Recommended Books and Study Materials for Mathematics Optional


- Linear Algebra by Hoffman and Kunze: This book covers the fundamentals of linear algebra, including vector spaces, linear transformations, eigenvalues, and eigenvectors.
- Algebra by G. C. Berndt: It provides a comprehensive understanding of abstract algebra, groups, rings, and fields.
- Abstract Algebra by Dummit and Foote: This book is recommended for an in-depth study of abstract algebra, including modules, Galois theory, and commutative algebra.


- Real Analysis by Walter Rudin: It covers the principles of real analysis, including limits, continuity, differentiation, and integration.
- Calculus of Several Variables by Serge Lang: This book is recommended for studying multivariable calculus, including partial differentiation, multiple integrals, and vector analysis.


- Ordinary Differential Equations by M. D. Raisinghania: It covers ordinary differential equations, including first-order equations, second-order linear equations, and systems of differential equations.
- Partial Differential Equations by Sankara Rao: This book provides a comprehensive understanding of partial differential equations, including various solution techniques and applications.


- Numerical Analysis by S. S. Sastry: It covers numerical methods for solving equations, interpolation, numerical integration, and numerical solutions of differential equations.


- Classical Mechanics by Goldstein, Poole, and Safko: This book covers the principles of classical mechanics, including Newtonian mechanics, Lagrangian mechanics, and Hamiltonian mechanics.
- Fluid Mechanics by Pijush K. Kundu and Ira M. Cohen: It provides a comprehensive understanding of fluid mechanics, including fluid properties, fluid statics, and fluid dynamics.


- An Introduction to Probability Theory and Mathematical Statistics by V. K. Rohatgi and A. K. Md. Ehsanes Saleh: It covers the basics of probability theory and mathematical statistics, including random variables, probability distributions, and estimation.


- Previous Years' Question Papers: Solving previous years' question papers will give you an idea of the exam pattern and help you practice different types of questions.
- Online Study Platforms: EduRev, an online learning platform, provides UPSC Mathematics Optional study material, notes, and practice questions that can be accessed for free.

Remember to practice numerical problems and solve mathematical problems regularly to strengthen your understanding and problem-solving skills.