TIFR GS Syllabus 2025, Download Subject Wise PDF

TIFR GS Syllabus 2025: The Tata Institute of Fundamental Research (TIFR) has released the TIFR GS Syllabus 2025 on the official website. This syllabus is essential for students preparing for the TIFR GS 2025 exam, which will take place on December 8, 2024. It provides a comprehensive outline of the topics across various subjects, including Mathematics, Physics, Chemistry, Biology, and Computer Science. By reviewing the syllabus, candidates can focus their studies on the key areas required for success in the exam. Check this article for TIFR GS Syllabus 2025.

TIFR GS Syllabus 2025 Overview

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TIFR GS Syllabus 2025 PDF Download

TIFR GS Syllabus 2025 Subject Wise

TIFR GS Syllabus 2025 for Biology

TIFR GS Syllabus 2025 for Chemistry

• Physical Chemistry
• Organic Chemistry
• Inorganic Chemistry
• Analytical Chemistry
• Electrochemistry
• Quantum Chemistry
• Biophysics
• Thermodynamics
• Spectroscopy (NMR, fluorescence, IR, UV, and X-ray)
• Logic and statistics
• Mathematical methods

TIFR GS Syllabus 2025 for Computer Science & Learning, Information and Data Sciences

Computer Science

• Discrete Mathematics : This includes concepts like sets, relations, combinatorics (counting), elementary probability theory, graph theory, and both propositional and predicate logic.
• Formal Languages and Automata Theory : Focus on the study of formal languages, automata, and computability.
• Data Structures and Algorithms : Understand arrays, lists, trees, sorting and searching techniques, graph algorithms, and the complexity of problems, including NP-completeness.
• Programming Languages and Compilers : Learn about control structures, parameter passing mechanisms, recursion, parsing, type checking, and memory management.
• Operating Systems and Concurrency : Explore how operating systems work and concepts related to concurrent processes.
• Switching Theory and Digital Circuits : Study the principles of switching theory and the design of digital circuits.
• Theory of Databases : Gain knowledge about database theory and management.

Learning, Information, and Data Sciences (LIDS)

• Engineering Mathematics : Review key topics like probability, linear algebra, basic optimization, basic analysis, and calculus.
• Electrical and Computer Sciences : Understand signals and systems, as well as digital signal processing.

TIFR GS Syllabus 2025 for Mathematics

• PhD and IntPhD programs at the School of Mathematics, TIFR, Mumbai
• IntPhD program at TIFR CAM, Bengaluru
• PhD program at ICTS, Bengaluru
• CAM-ICTS PhD program in Applied and Computational Mathematics

Syllabus for Stage I

• Algebra : Understand the definitions and examples of groups (both finite and infinite), cyclic groups, subgroups, homomorphisms, and quotient groups. Study group actions and Sylow theorems, as well as definitions and examples of rings and fields. Familiarize yourself with integers, polynomial rings, and their properties. Key concepts include vector spaces, matrices, determinants, ranks of linear transformations, and characteristic and minimal polynomials, along with inner products and positive definiteness.
• Analysis : Learn the basics of real and complex numbers, including the convergence of sequences and series. Study continuity, differentiability, and Riemann integration of real-valued functions on intervals, as well as elementary functions like polynomial, rational, exponential, logarithmic, and trigonometric functions. Understand the various types of convergence for sequences and series of functions.
• Geometry/Topology : Review the elementary geometric properties of shapes and figures in 2D and 3D Euclidean spaces, such as triangles, circles, and spheres. Familiarize yourself with plane analytic geometry and trigonometry, and learn about metric spaces, including their definitions and basic properties. Key topics include connectedness, compactness, and continuity of functions in metric spaces.
• General Concepts : Understand the pigeonhole principle, induction, basic properties of divisibility, elementary combinatorics (including permutations, combinations, and binomial coefficients), graph reasoning, and basic probability theory.

TIFR GS Syllabus 2025 for Mathematics PhD at CAM

• Real Analysis : Understand Riemann and Riemann-Stieltjes integration, sequences and series of functions, and concepts like uniform convergence and the Arzelà-Ascoli theorem. You should also learn about functions of several variables, continuity, directional derivatives, and fixed-point theorems.
• Ordinary Differential Equations (ODEs) : Focus on the existence and uniqueness of solutions for first-order ODEs, linear ODEs (both homogeneous and non-homogeneous), and the stability of linear equations. Be familiar with the Sturm-Liouville boundary value problem and Green's functions.
• Linear Algebra : Study vector spaces, linear transformations, matrix algebra, and determinants. Important topics include eigenvalues and eigenvectors, the Cayley-Hamilton theorem, and the spectral theorem.
• Topology : Learn about topological spaces, product topology, separation axioms, and concepts like connectedness and compactness. Familiarize yourself with continuous maps and homeomorphisms.
• Functional Analysis : Understand normed linear spaces, Banach spaces, and continuous linear functionals. Key theorems to know include the Hahn-Banach theorem and the open mapping theorem.
• Measure Theory : Get to grips with Lebesgue measure and integration, as well as convergence theorems like Fatou's and the monotone convergence theorem.
• Complex Analysis : Study the Cauchy-Riemann equations, contour integration, and important theorems like Cauchy's integral formula and Liouville’s theorem.
• Probability : Learn about discrete probability, random variables, expectations, variances, and the law of large numbers. Understanding conditional probabilities and limit theorems is essential.

TIFR GS Syllabus 2025 for Physics

• Classical Mechanics : Understand the laws of motion, forces, energy, and momentum.
• Mathematics Relevant to Physics : This includes calculus, linear algebra, and differential equations that are essential for solving physical problems.
• Electricity and Magnetism : Study electric fields, magnetic fields, circuits, and the principles of electromagnetism.
• Quantum Mechanics : Familiarize yourself with the basic concepts of quantum theory, including wave-particle duality and uncertainty principles.
• Heat, Thermodynamics, and Statistical Physics : Learn about temperature, heat transfer, laws of thermodynamics, and statistical methods used in physics.
• General Physics : This encompasses a broad range of fundamental topics in physics.
• Modern Physics : Explore recent developments in physics, including atomic and nuclear physics.
• Electronics and Experimental Physics : Gain knowledge in circuits, signals, and the practical aspects of conducting experiments in physics.

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