover in the GATE 2023 Mathematics paper?
Ans: GATE 2023 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 Mathematics 2023?
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 Mathematics 2023?
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 2023?
Ans: Candidates can refer to the following books:
- Chapterwise Solved Papers Mathematics GATE – By Suraj Singh, Arihant Publication
- GATE Engineering Mathematics for All Streams – By Abhinav Goel, Arihant Publication
Ques. What is the paper code for GATE Mathematics Syllabus 2023?
Ans. The paper code for GATE Mathematics is MA. The students are advised to check the eligibility criteria before appearing for GATE 2023. CheckGATE Eligibility
Ques. Which is the most important topic for GATE Mathematics Syllabus 2023?
Ans. The most important topics for GATE Mathematics Syllabus 2023 are Probability and Statistics, Numerical Methods, and Vector Calculus. However, the students are advised to go through every topic mentioned in the syllabus to score the desired marks.
Ques. What will be the difficulty level of GATE Mathematics Syllabus 2023?
Ans. The difficulty level of GATE Mathematics 2023 can be estimated by checking out GATE Paper Analysis. The candidates are advised to practice daily and try to solve every difficult question. In this case, they won’t find GATE 2023 difficult.
Ques. What is the syllabus for calculus in GATE Mathematics Syllabus 2023?
Ans. The syllabus for calculus in GATE Mathematics Syllabus 2023 consists of:
- 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.
GATE 2025 : 20 Answered QuestionsView All
Ans. An MS from IIT Kanpur is considered to be a highly respected and prestigious degree. The MS program at IIT Kanpur is reputed for its focus on excellent research and its strong focus on practical, hands-on learning. As an MS student, you get to work with some of the most experienced and respected scholars and researchers in their fields, which gives an insight into the latest industry developments and trends. Additionally, not being located near metropolitan areas, IIT Kanpur gives a peaceful learning environment and students don’t spend much time partying or clubbing. Although it is a 2-year program, with the right determination one can complete it in 18 months also. If you are true to your passion you can also complete a Ph.D. under an experienced thesis advisor and won’t have to go to a foreign university for a Ph.D. Overall, an MS from IIT Kanpur is a valuable and highly esteemed program that offers many opportunities in terms of career and professional advancement. Although it is challenging, the learning experience is worth the effort. Read more
Ans. Andhra University M.Tech admission is done in two ways, i.e. through GATE and through AP PGECET. To get admission, you need to have a valid GATE score or you need to score a valid rank in AP PGECET. Soon, Andhra University will release the notification for AP PGECET. Here are the tentative dates. Event Tentative dates Notification release date Second week of July 2022 Application form available Second week of July 2022 Admit card release date Second week of September 2022 Exam date Third week of September 2022 Result Second week of October 2022 Andhra University will release the application form online. Visit the official website of the institute regularly to get the updated information. Read more
Ans. Many GATE toppers leave PSU and join NITIE, instead of IITs because it offers better placements. Usually, students with good scores join ONGC, NTPC, BHEL, IOCL, and others. Despite the good salary, PSU jobs can get monotonous after a few years. So, the top rankers start looking for better career options. If they wish to do an MBA, they need to prepare for CAT. Some do prepare for CAT, but many join NITIE as it is an easier option. NITIE takes admission through GATE and the GATE score is valid for 3 years. So, they can easily get admission based on their GATE score. Also, the institute has a great placement record. During the NITIE Mumbai placement in 2022, the average CTC offered was INR 25.41 LPA. The video below will convince you further to join NITIE Mumbai Overall, its the excellent opportunities offered by NITIE that makes mant GATE toppers leave PSU and join NITIE Read more
Ans. Here are some strategies that can help you prepare for GATE and ESE simultaneously. Compare the syllabus of GATE and ESE. Go through the previous years' questions of both. The technical portion of both examinations overlaps a lot. The major difference is question patterns and styles. Different types of questions are asked on the same topics. GATE tests aptitude for solving technical questions. While ESE puts more emphasis on technical details. Figure out which subjects contribute more to which examinations. If you have less time, start with GATE preparation. The topics can be covered easily and in less time. Once you are through GATE preparation, you can solve ESE questions without much difficulty. Focus on GATE and ESE preparations only. First, go through the syllabus thoroughly. Once you are done with the syllabus, go through your notes and solve previous years' questions. Solve test series, and review hard questions. Analyze the tests you give and work on your mistakes. Read more
