UPPSC Mathematics Syllabus 2025, Exam Pattern, Preparation Tips
UPPSC Mathematics Syllabus 2025 has been discussed here for the candidates. Candidates can get details of section-wise UPPSC Mathematics Syllabus 2025 and Exam Pattern.
Priyanka Gupta4 Aug, 2025
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UPPSC Mathematics Syllabus 2025: The Uttar Pradesh Public Service Commission has released the UPPSC Mathematics Syllabus 2025 along with the official UPPSC Notification 2025. The candidates who are going to appear in the examination must go through the details of the UPPSC 2025 Mathematics Syllabus. The candidates must plan their studies with a well-structured preparation strategy.
The Mathematics syllabus includes two papers, Paper 1 and Paper 2 which the candidates have to appear in. Mathematics is one of the optional subjects the candidates will get to choose to appear in the main examination. The candidates can go through this article to learn about the Mathematics syllabus and the paper-wise topics that they need to prepare.UPPSC Mathematics Syllabus 2025
The UPPSC Mathematics Syllabus 2025 has been included in the UPPSC Syllabus 2025 and the exam pattern. The candidates appearing in the UPPSC 2025 must know the topics and the examination structure before going forward with the preparation. They must create a timetable surrounding their weak points, syllabus, and needs. The candidates need to choose an optional subject to appear in the UPPSC Mains 2025 examination, and Mathematics is a very popular topic that has been scoring topic. The candidates related to the Mathematics background in their academic life can choose Mathematics which will make it easy for them to prepare and appear in the examination. The UPPSC Prelims Exam 2025 will be conducted on 6th July 2025, the candidates who qualify for this round will be eligible for the mains stage.UPPSC Mathematics Syllabus 2025 Papers
The UPPSC Mathematics Syllabus 2025 includes two papers that the candidates need to appear in the examination. Paper 1 contains topics like Vector spaces, Sub Spaces, basis and dimensions, and Quotient. space, coordinates, linear transformation, rank and nullity of a linear transformation. On the other hand, Paper 2 includes the Mathematics of India, Resources, Industry, Agriculture, Contemporary Issues, Settlements, and Cultural Setting. The topics and sub-topics are discussed further in the article for the reference of the candidates. The candidates must note that they have to choose two optional subject papers for Paper 8 and Paper 9 in the main examination for which they will get 3 hours each to complete the paper.UPPSC Mathematics Syllabus 2025 Paper 1
The candidates can go through the details of the UPPSC Mathematics Syllabus 2025 Paper 1 from the table given below. Paper 1 is divided into a few sections which have been discussed in the table. Paper 1 contains topics like Mathematics, human Mathematics, Regional Planning, Models, Theories, and Laws in Human Mathematics.| UPPSC Mathematics Syllabus 2025 Paper 1 | |
| Topics | Details |
| 1 Linear Algebra and Matrix: | Vector spaces, Sub Spaces, basis and dimensions, Quotient. space, coordinates, linear transformation, rank and nullity of a linear transformation, matrix representation of linear transformation, linear functionals, dual space, transpose of a linear transformation, characteristic values, annihilating polynomials, Cayley Hamilton theorem, Inner product spaces, Cauchy Schwarz inequality, Or- orthogonal vectors, orthogonal complements, orthonormal sets and bases, Bessel's Inequality Of Finite dimensional spaces, Gram Schmidt orthogonalization process. |
| 2. Calculus: | Limits, continuity, differentiability, mean value theorems, Taylor's theorem, indeterminate forms, maxima and minima, tangent and normal, Asymptotes, curvature, envelope and evolute, curve tracing, continuity and differentiability of a function of several variables Interchangeability of partial derivatives, Implicit functions theorem, double and triple integrals. (techniques only), application of Beta and Gamma functions, Areas, Surface And volumes, and Centre Of Gravity. |
| 3. Analytical Geometry of two and three dimensions: | General equation of second degree, a system of conics, confocal, conics, polar equation of conics and its properties. Three-dimensional co-ordinates, plane, straight line, sphere, cone, and cylinder. Central conoids, paraboloids, plane section Of conoids, generating lines, Confocal conoids. |
| 4. Ordinary differential equations: | Order and Degree of a differential equation, linear, and exact differential equations of first order and first degree, , equations of first order but not of first degree, Singular solutions, Orthogonal trajectories, Higher order linear equations with constant coefficients, Complementary functions and particular integrals. Second order linear differential equations with variable coefficients: use of known solution to find another, normal form, method of undetermined coefficients method of variation of parameters. |
