 # BITS Pilani

• Page last updated on Thursday, July 18, 2019

# Courses ## M.Sc. (Hons.) Mathematics

M.Sc. (Mathematics)

Students in this programme will be expected to complete the following courses, normally over a period of eight semesters (4 years):

 Year First Semester Second Semester I BIO        F110      Biology Laboratory MATH     F112        Mathematics II BIO        F111      General Biology ME           F110        Workshop Practice CHEM   F110      Chemistry Laboratory CS            F111        Computer Programming CHEM   F111      General Chemistry EEE          F111        Electrical Sciences MATH   F111      Mathematics I BITS          F112         Technical Report Writing PHY       F110      Physics Laboratory MATH      F113       Probability and Statistics PHY       F111      Mechanics, Oscillations                              and Waves BITS         F111       Thermodynamics BITS      F110      Engineering Graphics II MATH     F211     Mathematics-III                   Humanities Electives ECON     F211      Principles of Economics                                  or MATH     F212     Optimization MGTS    F211       Principles of Management                        Humanities Electives MATH     F213     Discrete Mathematics MATH    F241      Mathematical Methods MATH     F214     Elementary Real Analysis MATH    F242     Operation Research MATH     F215     Algebra-I MATH    F243      Graphs & Networks BITS        F225     Environmental Studies MATH    F244     Measure & Integration III Open/Humanities electives Open/ Humanities elective MATH     F311     Introduction to topology MATH    F341     Introduction to functional     analysis MATH     F312     Ordinary Differential                               Equation MATH    F342     Differential Geometry MATH     F313     Numerical Analysis MATH    F343     Partial Differential                              Equations Discipline elective Discipline elective IV Open electives BITS    F412         Practice School – II or BITS    F421T       Thesis

MATH F111 Mathematics I

Functions and graphs; limit and continuity; applications of derivative and integral. Conics; polar coordinates; convergence of sequences and series. Maclaurin and Taylor series. Partial derivatives. Vector calculus in Rn; vector analysis; theorems of Green, Gauss and Stokes

MATH F112 Mathematics II

Complex numbers, analytic functions, Cauchy's theorems; elementary functions; series expansions; calculus of residues and applications. Vector space; basis and dimension; linear transformation; range and kernel of a linear transformation; row reduction method and its application to linear system of equations.

MATH F113 Probability & Statistics

Probability spaces; conditional probability and independence; random variables and probability distributions;marginal and conditional distributions; independent random variables; mathematical expectation; mean and variance; binomial, Poisson and normal distributions; sum of independent random variables; law of large numbers; central limit theorem (without proof);sampling distribution and test for mean using normal and student's t distribution; test of hypothesis; correlation and linear regression.

MATH F211 Mathematics III

Eigen-values and eigen-vectors. Inner product space and orthonormal bases. Elementary differential equations, Hypergeometric equations, Lengendre polynomials, Bessel functions; Fourier series; Sturm-Liouville problem, series solution for differential equation, systems of first order equations; Laplace transformation and application to differential equations; one dimensional wave equation, one dimensional heat equation & Laplace equation in rectangular form.

MATH F212 Optimization

Introduction to optimization; linear programming; simplex methods; duality and sensitivity analysis; transportation model and its variants; integer linear programming nonlinear programming; multi-objective optimization;evolutionary computation techniques.

MATH F213 Discrete Mathematics

Logic and methods of proof, Elementary Combinatorics, recurrence relations, Relations and digraphs, orderings, Boolean algebra and Boolean functions.

MATH F214 Elementary Real Analysis

Countability and uncountability of sets; real numbers; limits and continuity; compactness and connectedness in a metric space;

Riemann integration; uniform convergence.

MATH F215 Algebra-I

Groups, subgroups, a counting principle, normal subgroups and quotient groups, Cayley’s theorem, automorphisms, permutation groups, and Sylow’s theorems. Rings, ring of real quaternions, ideals and quotient rings, homorphisms, Eculidean rings, polynomial rings, and polynomials over the rational field.