Ans. GATE consists mostly of numerical questions. It tests the aptitude for solving questions in less time. BITS HD papers have 10-15 numerical questions usually. The numerical questions aren’t on the same level as GATE and are just formula-based problems. Usually, around 80-90% of BITS HD questions are theory oriented. You need to have a good grasp of your engineering subjects to score well in BITS HD. The questions can come from anywhere in the syllabus. BITS HD usually consists - 15 Mathematics questions (difficulty usually higher than GATE) 15 general English questions 70 Engineering discipline questions Also, note that BITS take admission based on GATE scores as well. Read more
Ans. The required GATE rank depends upon various parameters like The engineering branch Company (PSU) Number of vacancies for the stream People who are graduating in 3-4 years are lucky as both IOCL and ONGC are planning to recruit in bulk because of massive retirements in both the companies. The mechanical and chemical branches are expected to have the most vacancies. Candidates will be called in a 1:5 ratio and thus, interviews will be the major determining factor of your selection. If you are unable to showcase your knowledge and talent during the interview, even a single-digit rank cannot guarantee your admission. A minimum of 40% marks are required to pass the interview. So if you get a call for the interview, don’t let your rank discourage you or even make you overconfident. Read more
Ans. Sikkim Manipal University has been ranked at 17 for Private Engineering by India Today in 2020. The largest department within the institution is the CSE department and it has also won the best department in SMIT multiple times. Admissions: Class 12th with mandatory subjects in Physics, Maths, Chemistry/computer science/biology is the prerequisite for admission to CSE at Sikkim Manipal. SMIT online, MET, JEE Mains is the examinations accepted for BTech admission. The total intake for CSE is 180 and the course fee is 12.20 lakhs. Curriculum: The University offers a well-structured and detailed curriculum with exposure to major areas of computer science like Big data analytics, robotics, cloud computing, ethical hacking, and more. The course structure focuses on providing students with knowledge of the core subjects of computer science in order to strengthen their foundation and make them industry-ready. Faculty: The university has 33 highly experienced and qualified faculties for CS. The faculty members also conduct seminars and workshops with esteemed institutions like ISRO, IIT, and TIFR. Infrastructure: The University offers a great infrastructure for the CSE department as it receives funding from two highly esteemed agencies, AICTE and ISRO. There are nine state-of-the-art practical labs like the Networking lab, digital circuit and microprocessor labs, GIS and remote sensing lab, advanced programming lab, and more. It also has a huge library with over 2500 journals and books dedicated to the CSE branch. It has been updated with modern facilities and infrastructure all across the campus in order to provide students with the best experience. Placements: AGS Infotech, Amazon, Britannia, Cipla, Capgemini are some of the major recruiters at the institute. Placement Rate within CSE 92.5% Lowest CTC 3.5 LPA Average CTC 5 LPA Highest CTC 18 LPA Sikkim Manipal University is a great option for students who want to pursue a BTech degree program in the CSE department. Read more
Ans. It depends on your career goals. GATE offers more options for engineering students. It is an all-around examination. You can go for MTech, PSUs, MS, and FRM. If you want more options, GATE will be better for you. If you want to do an MBA, after graduation, CAT will be the better option. Almost all top B-Schools accept CAT scores for MBA. Read more
Ans. IIT Roorkee admission 2023 hasn’t been wrapped up yet, hence its GATE cutoff too hasn’t been released as of now. M.Tech admission process of IIT Roorkee is conducted on the basis of the GATE cutoff, and all the candidates applying for admission into the M.Tech course under the non-sponsored category will be required to clear the cutoff for admission. The cutoff scores for M.Tech admission at IIT Roorkee for 2022 and 2021 have not been disclosed by the admission authority. Let’s consider GATE 2020 cutoff for a slight idea. Category GATE 2020 Cutoff General 77.1 EWS 79.1 OBC 72.32 SC 58.62 ST 61.33 Read more
Ans. First of all, admission to the IIT Roorkee MTech program is not given on the basis of GATE rank. The final shortlisting is done on the basis of Normalized GATE marks were used which is calculated by IIT Roorkee as follows: Normalized GATE marks = Normalized marks out of 100 or Marks*100\Maximum marks awarded in the paper that year For example if a candidate has scored 64 marks and the maximum marks given that year are 92, the Normalized GATE marks are 64*100/92=69.57. The table below comprises the expected GATE 2023 cut-off for IIT Roorkee based on the previous year's cut-off trends. MTech Course Cutoff Alternate Hydro Energy Centre 760-839 Architecture & Planning 650-844 Biotechnology 570-577 Civil Engineering 656-780 Chemical Engineering 650-657 Computer Science & Engineering 840-844 Disaster Mitigation & Management 700-710 Electronics and Communication Engineering 736-750 Electrical Engineering 760-779 Mechanical and Industrial Engineering 748-785 Read more
*The article might have information for the previous academic years, which will be updated soon subject to the notification issued by the University/College
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