### 2.6 Inter-disciplinary Core Courses and Core Electives

#### IDC101: Introduction to computers

[Cr:2, Lc:1, Tt:0, Lb:3]

Course Outline

• Overview of scientific computing and the role of computers in solving scientific problems.
• Linux Essentials. Operating System concepts and features. Basic commands (file, directory and disk related commands). File system and attributes. I/O devices. Shell and elements of shell programming.
• Editors (Vi and Emacs)
• Number representation in computers and roundoff error. Implications for numerical computing.
• Python programming. Basics and flowcharts. Data types and building blocks. Control statement. Functions. Arrays. Input/Output.
• Data visualisation and analysis, statistical analysis, curve fitting using the least square fit approach.
• Series summation, numerical integration.
• Pseudo random numbers, applications of random sequences in scientific computing, simulating data and experiments, estimating errors in experiments using simulations.
• Solutions of algebraic equations, iterative solutions. Recursion relations, logistics map. Brief overview of fractals resulting from simple maps. Bisection method. Newton-Raphson method.
• Ordinary differential equations, coupled equations, second order equations. Applications in evolution of population, reaction rates, mechanics.
• Systems of linear equations, matrices, row reduction, diagonalisation. Two dimensional arrays. Cellular automata.

• Richard Peterson, Linux: The Complete Reference 6th edition, Tata McGraw (2008).
• The online material available at http://docs.python.org/

#### IDC102: Hands-on electronics

[Cr:2, Lc:1, Tt:0, Lb:3]

Course Outline

• In this course the emphasis will be on practical knowledge and not on teaching electronics as a theory subject. The topics below provide a framework from which the instructor can choose experiments:
• Electronic Devices: Basic concepts of AC & DC current and voltage. Signals(sinusoidal and other) and signal sources. Voltage and current relationships in lumped circuit elements(Resistor, Capacitor and Inductor). Reactance and Impedance. Voltage current sources.
• Passive components. Device principle. Device characteristics( Semiconductor Diode and diac, power diode, signal diode, zener diode, LED photo diode varicap). Electromechanical devices, Indicators, variable components
• Active components: BJT, FET & MOSFET (Device principles, Characteristics, Comparison and applications). Amplifier. Switching. Current source.
• Negative resistance Devices: Unijunction Transistor, SCR, TRIAC.
• Power supply principles: Introduction to Linear and SMPS power supplies, basic principles and differences. Introduction to three terminal regulators (78XX, 79xx and LM317).
• Device applications. Diode applications (Rectification, Voltage regulation, Clipping, Clamping, voltage multipliers). Transistor applications (Amplification, oscillator, current source and Switch). Configurations(pushpull, Darlington, Bootstrapping, Differential amplifier).
• Integrated Circuits. Operational amplifier basics. Applications: Offset null, inverting amplifier, noninverting amplifier, logarithmic amplifier, integrator, differentiator, comparator, active rectifier, current to voltage convertion. Timer IC 555 basics , application as astable, monostable, bistable multivibrator.
• Digital Electronics: Introduction to Boolean Algebra, Number systems, Logic gates. Short project on a design/simulation application involving one of the devices studied using circuit simulator and realise the design on a PCB.

• P. Horowitz & Winfield Hill, The Art of Electronics, 02nd edition, Cambridge University Press (1989).
• R. L. Boylestad and L. Nashelsky, Electronics devices and circuit theory, 09th edition, Prentice Hall (2005).
• A. P. Malvino, Electronic principles, 06th edition, Career Education (1998).

#### IDC201: Astronomy and astrophysics

[Cr:2, Lc:2, Tt:0, Lb:0]

Course Outline

• Celestial coordinates, time measurement, rising, setting, meridian crossing of sources. circumpolar objects.
• Quantifying fluxes, magnitudes, absolute magnitudes, colour. Extinction, estimation of extinction.
• Distance measurements: parallax, moving cluster method, HR-Diagram method, Cepheid variables, Supernovae of type Ia.
• Two body systems, orbits, the effect of radiation pressure on orbits and cometary tails. Using observations of binary stars to infer physical properties of stars. Discovering exo-planets. Röche limit. Lagrange points.
• Stars: observed properties of stars, main sequence. Central pressure and temperature in stars. Nuclear reactions and generation of energy. Relation between mass, radius and luminosity of main sequence stars. Life time on main sequence, variation with mass of stars. Evolution of stars beyond the main sequence.
• Stellar remnants: white dwarfs, Chandrasekhar limit, Neutron stars, Black holes.
• Gravitational waves and other probes of compact binaries.
• Inter-stellar medium (ISM), Jeans length. phases of ISM, estimation using pressure equilibrium. photo-ionization equilibrium.
• Galaxies. Properties of galaxies, morphological classification. Structure and dynamics of spiral galaxies. Oort’s constants, rotation curves. Structure and dynamics of elliptical galaxies. Groups and Clusters of galaxies.
• Expansion of the universe, Hubble’s law. Newtonian cosmology. Estimating cosmological parameters from observations. Thermal and expansion history of the universe.

