• Inorganic Chemistry

• Chemical periodicity
• Structure and bonding in homo-and heteronuclear molecules, including shapes of molecules(VSEPR Theory).
• Concepts of acids and bases, Hard-Soft acid base concept, Non-aqueous solvents.
• Main group elements and their compounds: Allotropy, synthesis, structure and bonding, industrial importance of the compounds.
• Transition elements and coordination compounds: structure, bonding theories, spectral and magnetic properties, reaction mechanisms.
• Inner transition elements: spectral and magnetic properties, redox chemistry, analytical applications.
• Organometallic compounds: synthesis,bonding and structure, and reactivity. Organometallics in homogeneous catalysis.
• Cages and metal clusters.
• Analytical chemistry-separation, spectroscopic, electro-and thermoanalytical methods.
• Bioinorganic chemistry: photosystems, porphyrins, metalloenzymes, oxygen transport, electron-transfer reactions; nitrogen fixation, metal complexes in medicine.
• Characterisation of inorganic compounds by IR, Raman, NMR, EPR, Mössbauer, UV-vis, NQR, MS, electron spectroscopy and microscopic techniques.
• Nuclear chemistry: nuclear reactions, fission and fusion, radio-analytical techniques and activation analysis.

• Physical Chemistry:

• Basic principles of quantum mechanics: Postulates; operator algebra; exactly-solvable systems:particle-in-a-box, harmonic oscillator and the hydrogen atom, including shapes of atomic orbitals; orbital and spin angular momenta; tunneling.
• Approximate methods of quantum mechanics: Variational principle; perturbation theory up to second order in energy; applications.
• Atomic structure and spectroscopy; term symbols; many-electron systems and antisymmetry principle.
• Chemical bonding in diatomics; elementary concepts of MO and VB theories; Huckel theory for conjugated π-electron systems.
• Chemical applications of group theory; symmetry elements; point groups; character tables; selection rules.
• Molecular spectroscopy: Rotational and vibrational spectra of diatomic molecules; electronic spectra; IR and Raman activities –selection rules; basic principles of magnetic resonance.
• Chemical thermodynamics: Laws, state and path functions and their applications; thermodynamic description of various types of processes; Maxwell’s relations; spontaneity and equilibria; temperature and pressure dependence of thermodynamic quantities; Le Chatelier principle; elementary description of phase transitions; phase equilibria and phase rule; thermodynamics of ideal and non-ideal gases, and solutions.
• Statistical thermodynamics: Boltzmann distribution; kinetic theory of gases; partition functions and their relation to thermodynamic quantities –calculations for model systems.
• Electrochemistry: Nernst equation, redox systems, electrochemical cells; Debye-Huckel theory; electrolytic conductance –Kohlrausch’s law and its applications; ionic equilibria; conductometric and potentiometric titrations.
• Chemical kinetics: Empirical rate laws and temperature dependence; complex reactions; steady state approximation; determination of reaction mechanisms; collision and transition state theories of rate constants; unimolecular reactions; enzyme kinetics; salt effects; homogeneous catalysis; photochemical reactions.
• Colloids and surfaces: Stability and properties of colloids; isotherms and surface area; heterogeneous catalysis.
• Solid state: Crystal structures; Bragg’s law and applications; band structure of solids.
• Polymer chemistry: Molar masses; kinetics of polymerization.
• Data analysis: Mean and standard deviation; absolute and relative errors; linear regression; covariance and correlation coefficient.

1. The Earth and the Solar System: Milky Way and the solar system. Modern theories on the origin of the Earth and other planetary bodies. Earth‟s orbital parameters, Kepler‟s laws of planetary motion, Geological Time Scale; Space and time scales of processes in the solid Earth, atmosphere and oceans. Radioactive isotopes and their applications.Meteorites Chemical composition andthe Primary differentiation of the earth. Basic principles of stratigraphy. Theories about the origin of life and the nature of fossil record.Earth‟s gravity and magnetic fields and its thermal structure: Concept of Geoid and, spheroid; Isostasy.
2. Earth Materials, Surface Features and Processes: Gross composition and physical properties of important minerals and rocks; properties and processes responsible for mineral concentrations; nature and distribution of rocks and minerals in different units of the earth and different parts of India.Physiography of the Earth; weathering, erosion, transportation and deposition of Earth‟s material; formation of soil, sediments and sedimentary rocks; energy balance of the Earth‟s surface processes; physiographic features and river basins in India
3. Interior of the Earth, Deformation and Tectonics Basic concepts of seismology and internal structure of the Earth. Physico-chemical and seismic properties of Earth‟s interior. Concepts of stress and strain. Behaviour of rocks under stress; Folds, joints and faults. Earthquakes –their causes and measurement. Interplate and intraplate seismicity. Paleomagnetism, sea floor spreading and plate tectonics.

• UNIT –1

• Elementary set theory, finite, countable and uncountable sets, Real number system as a complete ordered field, Archimedean property, supremum, infimum.
• Sequences and series, convergence, limsup, liminf. Bolzano Weierstrass theorem, Heine Borel theorem. Continuity, uniform continuity, differentiability, mean value theorem.
• Sequences and series of functions, uniform convergence.
• Riemann sums and Riemann integral, Improper Integrals.
• Monotonic functions, types of discontinuity, functions of bounded variation, Lebesgue measure, Lebesgue integral.
• Functions of several variables, directional derivative, partial derivative, derivative as a linear transformation, inverse and implicit function theorems.
• Metric spaces, compactness, connectedness.
• Normed linear Spaces. Spaces of continuous functions as examples.
Linear Algebra:
• Vector spaces, subspaces, linear dependence, basis, dimension, algebra of linear transformations.
• Algebra of matrices, rank and determinant of matrices, linear equations. Eigenvalues and eigenvectors, Cayley-Hamilton theorem.
• Change of basis, canonical forms, diagonal forms, triangular forms, Jordan forms.
• Quadratic forms, reduction and classification of quadratic forms

• Algebra of complex numbers, the complex plane, polynomials, power series, transcendental functions such as exponential, trigonometric and hyperbolic functions.
• Analytic functions, Cauchy-Riemann equations.
• Contour integral, Cauchy’s theorem, Cauchy’s integral formula, Liouville’s theorem, Maximum modulus principle, Schwarz lemma, Open mapping theorem.
• Taylor series, Laurent series, calculus of residues. Conformal mappings, Mobius transformations.
Algebra:
• Permutations, combinations, pigeon-hole principle, inclusion-exclusion principle, derangements.
• Fundamental theorem of arithmetic, divisibility in Z, congruences, Chinese Remainder Theorem, Euler’s Ø-function, primitive roots.
• Groups, subgroups, normal subgroups, quotient groups, homomorphisms, cyclic groups, permutation groups, Cayley’s theorem, class equations, Sylow theorems.
• Rings, ideals, prime and maximal ideals, quotient rings, unique factorization domain, principal ideal domain, Euclidean domain.
• Polynomial rings and irreducibility criteria. Fields, finite fields, field extensions, Galois Theory.