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Syllabus for 2 Year M Sc Applied Mathematics Admission Batch 2015 16. Course Structure for 2yr M Sc in Applied Mathematics 2015 16. 1st Semester 2nd Semester,Theory Contact Hours Theory Contact Hours. Code Subject L T P Credit Code Subject L T P Credit. 15 MMCC101 Real analysis 3 1 0 4 15 MMCC201 Topology 3 1 0 4. 15 MMCC103 Discrete 3 1 0 4 15 MMCC203 Complex 3 1 0 4. Mathematics Analysis, 15 MAMC102 Ordinary 3 0 0 3 15 MMCC202 Numerical 3 0 0 3. Differential Analysis, 15 MMCF107 Data Structure 3 0 0 3 15 MAMC204 Partial 3 0 0 3. with C Differential, 15 MMCC104 Abstract Algebra 3 0 0 3 15 MAMC205 Continuum 3 1 0 4. 15 MAMC105 Linear Algebra 3 1 0 4 15 MAMF206 RDBMS 3 0 0 3. Total 21 Total 21,Practical Sessional Practical Sessional.

Code Subject L T P Credit Code Subject L T P Credit. 15 MMCF151 Data Structure 0 0 3 2 15 MMCC251 Lab on 0 0 3 2. using C Lab Numerical, 15 MAMC152 Seminar 0 0 3 2 15 MAMF252 RDBMS Lab 0 0 3 2. 15 MAMC153 Ethics,Human Values,Total 4 Total 4,Total 21 4 25 Total 21 4 25. Syllabus for 2 Year M Sc Applied Mathematics Admission Batch 2015 16. 3rd Semester 4th Semester,Theory Contact Hours Theory Contact Hours. Code Subject L T P Credit Code Subject L T P Credit. 15 MMCC304 Optimization 3 0 0 3 15 MAMC402 Design Analysis 3 1 0 4. Techniques and Algorithm, 15 MMCC301 Functional 3 1 0 4 15 MMCC401 Differential 3 0 0 3. Analysis Geometry, 15 MAMC302 Probabilities 3 1 0 4 15 MAMC403 Matrix 3 0 0 3.

Stochastic Computation,Elect I 3 1 0 4 Elective III 3 0 0 3. Elect II 3 1 0 4,Total 19 Total 13,Practical Sessional Practical Sessional. Code Subject L T P Credit Code Subject L T P Credit. 15 MMCC351 Optimization Lab 0 0 3 2 15 MAMC451 LAB DAA 2. 15 MMCC352 MAT lab 0 0 3 2 15 MAMC452 LAB Matrix 2. Computation,15 MAMC353 Industry Orient 2 15 MAMC453 PROJECT 8. Total 6 Total 12,Total 19 6 25 Total 13 12 25, Syllabus for 2 Year M Sc Applied Mathematics Admission Batch 2015 16. ELECTIVE I,Sl No CODE,1 15 MAME301 Fluid Dynamics,2 15 MAME302 Computational Finance.

3 15 MAME303 Convex Analysis and optimization,4 15 MAME304 Parallel and Distributive Computing. 5 15 MAME305 Number Theory and Cryptography,6 15 MAME306 Advanced Operating System. 7 15 MAME307 Computer Architecture,ELECTIVE II,Numerical Solution of Differential. 1 15 MAME308 Equation,2 15 MAME309 Advanced Statistics. 3 15 MAME310 Computational Biology,4 15 MAME311 Graph Theory.

5 15 MAME312 Fourier Analysis,6 15 MAME313 Theory of Computation. 7 15 MAME314 Finite Element Method,ELECTIVE III,1 15 MAME401 Computational Fluid Dynamics. Distribution Theory and Sobolev,2 15 MAME402,3 15 MAME403 Artificial Intelligence. 4 15 MAME404 Machine learning,5 15 MAME405 Hydrostatics. 6 15 MAME406 Fuzzy and Rough set theory,7 15 MAME407 Numerical Optimization.

