The IUCAA-NCRA graduate school (conducted jointly with the National Centre for Radio Astrophysics (NCRA), Pune) is meant for the Ph.D. students of IUCAA and NCRA. Coursework is divided into two semesters (four terms) spread over one year. Each term is of roughly seven weeks duration. Students are taught relevant advanced courses in physics and are also introduced to courses in astronomy and astrophysics. The graduate school structure is shown below. The number of teaching hours is shown in parentheses; the dates may vary slightly.

Syllabus for the IUCAA - NCRA graduate school courses

(a) The courses are designed, emphasizing the aspects which are directly relevant to Astronomy and Astrophysics. It is assumed that unnecessary repetition of material which is already taught at M.Sc. is avoided. While selecting students for IUCAA/NCRA we usually ensure that the student is familiar with physics at the level of M.Sc. and there is no need for routine material to be repeated in the graduate course.

(b) The syllabus provide enough avenues for topics which are of "local interest" to be included in the graduate school. This is necessary so that graduate students coming out of IUCAA/NCRA not only have a comprehensive grasp of the A & A but are also aware of the key research areas in which these two institutions are concentrating at present.

01. Methods of Mathematical Physics I

[The emphasis will be on practical aspects of using mathematics to solve problems rather than on formal mathematical proofs. Emphasize on Green functions, and Fourier analysis].

Sturm-Liouville problem and its connection with special functions - Partial differential equations (inhomogeneous and homogeneous wave equations, diffusion equation, Green functions) - WKB and other approximation methods, series expansions, saddle-point, etc. - Fourier analysis.

02. Introduction to Astronomy and Astrophysics I

[All these topics will come up for detailed study later; the aim of this course will be to connect physics with astrophysics at an order-of-magnitude level and to introduce conventions and jargons of A & A to a physics student].

Earth-solar system - The Sun as a star - Stellar structure and evolution - The HR diagram - Colours, magnitudes, Spectral classification - White dwarfs, neutron stars, black holes - Binaries - ISM - Structure of Milky Way - Stellar population and galactic structure - Cosmology - Brief description of Galaxy morphology and evolution - Active Galaxies - Clusters of Galaxies.

03. Electrodynamics and Radiative Processes I

Review of Maxwell's equations, and M.Sc. level electrodynamics - Motion of charged particle in E, B fields - Electromagnetic waves - Polarization and geometrical optics - Radiation of electromagnetic waves - Scattering of radiation (Thomson and Compton) - Bremsstrahlung and synchrotron radiation.

04. Quantum and Statistical Mechanics I (Quantum Mechanics)

[The Course will emphasize the functionality of QM rather than its mathematical or conceptual structure].

Overview of M.Sc. level quantum mechanics - Solution of Schrodinger equation in 1 d and potential motion - Quasi classical case, WKB - Hydrogen atom and the structure of periodic table - Perturbation theory - Fine structure and hyperfine structure (21 cm) - Quantum theory of radiation - Energy levels of atoms, and molecules and selection rules.

05. Methods of Mathematical Physics II (General Relativity)

Physical basis for GR - Tensor analysis - Geodesics, connection and curvature - Einstein equations - Schwarzschild metric (orbits and classical tests of GR) - Black holes - Gravitational waves - FRW spacetime.

06. Introduction to Astronomy and Astrophysics II (Stellar Physics)

Observational data on stars (types of stars, spectral classification, regions of HR diagram) - Basics of nuclear energy generation - Sources of opacity - Steady state stellar models (homologous models and multilayered configurations) - Stellar evolution (simple analytical estimates and summary of numerical results) - Supernova and SNR - End stages of stellar evolution (white dwarfs, neutron stars and black holes) - Pulsars - Evolution of binary star systems - Star formation (including brown dwarfs) - Star cluster.

07. Electrodynamics and Radiative Processes II (Astrophysical Processes : Fluid dynamics, Radiative processes and Plasmas)

Basics of fluid dynamics - Hydrostatic equilibrium, with applications to self gravitating bodies - Instabilities - Accretion and winds - Shocks - Turbulence - Basics of plasma physics - MHD - Dynamos - Radiative processes in astrophysical systems : Bremsstrahlung, synchrotron radiation, Compton and inverse Compton processes - Macroscopic description of radiation field - Moments of radiative transfer equations and simple approximate solutions - Ionisation and recombination processes.

