UPSC Mains Exam: Booklist and Strategy for Mathematics

Here we bring you a list of books for Mathematics optional subject of UPSC Mains Exam as well as some preparation strategies.

**Booklist for Mathematics Optional Subject Paper I**

**Linear Algebra :**- Schaum’s outline on Linear Algebra
- Krishna Series on Matrices

**Calculus :**- Krishna Series on Differential calculus
- Krishna Series on Integral calculus
- Mathematical Analysis by Malik and Arora : a must read book for both Paper I and II

**Analytical Geometry :**- Krishna Series on Analytical Geometry : this book is better than Shantinarayan and has many solved examples
- Krishna Series on Analytical Solid Geometry : for Conicoids, Generating Lines

**Ordinary Differential Equations:**- Ordinary and Partial Differential Equations by MD Raisinghania
- Advanced Differential Equations by MD Raisinghania for Laplace Transforms (Paper-I) and Boundary value problems (Paper-II)

**Dynamics and Statics**- Krishna Series on Statics
- Krishna Series on Dynamics

**Vector Analysis**- Krishna Series on Vector Calculus (~ 330 pages)
- Schaum’s outline on Vector Analysis

**Booklist for Mathematics Optional Subject Paper II**

**Abstract Algebra**:- Abstract Algebra, Group Theory by R Kumar (Vardhaman Publications)
- Abstract Algebra, Ring Theory by R Kumar (Vardhaman Publications)
- Abstract Algebra by Joseph Gallian (
*optional*)

**Real Analysis:**- Mathematical Analysis by Malik and Arora
- Real Analysis by MD Raisinghania

**Complex Analysis:**- Krishna Series

**Linear Programming:**- Operations Research by JK Sharma or Kanti Swarup or Krishna Series

**Partial Differential Equations:**- ODE and PDE by MD Raisinghania
- Engineering Maths by Grewal : for boundary value problems
- Advanced Differential Equations by M.D Raisinghania (for boundary value problems)

**Numerical Analysis and Computer programming:**- Numerical Methods by Jain and Iyengar
- Numerical Analysis chapter from Grewal, Engineering Mathematics

**Mechanics and Fluid Dynamics:**- Fluid Dynamics by MD Raisinghania
- Krishna Series, Dynamics for Moment of Inertia and D Alembert’s Principle
- Krishna Series, Rigid Dynamics for Lagrangian and Hamiltonian.

**Strategy for Paper I**

- Candidates should cover each and every topic of Mathematics Paper I in detail and the Paper-I is easier than Paper II.
- For Analytical Geometry, one should solve all the given examples in the aobe mentioned books and revise regularly on topics like skew lines, sphere, cone and conicoids. Candidates should mug up some specific problems and should remember the methods to begin with while solving these problems.
- For calculus, one must focus on Calculus of many variables for which one can refer the Mathematical Analysis by Malik and Arora
- In Statics & Dynamics, one should practice solving all the problems.
- Candidates should make a list of formulas in every chapter and revise it regularly.
- When it comes to Maths indeed practice makes one perfect, hence, after reading each and every topic one should practice solving problems.

**Strategy for Paper II**

- Maths Optional Paper II is generally considered as a tough paper by many. But if one masters the topics of this paper one can score high and get an edge over others aspirants.
**Abstract Algebra**is a unique topic. For those candidates who find this topic difficult it is advised to focus on topics that can fetch 10 marks like theorems (recommended to refer UPSC Previous Years’ Question Papers). Candidates can skip proofs of theorems that are big like Cayley’s Theorem, PID, Permutation groups, Euclidean Domain and UFDs. Refer Abstract Algebra, Group Theory by R Kumar (Vardhaman Publications) and Abstract Algebra, Ring Theory by R Kumar (Vardhaman Publications)- For
**Real Analysis**, the Mathematical Analysis by Malik and Arora is recommended. For additional studies, one can refer to Real Analysis by MD Raisinghania. One should focus more on Riemann Integral, Improper Integrals and Series and Sequences of functions and advised not to give much importance to proofs. **Linear Programming**: To cover this topic, one can refer the book Operations Research by JK Sharma which covers the topic precisely.**PDE:**Under this topic, candidates should focus on Charpit’s method as questions are regularly asked. For Boundary Value problems (heat equation etc.) one should first read Engineering Maths by Grewal.**Mechanics and Fluid Dynamics:**If one observes UPSC previous years’ question papers, UPSC has assorted the questions from various topics like PDE, Numerical Analysis and Fluid & Rigid Dynamics, therefore it is important to cover these topics to score high as well.**Areas to focus on:**In Fluid dynamics would be Kinematics of Fluids in Motion; Vortex Motion; Sources and Sinks; Equations of Motions of Inviscid Fluids. Proof of any theorems can be ignored but if you have time, just run through it. For Navier Stokes Equations solve all the problems given as examples. To cover the Rigid Dynamics one can refer the books mentioned in the above booklist.