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ISI

B Stat:
Algebra
  1. Sets
  2. Operations on sets
  3. Prime numbers
  4. Factorization of integers and divisibility
  5. Rational and irrational numbers
  6. Permutations and combinations
  7. Basic probability
  8. Binomial Theorem
  9. Logarithms
  10. Polynomials
  11. Remainder Theorem
  12. Theory of quadratic equations and expressions
  13. Relations between roots and coefficients
  14. Arithmetic and geometric progressions
  15. Inequalities involving arithmetic
  16. Geometric & harmonic means
  17. Complex numbers
  18. Matrices and determinants
Geometry:
  1. Plane geometry
  2. The geometry of 2 dimensions with Cartesian and polar coordinates
  3. The equation of a line
  4. The angle between two lines
  5. Distance from a point to a line
  6. The concept of a Locus
  7. Area of a triangle
  8. Equations of circle
  9. Parabola
  10. Ellipse and hyperbola and equations of their tangents and normal
  11. Mensuration
Trigonometry:
  1. Measures of angles
  2. Trigonometric and inverse trigonometric functions
  3. Trigonometric identities including addition formulae
  4. Solutions of trigonometric equations
  5. Properties of triangles
  6. Heights and distances
Calculus:
  1. Sequences
  2. Bounded sequences
  3. Monotone sequences
  4. Limit of a sequence
  5. Functions
  6. One-one functions
  7. Onto functions
  8. Limits and continuity
  9. Derivatives and methods of differentiation
  10. Slope of a curve
  11. Tangents and normal
  12. Maxima and minima
  13. Using calculus to sketch graphs of functions
  14. Methods of integration
  15. Definite and indefinite integrals
  16. Evaluation of area using integrals
M.S. (QE)
Syllabus for PEA (Mathematics)
 
  1. Algebra
  2. Binomial Theorem
  3. AP
  4. GP
  5. Series
  6. Permutations and Combinations
  7. Theory of Polynomial Equations
Linear Algebra
  1. Vector spaces
  2. Linear transformations
  3. Matrix representations and elementary operations
  4. Systems of linear equations
Calculus
  1. Functions
  2. Limits
  3. Continuity
  4. Differentiation of functions of one or more variables
  5. Unconstrained Optimization
  6. Definite and Indefinite Integrals
  7. Integration by parts and integration by substitution
  8. Convexity and quasi-convexity
  9. Constrained optimization of functions of not more than two variables
  10. The implicit function theorem
  11. Homogeneous and homothetic functions.
Elementary Statistics
  1. Elementary probability theory
  2. Measures of central tendency
  3. Dispersion
  4. Correlation and regression
  5. Probability distributions
  6. Standard distributions-Binomial and Normal.
Syllabus for PEB (Economics)
 
  1. Microeconomics
  2. Theory of consumer behavior
  3. Theory of production
  4. The market structure under perfect competition
  5. Monopoly
  6. Price discrimination
  7. Duopoly with Cournot and Bertrand competition
  8. Public goods
  9. Externalities
  10. General equilibrium
  11. Welfare economics
Macroeconomics
  1. National income accounting
  2. Simple Keynesian Model of income determination and the multiplier
  3. IS-LM Model
  4. Models of aggregate demand and aggregate supply
  5. Money
  6. Banking and inflation
  7. Phillips Curve
  8. Elementary open-economy macroeconomics
  9. Harrod-Domar
  10. Solow
  11. Optimal growth models.
M.S. (QMS)
Algebra
Binomial Theorem, AP, GP, HP, Exponential and Logarithmic Series, Sequence, Permutations and Combinations, Theory of Equations.
 
Matrix Algebra
Vectors and Matrices, Matrix Operations, Determinants
 
Calculus
Functions, Limits, Continuity, Differentiation of functions of one or more variables Unconstrained Optimization, Definite and Indefinite Integrals: Integration by parts and integration by substitution. Elements of Probability and Probability Distributions.
 
M.Tech.(QROR)
PART I: STATISTICS / MATHEMATICS STREAM Statistics (S1)
  1. Descriptive statistics for univariate, bivariate and multivariate data.
  2. Standard univariate probability distributions [Binomial, Poisson, Normal] and their fittings, properties of distributions. Sampling distributions.
  3. Theory of estimation and tests of statistical hypotheses.
  4. Simple and Multiple linear regression, linear statistical models, ANOVA.
  5. Principles of experimental designs and basic designs [CRD, RBD & LSD], Full factorial design, Confounding and blocking in 2k factorial designs
  6. Elements of nonparametric inference.
  7. Elements of the categorical data analysis.
  8. Sample surveys – simple random sampling with and without replacement, stratified and cluster sampling.
Probability (S2)
  1. Classical definition of probability and standard results on operations with events, conditional probability, and independence.
  2. Distributions of discrete type [Bernoulli, Binomial, Multinomial, Hypergeometric, Poisson, Geometric and Negative Binomial] and continuous type [Uniform, Exponential, Normal, Gamma, Beta] random variables and their moments.
  3. Bivariate distributions (with special emphasis on bivariate normal), marginal and conditional distributions, correlation and regression.
  4. Multivariate distributions, marginal and conditional distributions, regression, independence, partial and multiple correlations.
  5. Order statistics [including distributions of extreme values and of sample range for uniform and exponential distributions].
  6. Distributions of functions of random variables.
  7. Multivariate normal distribution [density, marginal and conditional distributions, regression].
  8. Weak law of large numbers, central limit theorem.
  9. Basics of Markov chains and Poisson processes. PART II: ENGINEERING STREAM Mathematics (E1)
  10. Quadratic equations, Roots of polynomial, AP, GP, HP, Divisibility and Prime numbers, Binomial theorem
  11. Inequalities, permutation and combination, complex numbers and De Moivre’s theorem.
  12. Elementary set theory, functions, and relations, matrices, determinants, solutions of linear equations.
  13. Trigonometry [multiple and sub-multiple angles, inverse circular functions, identities, solutions of equations, properties of triangles].
  14. Coordinate geometry (two dimensions) [straight line, circle, parabola, ellipse, and hyperbola], plane geometry, Mensuration.
  15. Sequences, series and their convergence and divergence, power series, limit and continuity of functions of one or more variables, differentiation and its applications, maxima and minima, integration, definite integrals areas using integrals, ordinary and partial differential equations (up to second order) Engineering and Technology (E2) Engineering Mechanics and Thermodynamics
  16. Forces in plane and space, analysis of trusses, beams, columns, friction, principles of strength of materials, work-energy principle, a moment of inertia, the plane motion of rigid bodies, belt drives, gearing.
  17. Laws of thermodynamics, internal energy, work and heat changes, reversible changes, adiabatic changes, the heat of formation, combustion, reaction, solution and dilution, entropy and free energy and maximum work function, reversible cycle and its efficiency, principles of internal combustion engines. Principles of refrigeration. Electrical and Electronics Engineering
  18. DC circuits, AC circuits (1-φ), energy and power relationships, Transformer, DC and AC machines, concepts of control theory and applications.
  19. Network analysis, 2 port network, transmission lines, Elementary electronics (including amplifiers, oscillators, and op-amp circuits), analog and digital electronic circuits. Engineering Drawing
  20. The concept of projection, point projection, line projection, plan, elevation, sectional view (1st angle / 3rd angle) of simple mechanical objects, isometric view, dimensioning, A sketch of machine parts. (Use of Set Square, compass and diagonal scale should suffice).
 
 
 

 

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