MATH F241 Mathematical Methods

Integral Transforms: Fourier, Fourier sine/cosine and their inverse transforms (properties, convolution theorem and application to solve differential equation), Discrete Fourier Series, Fast Fourier transform, Calculus of Variation: Introduction, Variational problem with functionals containing first order derivatives and Euler equations, Variational problem with moving boundaries. Integral equations: Classification of integral equations, Voltera equations, Fredholm equations, Greens functions.

MATH F242 Operations Research

Introduction to Data Processing; Files and File Structures; Indexing Techniques; Sorting, Searching and Merging Techniques; Introduction to Database Management Systems; Design of Information Systems; Emerging trends in Data Processing.

MATH F243 Graphs and Networks

Basic concepts of graphs and digraphs behind electrical communication and other networks behind social, economic and empirical structures; connectivity, reachability and vulnerability; trees, tournaments and matroids; planarity; routing and matching problems; representations; various algorithms; applications.

MATH F244 Measure and Integration

Lebesgue measure and integration in real numbers, Convergence and Convergence theorems, absolutely continuous functions, differentiability and integrability, theory of square integrable functions, and abstract spaces.

MATH F311 Introduction to Topology

Metric Spaces; Topological Spaces - subspaces, Continuity and homoeomorphism, Quotient spaces and product spaces; separation Axioms; Urysohn’s Lemma and Tietze extension Theorem; Connectedness; Compactness, Tychonoff’s Theorem, Locally Compact Spaces; Homohtopy and the fundamental group.

MATH F341 Introduction to Functional Analysis

Banach spaces; fundamental theorems of functional analysis; Hilbert space; elementary operator theory; spectral theory for self-adjoint operators.

MATH F342 Differential Geometry

Curve in the plane and 3D-space; Curvature of curves; Surfaces in 3D-space; First Fundamental form; Curvature of Surfaces; Gaussian and mean Curvatures; Theorema Egreguim; Geodesics; Gauss-Bonnet Theorem.

MATH F343 Partial Differential Equations

Nonlinear equations of first order, Charpits Method, Method of Characteristics; Elliptic, parabolic and hyperbolic partial differential equations of order 2, maximum principle, Duhamel’s principle, Greens function, Laplace transform & Fourier transform technique, solutions satisfying given conditions, partial differential equations in engineering & science.

MATH F312 Ordinary Differential Equations

Existence and uniqueness theorems; properties of linear systems; behaviour of solutions of nth order equations; asymptotic behaviour of linear systems; stability of linear and weakly nonlinear systems; conditions for boundedness and the number of zeros of the nontrivial solutions of second order equations; stability by Liapunov's direct method; autonomous and non-autonomous systems.

MATH F313 Numerical Analysis

Solution of non-linear algebraic equation; interpolation and approximation; numerical differentiation and quadrature; solution of ordinary differential equations; systems of linear equations; matrix inversion; eigenvalue and eigenvector problems; round off and conditioning.

DISCIPLINE ELECTIVE COURSES

BITS F314     Game Theory and Its Applications

BITS F343     Fuzzy Logic and Applications

BITS F463     Cryptography

CS F211        Data Structures and Algorithms

CS F364         Design and Analysis of Algorithms

MATH F231   Number Theory

MATH F314   Algebra-II

MATH F353   Statistical Inference and Applications

MATH F354   Complex Analysis

MATH F420   Mathematical Modeling

MATH F421   Combinatorial Mathematics

MATH F422   Numerical Methodology for Partial Differential Equations

MATH F423   Introduction to Algebraic Topology

MATH F424   Applied Stochastic Process

MATH F431   Distribution Theory

MATH F432   Applied Statistical Methods

MATH F441   Discrete Mathematical Structures

MATH F444   Numerical Solutions of Ordinary Differential Equations

MATH F445  Mathematical Fluid Dynamics

MATH F456  Cosmology

MATH F471  Nonlinear Optimization

MATH F481 Commutative Algebra

MATH F492 Wavelet analysis and applications

### Picture gallery for Mathematics Picture gallery for Mathematics