| 5. Vector And Tensor Analysis: | Vector Algebra, Differentiation, and Integration of vector function of a scalar variable gradient, divergence and curl in cartesian, cylindrical, and spherical coordinates and their physical interpretation, Higher order derivates, vector identities and, vector equations, Gauss and stoke's theorems, Curves in Space, curvature and torsion, Serret Frenet's formulae. Definition Of Tensor, Transformation Of Coordinates, contravariant And covariant tensors, addition and outer product of tensors. Contraction of tensors, inner product tensor, fundamental tensors, Christoffel symbols, covariant differentiation, gradient, divergence, And Curl In Tensor notation. |
| 6. Statics and Dynamics: | Virtual work, stability of equilibrium. Catenary, Catenary Of uniform strength, Equilibrium Of Forces In Three dimensions. Rectilinear motion, simple harmonic motion, velocities, and accelerations along the radial and transverse. |
UPPSC Mathematics Syllabus 2025 Paper 2
The candidates can go through the details of the UPPSC Mathematics Syllabus 2025 Paper 2 from the table given below. Paper 2 is divided into a few sections which has been discussed in the table. Paper 2 includes the India, Resources, Industry, Agriculture, Contemporary Issues, Settlements, and Cultural Setting.| UPPSC Mathematics Syllabus 2025 Paper 2 | |
| Topics | Details |
| 1. Algebra: | Groups, Cyclic groups, subgroups, Cosets of a subgroup, Lagrange's theorem, Normal subgroups, Homo- morphism of groups, Factor groups, basic Isomorphism theorems, Permutation groups, Cayley's theorem. Rings, Subrings, Ideals, Integral domains, Fields of quotients of an integral domain, Euclidean domains, Principal ideal domains, Polynomial rings over a field, Unique factorization domains. |
| 2. Real Analysis: | Metric spaces And Their Topology With special reference to sequence, Convergent sequence, Cauchy sequences, Cauchy's criterion of convergence, infinite series And Their convergence, Nth Term test, Series Of positive Terms, Ratio And Root tests, Limit Comparison tests, Logarithmic Ratio test, Condensation Test, Absolute And conditional convergence Of general Series In R,Abel's Dirichlet'stheorems. Uniform convergence of sequences and series of functions over an interval, Weierstrass Mtest, Abel's And Dirichlet's Tests, Continuity Of Limit function. Term By Term Integrability And differentiability. Riemann's Theory Of Integration For Bounded Functions, Integrability Of continuous functions. Fundamental theorem of calculus. Improper integrals and conditions for their existence,test. |
| 3.Complex Analysis: | Analytic functions, Cauchy, Riemann equations, Cauchy's theorem, Cauchy's integral formula, Power series representation of an anal ytic function. Taylor's series. Laurent's series, Classification of singularities, Cauchy's Residue theorem, Contour integration. |
| 4.Partial Differential Equations: | Formation Of Partial Differentia equations. Integrals Of partial differential equations of first order, Solutions of quasi linear partial differential equations Of First order, Charpit's Method For non-linear partial differential Equations Of first order, Linear Partial differential equations of the second order with constant coefficients and their canonical forms, Equation of vibrating string. Heat equation. Laplace equation and their solutions. |
UPPSC Mathematics Marking Scheme 2025
It is necessary to update the UPPSC Mathematics syllabus and marking structure so that applicants can organize their studies based on both total and negative marks. They increase their chances of getting good exam scores by doing this. The following is a list of the UPPSC Mathematics Marking Scheme requirements for applicants to review:- There are multiple-choice, objective questions on the preliminary exam.
- This is divided into two papers, Paper 1 and Paper 2, the specifics of which are given in the preceding paragraph.
- On paper 1, a correct response will yield 1.33 marks.
- On paper 2, each correct response will be worth two marks.
- Each incorrect response will result in a reduction of 0.33 marks.
UPPSC Mathematics Syllabus 2025 Preparation Tips
The UPPSC Mathematics Syllabus 2025 Preparation Tips have been mentioned below for the reference of the candidates. The candidates can include these tips in their preparation strategy to implement effective planning.- The candidates are required to select an elective that they are knowledgeable in and in which they may earn the highest grade.
- To study in a method that will help you reach your goals, make a plan and mark your daily, weekly, and monthly objectives.
- Additionally, be sure to show up for enough practice exams so that you are ready for the primary and final exams. The best method for assessing a candidate's anticipated performance in the main exam is through mock exams.
| Other Related Links of UPPSC Exam 2025 | |
| UPPSC Notification | UPPSC Salary |
| UPPSC Result | UPPSC Syllabus |
| UPPSC Answer Key | UPPSC Eligibility Criteria |
| UPPSC Admit Card | UPPSC Apply Online |
| UPPSC Previous Year Question Paper | UPPSC Selection Process |
| UPPSC Cut Off | |
UPPSC Mathematics Syllabus FAQs
Q1. What type of questions are asked in the exam of UPPCS Maths?
Ans. The questions are asked in the objective pattern.
Q2. Where can we get the detailed syllabus for UPPCS Maths?
Ans. the candidates can get all the updates on the official website.
Q3. Is there any negative marking in the exam?
Ans. Yes, might there will be a negative marking of 1.33 marks.
Q4. Are there any fees required to download the syllabus?
Ans. No, there are not any fees required for the syllabus.
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