08. Quantum and Statistical Mechanics II (Statistical Mechanics)

Overview of M.Sc. level statistical physics - Basics of statistical mechanics and thermodynamics - Boltzmann, Bose, Fermi distributions - Applications to classical gases, electron degeneracy in white dwarfs - Photons - Bose condensation and superfluidity - Ionisation and pair creation equilibria - Phase transitions - Elementary introduction to stochastic processes.

09. Astronomical Techniques I (Incoherent Detection)

Time and coordinate measurements - Atmospheric effects (absorption, seeing, ...) - Basics of telescopes - Noise and statistics - Photon detectors - Basics of photometry - Spectroscopy and polarimetry.

10. Galaxies : Structure, Dynamics and Evolution

Galaxies as self gravitating objects, virial equilibrium - Estimates of collision times - Collisionless Boltzmann equation and some steady state solutions - Globular clusters - stability - Spiral structure, bars and disc dynamics - Ellipticals - Galaxy morphology - Chemical evolution - Galaxy formation and evolution.

11. Extragalactic Astronomy I (Cosmology)

Friedmann models (geometrical and physical aspects) - Thermal history of the universe from T = 1 GeV to T = 900 K - Linear growth of perturbations - Anisotropies in CMBR and comparison with observations - Nonlinear evolution of perturbations (Zeldovich approximation, spherical top hat, basic idea of simulation results) - Segregation of baryons and dark matter - Very early universe and inflation - Clusters and superclusters - Overall structure of IGM - Gunn-Peterson effect - Quasar absorption systems - High reshift galaxies.

12. Astronomical Techniques II (Coherent Detection)

Partial coherence - Aperture synthesis and image reconstruction - High angular resolution techniques and astrometry - Databases in astronomy.

13. Interstellar Medium

Extinction and reddening of star light, dust - 21 cm, galaxy rotation curves, HI distribution - Ionised gas, pulsar DM - HII regions - Cooling and heating - Shocks - Supernovae remnants - Phases of the ISM - Magnetic field and Faraday rotation - Cosmic rays - Molecular clouds and star formation.

14. Extragalactic Astronomy II (Radio Galaxies and Quasars)

Phenomenology of AGNs (Seyferts, Quasars, Radio Galaxies, LINERS, BL Lacs) with a survey of continuum, emission and absorption features of spectra - Black hole and accretion disc models for AGNs - Emission line regions (BLR, NLR) - Physics of jets and hot spots.

15. Project Work

This lasts for two months, and the student is expected to submit a report and give a seminar.

16. Topical Course (Not for first year students)

Topical courses will be given by IUCAA/NCRA members and visiting faculty which graduate students can take for credit. Each of the topical courses will credit as half course and will involve a maximum of 12 lectures on a focused topic. Students can take a project or a reading course with a faculty member other than their guide, to count as a Topical Course. Students will be graded pass/fail by the lecturer. Thesis supervisors will ensure that their students pass at least one of these topical courses before they submit the thesis.

**Grading System :**

Marks out of 100

< 41 C

41-50 B minus

51-60 B

61-70 B plus

71-80 A minus

81-90 A

91-100 A plus

(a) Any Research Scholar getting less than 41 % marks (grade C) fails the course.

(b) Any Research Scholar can get only two Cs (less than 41 % marks) overall.

(c) If any Research Scholar gets three or more Cs overall, then he/she will be asked to leave the Graduate School.

(d) At the end of the Graduate School, the over all performance should be B+ (65%) or above.

(e) Any Research Scholar satisfactorily fulfils all the above norms is said to clear the Graduate School successfullly.

(f) All Research Scholars must clear all Graduate School courses before they submit their thesis to the University of Pune.

(g) All Research Scholars must pass/clear at least one Topical Course before they submit their thesis to the University of Pune.

(h) All Indian Research Scholars should pass the CSIR/UGC NET JRF (or at least Lecturership (LS)) within two years of joining IUCAA.