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UPSC Mathematics Syllabus 2024 for IAS Math Optional Subject

UPSC Mathematics Syllabus 2024: The Union Public Service Commission conducts the Civil Services Examination, one of the most prestigious competitive exams in India. Among the various optional subjects available, Mathematics is a popular choice for candidates with a strong mathematical background and an interest in the subject.

UPSC Mathematics Syllabus 2024

This article provides an overview of the UPSC Mathematics syllabus 2024, which consists of two papers: Paper 1 and Paper 2. The syllabus covers a wide range of topics including algebra, calculus, differential equations, linear algebra, statistics, and more. A thorough understanding of the syllabus and effective preparation can help aspirants excel in the Mathematics optional paper of the UPSC examination.

UPSC Mathematics Syllabus 2024 Optional Paper

The UPSC Mathematics Syllabus 2024 consists of two papers: Paper I and Paper II. Each paper is of 250 marks, making a total of 500 marks for the Mathematics optional subject. The syllabus is designed to test the candidate’s knowledge and understanding of various mathematical concepts and their application in real-world scenarios.

UPSC Mathematics Syllabus 2024 for Paper 1

The UPSC Mathematics Syllabus 2024 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 2024 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 2024 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 2024 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 2024 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 2024 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 2024 PDF, follow these steps:

• Visit the official UPSC website at www.upsc.gov.in.
• Navigate to the “Examinations” section.
• Click on the link for “Civil Services Examination.”
• Look for the “UPSC Maths Syllabus PDF” section and click on it.
• Scroll down to find the syllabus for the Mathematics Optional subject.

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

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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.