UPSC Mathematics Syllabus 2025 for IAS Math Optional Subject

UPSC Mathematics Syllabus 2025 for IAS Math Optional Subject Syllabus is provided below explaining all the topic wise Paper 1 and 2 syllabus. Get to download the UPSC Maths Syllabus PDF.

Table of Contents

The Civil Services Examination, conducted by the Union Public Service Commission (UPSC), is one of the most prestigious competitive exams in India. Mathematics is a popular choice for the optional paper, especially among candidates who have a strong background in the subject or a keen interest in it. It is also known for having a relatively high success rate.

UPSC Mathematics Syllabus 2025

This article gives an overview of the UPSC Mathematics syllabus, which has two papers: Paper 1 and Paper 2. The syllabus includes topics like Algebra, Calculus, Differential Equations, Linear Algebra, Statistics, and more. Having a clear understanding of these topics and preparing well can help candidates do well in the Mathematics optional paper of the UPSC exam. Good preparation can improve your chances of scoring high and achieving a better rank.

UPSC Syllabus 2025
Category	Syllabus
Paper	Maths
Types of Paper	Conventional Papers (Descriptive Type)
Duration of Exam	3 hours Each Paper
Total Marks	1750
Negative Marking	No negative marking… Read more at: https://www.adda247.com/upsc-exam/upsc-mains-syllabus/

UPSC Mains Result 2024

UPSC Maths Optional Syllabus 2025

There are two papers in the UPSC Mathematics Syllabus Paper I and Paper II. The Mathematics optional subject carries 500 total marks(250 marks each paper). The syllabus aims to assess a candidate’s knowledge, comprehension, and application of numerous mathematical ideas in practical situations.

UPSC Mathematics Syllabus 2025 for Paper 1

The UPSC Mathematics Syllabus 2025 for Paper 1 is designed to assess candidates’ knowledge and understanding of various mathematical concepts. The topics covered in Paper 1 include:

UPSC Mathematics Syllabus 2025 for Paper 1

Mathematics syllabus for UPSC Paper 1

Algebra:
- Linear Algebra: Vector spaces, Linear transformations, Eigenvalues and eigenvectors, Matrix representation, Cayley-Hamilton theorem.
- Abstract Algebra: Groups, Subgroups, Normal subgroups, Lagrange’s theorem, Cyclic groups, Permutation groups, Rings, Fields.
Calculus:
- Real Analysis: Sequences and series, Continuity and differentiability of functions, Mean value theorems, Riemann integrals.
- Complex Analysis: Analytic functions, Cauchy’s theorem, Taylor and Laurent series, Residue theorem, Conformal mappings.
Analytical Geometry:
- Cartesian and Polar coordinates: Equation of a line, Circle, Ellipse, Hyperbola, Parabola.
- Three-dimensional Geometry: Direction cosines and ratios, Plane, Straight line, Sphere.
Linear Programming:
- Formulation of linear programming problems, Basic concepts of linear programming, Graphical method, Simplex method, Duality.
Dynamics and Statics:
- Rectilinear motion, Projectile motion, Newton’s laws of motion, Moment of inertia, Equilibrium of particles and rigid bodies.

UPSC Mathematics Syllabus 2025 for Paper 2

The syllabus for UPSC Mathematics Paper 2 is designed to assess candidates’ knowledge and understanding of various mathematical concepts. The topics covered in Paper 2 include:

UPSC Mathematics Syllabus 2025 For Paper 2

Mathematics Syllabus For UPSC Paper 2

Algebra:
- Matrices and Determinants: Rank, Eigenvalues and eigenvectors, Orthogonal and unitary matrices, Hermitian, Skew-Hermitian, and Normal matrices.
- Calculus of Variations: Variational problems, Euler-Lagrange equation, and its applications.
Differential Equations:
- Ordinary Differential Equations: First-order differential equations, Second-order linear equations with constant coefficients, Laplace transforms.
- Partial Differential Equations: Classification, Solution of wave equation, Heat equation, and Laplace equation.
Numerical Analysis:
- Numerical methods: Solution of linear and non-linear equations, Interpolation and approximation, Numerical integration and differentiation.
- Computer programming: Basics of programming languages, Algorithms and flowcharts.
Linear Programming:
- Formulation of linear programming problems, Basic concepts of linear programming, Graphical method, Simplex method, Duality.
Probability and Statistics:
- Probability Theory: Sample space, Events, Probability of an event, Conditional probability, Random variables, Probability distributions.
- Statistical Methods: Measures of central tendency and dispersion, Correlation, and regression, Sampling distributions, Estimation, and hypothesis testing.

UPSC Mathematics Syllabus 2025 Optional Syllabus Books

The following is a list of recommended books for the UPSC Maths Optional syllabus for Paper 1:

Dynamics, Statics, and Hydrostatics – M. Ray
Differential Calculus – Shanti Narayan, PK Mittal
Analytic Geometry – Shanti Narayan, DK Jha, HC Sinha, and Sharma
Differential equations:- Golden series – NP Bali
Vector Analysis – Shanti Narayan, PK Mittal
Linear Algebra – K.C. Prasad, K B Datta

The following is a list of recommended books for the UPSC Maths Optional syllabus for Paper 2:

Linear Programming & Theory of Games – SD Sharma
Algebra – K C Prasad, KB Datta
Mechanics & Fluid Dynamics – Azaroff Leonid, AP Mathur
Complex Analysis – GK Ranganath
Real Analysis – H.L Royden
Ordinary & Partial Differential Equation – M.D. Raisinghania
Introductory Methods of Numerical Analysis – SS Sastry

UPSC Mathematics Syllabus 2025 PDF

The UPSC Mathematics Syllabus PDF can be obtained from the official website of the Union Public Service Commission (UPSC). To download the UPSC Mathematics Syllabus 2025 PDF, follow these steps:

Go to www.upsc.gov.in, the official website of the UPSC.
Open “Examinations” from the menu.
Select the “Civil Services Examination” link.
Locate and click on the “UPSC Mathematics Syllabus PDF” section.
To see the Mathematics Optional course syllabus, scroll down.
To obtain the UPSC Mathematics Syllabus PDF file, click the provided link.

The UPSC Mathematics Syllabus PDF provides a detailed overview of the topics and sub-topics that candidates need to study for the examination. It is important to understand the syllabus and plan your preparation accordingly thoroughly.

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FAQs

What is the syllabus for UPSC Mathematics optional paper?

The syllabus for UPSC Mathematics optional paper covers a wide range of topics including algebra, calculus, linear algebra, differential equations, statistics, and probability, among others. It is designed to test the candidate's understanding and proficiency in mathematical concepts.

How many papers are there for the Mathematics optional in UPSC?

The Mathematics optional in UPSC consists of two papers: Paper 1 and Paper 2. Each paper carries a maximum of 250 marks, making a total of 500 marks for the Mathematics optional subject.

Is the Mathematics optional subject popular among UPSC aspirants?

Yes, Mathematics is a popular optional subject among UPSC aspirants, especially those with a background or interest in mathematics. Its logical and analytical nature attracts candidates who are comfortable with mathematical concepts.

Can I choose Mathematics as an optional subject if I am not from a mathematical background?

Yes, you can choose Mathematics as an optional subject even if you do not have a strong mathematical background. However, it is recommended to have a basic understanding of mathematics and a willingness to learn and master the subject.