• H. Karttunen, P. Kröger, H. Oja, M. Poutanen and K. J. Donner, Fundamental Astronomy, 5th edition, Springer (2007).
• A. E. Roy and D. Clarke, Astronomy: Principles and Practice, 4th edition, CRC Press (2003).
• Bradley W. Carroll and Dale A. Ostlie, Introduction to Modern Astrophysics, IInd Edition, Addison Wesley (2006)

#### IDC202: Chemical biology

[Cr:2, Lc:2, Tt:0, Lb:0]

Course Outline

• An introduction to biological molecules and chemical biology
• Physicochemical interactions, water structure, molecular symmetry and chirality
• The molecules of life: Carbohydrates, steroids, vitamins, coenzymes, hormones, lipids and nucleic acids, amino acids, peptides, and proteins
• Protein structure, function, conformation, folding and misfolding
• Enzyme catalysis, inhibition and drug design
• Chemical and biological synthesis
• Molecular recognition, binding, supramolecular assemblies and conformational dynamics
• Molecular selection, evolution and chemical genetics
• Techniques in Chemical Biology: Fluorescence, IR, CD, NMR, X-ray, microscopy, mass spectrometry, light scattering, ultrafast spectroscopy and single molecule biophysics

• R. J. Simmonds, Chemistry of Biomolecules, RSC (1992).
• Berg, Tymoczko and Stryer, Biochemistry W. H Freeman, 6th edition (2006).
• A. D. Miller, J. Tanner Essentails of Chemical Biology Wiley (2008).
• Editors: B. Larijani, C. A. Rosser, R. Woscholski, Chemical Biology: Techniques and Applications Wiley (2006).

#### IDC203: Introduction to earth sciences

[Cr:2, Lc:2, Tt:0, Lb:0]

Course Outline

• Introduction to the Earth System
• From the Big Bang to the formation of the Solar system
• Planetary formation and differentiation
• The Earths Interior
• Plate tectonics the unifying theory of Geology
• Folding and faulting
• Earthquakes and Volcanoes
• Classes of rock forming minerals
• Mineral structures
• Igneous Rocks
• Metamorphic Rocks
• Sedimentary rocks: Sedimentary basins, deposition and burial, diagenesis, classes of sedimentary rocks
• Rock cycle, basic rock identification
• Weathering Erosion and Mass wasting
• Stream Transport: From Mountains to Oceans
• Wind as transporting and depositional agent
• sedimentary rocks and fossil fuel reserves
• Sedimentary rocks and fossils
• The special role of sedimentary rocks for dating
• Sedimentary rocks, the evolution of life and Geobiology
• Absolute dating tools
• The Climate System
• The Hydrological Cycle and Ground water
• The Human Impact on the environment

• Grotzinger and Jordan, Understanding Earth R. Ruddiman, Earths climate, Past Present Future, W. H. Freeman (2000), Paperback, 465 pages, ISBN 0716737418 / 9780716737414
• Assignments from the ”Big History Project” Unit 1-6, 8 &10 on Khan academy Topics: ”What is Big History”, ”The Big Bang”, ”Stars & Elements”,”Our Solar System and Earth”, ”Life”, ”Early Humans”, ”The Acceleration”, ”Future”.

#### IDC204: Theory of computation

[Cr:2, Lc:2, Tt:0, Lb:0]

Course Outline

• Mathematical notions: Sets, Functions, Sequences, Graphs, Boolean Logic, Proofs and types of proofs.
• Languages: Context free grammar, Examples, Ambiguity, Chomsky normal forms.
• Computability: Origin of Computability Theory, Gödel and the discovery of incomputability, Church-Turing thesis, Turing machines and their variants, Examples, Decidability, Reducibility, Recursion Theorem, Self referencing, Russell’s Paradox.
• Time Complexity: Big-O and small-o notation, Analysing algorithms, P and NP problems, Vertex cover problem, Hamiltonian path problem, Subset sum problem.
• Space Complexity: Savitch’s problem, The class PSPACE, Classes L and NL.
• Computing time and space complexity for various algorithms.

• Michael Sipser, Introduction to the Theory of computation, Course Technology Publishers (1996).
• S. Barry Cooper, Computability Theory, CRC Press (2003).

#### IDC205: Differential equations for scientists

[Cr:2, Lc:2, Tt:0, Lb:0]

Course Outline

• Meaning of a differential equation and its solution, examples, families of curves, orthogonal trajectories.
• First order equations: Homogeneous, exact, linear, Bernoulli, Riccati and Clairaut equations, equations reducible to first order equations.
• Second and higher order linear equations, linear equations with constant coefficients, general solution of homogeneous equations, operator method for finding a particular solution, vibra- tions in mechanical and electrical systems. Power series method: Legendre, Hermite, Bessel and hypergeometric equation.
• Special functions: Legendre, Hermite and Chebychev polynomials, Bessel functions and appli- cations.

