The Joint Entrance Screening Test (JEST) is a national level qualifying examination for admissions to PhD programmes in Physics at premier Indian research institutions and a PhD programme in Theoretical Computer Science at the Institute of Mathematical Sciences.
Using JEST results, each institute will call a limited number of candidates for its own selection procedure depending, on its requirements. All selected candidates will receive Research Fellowships from the respective institutes.
Joint Entrance Screening Test (JEST) Syllabus
Vector algebra and vector calculus; linear vector spaces, linear operators, matrices and Eigenvalue problem; SturmLiouville theory, classical orthogonal polynomials; linear ordinary differential equations, exact and series methods of solution ; linear partial differential equations, solution by separation of variables; complex variables, analytic functions, Taylor and Laurent expansions, contour integration; Fourier and Laplace transforms.
Newton's laws, conservation of energy and momentum, collisions; generalized coordinates, the principle of least action, Lagrangian and Hamiltonian formulations of mechanics; symmetry and conservation laws; central force problem, Kepler problem; rigid body motion; small oscillations and normal modes; special relativity in classical mechanics.
Laws of electrostatics and magnetostatics, methods of solving boundary value problems, multipole expansion; fields in conducting, dielectric, diamagnetic and paramagnetic materials; Faradays law and time varying fields; conservation of charge, displacement current; Maxwells equations; energy and momentum of electromagnetic fields, Poynting theorem; propagation of plane electromagnetic waves, reflection and refraction of plane electromagnetic waves, electromagnetic waves in dispersive and conducting media; scalar and vector potentials, Coulomb and Lorentz gauge, wave equation in terms of electromagnetic potentials; radiation from moving charges, retarded and advanced potentials,
Lienard-Wiechert potentials, multipole radiation, Larmor formula.
The uncertainty principle; conceptual basis of quantum mechanics; Schrodinger equation, problems in one, two and three dimensions, bound states and tunnelling, particle in a box, harmonic oscillator, hydrogen atom; matrix formulation of quantum theory, unitary transformations and Hermitian operators and their properties; orbital and spin angular momenta, addition of angular momenta; time independent and time dependent perturbation theory, Fermi golden rule; elementary scattering theory.
Thermodynamics and Statistical Physics
Laws of thermodynamics; work and heat; thermodynamic potentials, Maxwell's relations; statistical ensembles; partition function; classical ideal gas, harmonic oscillators; classical and quantum statistics; Fermi and Bose gases; black body radiation; first and second order phase transitions.
Solid State Physics
Simple crystal structures and X-ray diffraction; lattice vibrations and thermal properties of solids; free electron theory; band theory of solids; metals, semiconductors, and insulators; basic electrical, optical and magnetic properties of solids; elements of superconductivity.
Electronics Diodes, rectifier circuits, junctions, transistors and field effect devices; device characteristics, frequency dependence and applications like active filters and oscillator circuits; solar cells, photodetectors, and LEDs; operational amplifiers and their applications; Boolean algebra, digital techniques and applications: registers, counters, comparators and similar circuits; A/D and D/A converters; microprocessor and microcontroller basics.
Nuclear and Particle Physics
The structure of the nucleus; binding energy, nuclear fusion and fission; radioactive decay, barrier penetration by alpha particles; classification of elementary particles and fundamental interactions, leptons and hadrons, elementary ideas of quark model; conservation laws in particle reactions.
Atomic and Optical Physics
Interference, diffraction, and polarization of light; photoelectric effect; spectra of single and multiple electron atoms; Zeeman and Stark effects; electric dipole transition and selection rules; hyperfine structure; spontaneous and stimulated emission.
Experimental data and error analysis Probability theory
Gaussian and Poisson distributions; error analysis; propagation of errors; significant figures; least square fitting
Mathematic syllabus will cover all books units of B.Sc maths and most of the portion of exam will from the books of M.Sc.
JEST (Theoretical Computer Science)
- Elements of Discrete Mathematics
- Discrete Mathematical Structures with Applications to Computer Science,
- Compilers: Principles, Techniques and Tools
- Fundamentals of Data Structures
- An Introduction to Data Structures with Applications
- Fundamentals of Computer Algorithms
- The Design and Analysis of Computer Algorithms
- Introduction to Algorithms