• Earl A. Coddington, An Introduction to Ordinary Differential Equations, Dover Publications (1989).
• Ravi P. Agarwal and Donal O’Regan, Ordinary and Partial Differential Equations, Springer (2008).
• Shepley L. Ross, Differential Equations, Wiley (1984).
• George F. Simmons, Differential Equations with Applications and Historical Notes, Tata McGraw-Hill Publishing Company (1978).

#### IDC206: Quantum physics for scientists

[Cr:2, Lc:2, Tt:0, Lb:0]

Course Outline

• This course is meant to provide a full overview of quantum physics and its impact on our understanding of the physical world. The course will cover aspects of modern physics for non-physics majors who will most probably not encounter these concepts in their major years, and will cover introductory quantum mechanics for physics majors, who will do more specialized courses later on.
• The birth of quantum theory will be explored from a historical point of view. Black body radiation, Photoelectric effect, photons, Compton scattering, Franck-Hertz experiment, Bohr atom and electron diffraction, deBroglie waves and the Wave particle duality of matter and light. An introduction to wave mechanics and Schroedinger’s equation in one, two and three dimensions.
• An appreciation of the quantum world at an informal level will be taken up across systems and across scales. Examples from particle physics, collective quantum phenomena, possibilities of building quantum computers etc will be discussed at a non-technical level.

• R. M. Eisberg and R. Resnick, Quantum physics of atoms, molecules, solids, nuclei and particles, Wiley (1974).
• R. P. Feynman, R. B. Leighton and M. L. Sands, The Feynman Lectures on Physics Vol. 3 Addison-Wesley (1989).
• S Gasiorowicz, Quantum Physics , Wiley (2003).
• A. P. French and E. F. Taylor, Introduction to quantum physics, Norton Publishing (1978).

#### IDC207: Number theory and cryptography

[Cr:2, Lc:2, Tt:0, Lb:0]

Course Outline

• Number Theory: Diophantine equations, primes and their distribution, cryptography, divisibility, Euclidean algorithm, linear Diophantine equations, Fermat and Mersenne numbers, fundamental theorem of arithmetic, Pythagorean triples, differences of squares, prime factorization of factorials, Riemann-zeta function, congruences, Chinese remainder theorem, Fermats little theorem, Eulers theorem, Wilsons theorem.
• Cryptographic applications: Shift and affine ciphers, secret sharing, RSA algorithm
• Congruences: Polynomials mod primes, solutions modulo prime powers, composite moduli.
• Primitive roots: Orders of elements, primitive roots, discrete log problem, existence of primitive roots, Diffie-Hellman key exchange, ElGamal public key cryptosystem, digital dignatures.
• Quadratic reciprocity: Squares and square roots mod primes, Legendre symbol, quadratic reciprocity, applications to cryptography.

• James S. Kraft, Lawrence C. Washington An Introduction to Number Theory with Cryptography,Chapman and Hall/CRC.
• Neal Koblitz, A Course in Number Theory and Cryptography (Graduate Texts in Mathematics), Springer. ISBN-10: 0387942939 ISBN-13: 978-0387942933.
• V V Yaschenko, Cryptography: An Introduction, Student Mathematical Library, AMS, Universities Press India (2009).

#### IDC208: Introduction to environmental sciences

[Cr:2, Lc:2, Tt:0, Lb:0]

Course Outline

• History of the Universe and Earths Geosphere, Atmosphere, Biosphere and the Evolution of Life
• Natural Biogeochemical Cycles and influence of Anthropogenic perturbations: Case study of global carbon cycle
• Soil and Land use: Impact of soil loss and land cover on biogeochemical cycle, Fertilizers and Green Revolution, Agricultural practices and environmental footprints
• Biodiversity. Problems and issues in biodiversity and forestry. Conservation and utilization of biodiversity, Biomes, landscapes, ecosystems
• Hydrological cycle, water resource conservation, rain water harvesting methods, Water Treatment, Regulation of Water Quality, Water purification methods: pros and cons, Water footprint of consumer products
• Renewable and non-renewable sources of energy, fossil fuels and biofuels
• Earths Climate: Radiation balance, Albedo: Particles and Clouds, Greenhouse Effect, International Agreements on Greenhouse Gases, Global warming and Climate change, Impacts of climate change on the Indian environment
• Air quality determinants and criteria air pollutants and their effects
• Toxic Chemicals, Acute and Chronic Toxicity, Persistent Organic Pollutants in the Environment, Waste treatment and segregation, Waste as a resource through 3Rs
• Sustainable development, Case Studies of Environmental Pollution Episodes and Successful Interventions, Glimpses of Field Work; Composting methods

• D. B. Botkin & E. A. Keller, Earth as a Living Planet, 08th edition, John Wiley & Sons (2010).
• Stanley E. Manahan, Environmental Chemistry, Publisher: CRC Press; 9th edition ISBN-10: 1420059203; ISBN-13: 978-1420059205
• J. Girard, Principles of Environmental Chemistry, Jones & Bartlett Learning; ISBN-10: 0763759392; ISBN-13: 978-0763759391