Syllabus for 2 Year M Sc Applied Mathematics Admission Batch 2015 16. DETAILED SYLLABUS,OF SEMESTER I, Syllabus for 2 Year M Sc Applied Mathematics Admission Batch 2015 16. 15 MMCC 101 REAL ANALYSIS 3 1 0,Module I 14 Hours, Introduction to Metric spaces compact set connected set Weistrass Approximation. Theorem Sequence and series of function Uniform convergence Lebesgue measure. Introduction outer measure measurable sets and Lebesgue measure A non measurable. set measurable function The Lebesgue Integral The Rimann integral The Lebesgue. integral of a bounded function over a set of finite measure The integral of a non negative. function The general Lebesgue integral,Module II 14 Hours. Measure and Integration measure spaces measureable functions Integration General. convergence theorem Signed measures The Random Nikodyn theorem The Lp spaces. Measure and Outer measure Outer measure and measurability The extension theorem. The Lebesgue Stieltjes integral Product measures Integral operators Inner measure. Extension by sets measure zero,Module III 12 Hours. Introduction Properties of monotonic functions Functions of bounded variation Total. variation Additive property of total variation Total variation on a x as a function of x. Functions of bounded variation expressed as the difference of two increasing functions. Continuous functions of bounded variation, The Riemann Stieltjes Integrals Introduction Notation The definition of Riemann.

Stieltjes Integral Linear operators Integration by parts Change of variable in Riemann. StetiItjes integrals Reduction to a Riemann Integral Euler s summation formula. Monotonically increasing integrals,1 Real Analysis by H L Royden 3rd edition. Chapter 3 3 1 to 3 5 Chapter 4 1 to 4 4 Chapter 11 Chapter 12 1 to 12 7. 2 Mathematical analysis by Tom M Apostol 2nd Edition Addison Wesley publication. company Inc Newyork 1974,Chapter6 6 1 to 6 8 Chapter7 7 1 to 7 11. Reference Book, 1 Bartle R G Real Analysis John Wiley and Sons Inc 1976. 2 Rudin W Principles of Mathematical Analysis 3rd Edition McGraw Hill Company. New York 1976, 3 Malik S C and Savita Arora Mathematical Anslysis Wiley Eastern Limited New. Delhi 1991, 4 Sanjay Arora and Bansi Lal Introduction to Real Analysis Satya Prakashan New.

Delhi 1991, 5 Gelbaum B R and J Olmsted Counter Examples in Analysis Holden day San. Francisco 1964, Syllabus for 2 Year M Sc Applied Mathematics Admission Batch 2015 16. 6 A L Gupta and N R Gupta Principles of Real Analysis Pearson Education Indian. print 2003, 7 Measure theory and integration by G De Barra willey estern ltd. 15 MMCC 103 DISCRETE MATHEMATICS 3 1 0,Module I 13 Hours. Propositional logic operations First order logic basic logical Operations Propositional. Equivalence Predicates and Universal Existential Quantifiers Nested Quantifiers. Rules of Inference Proof methods and Strategies Sequences and Summations. Mathematical Induction Recursive definition and structural induction Program. Correction, Recurrence relation Solution to recurrence relation Generating functions Principle of.

Inclusion and exclusion Application of Inclusion and Exclusion Principle. Set Theory Relation and their properties Partitions Closure of Relations Warshall s. Algorithm Equivalence relations Partial orderings,Module II 14 Hours. Introduction to graph theory Graph terminology Representation of graphs Isomorphism. Connectivity Euler and Hamiltonian paths Shortest path problems Planar graph Graph. Introduction to trees Application of trees Tree Traversal Minimum Spanning tree. Module III 13 Hours, Matrix representation of a graph Basic ideas of Incidence matrix sub matrix circuit. matrix fundamental circuit matrix cut set matrix path matrix and adjacency matrix. Coloring Chromatic number chromatic partitioning chromatic polynomial matching. Algebraic systems Lattices Distributive and Complemented Lattices Boolean Lattices. Boolean Algrebra Boolean Functions and Boolean Expressions. Text Books, 1 Kenneth H Rosen Discrete Mathematics and its Applications Sixth Edition 2008. Tata McGraw Hill Education New Delhi,Chapters 1 2 2 4 4 6 6 1 6 2 6 4 6 6 7 8 9. 2 C L Liu and D Mohapatra Elements of Discrete Mathematics Third Edition 2008. Tata McGraw Hill Education New Delhi,Chapters 10 10 1 10 10 11 11 1 11 7.

1 J L Mott A Kandel T P Baker Discrete mathematics for Computer Scientists. Mathematicians Second Edition PHI,Chapters 1 2 3 4 4 1 4 5 5 6 6 1 6 5. Chapters 10 10 1 10 10 11 11 1 11 7, Syllabus for 2 Year M Sc Applied Mathematics Admission Batch 2015 16. 15 MAMC102 ORDINARY DIFFERENTIAL EQUATION 3 0 0,Module I 8 hours. Existence and uniqueness of Solution Lipchitz condition Gronwall inequality. Successive approximations Picard s theorem Second order linear equations Separation. and comparison theorems Solutions in series Legendre and Bessel functions. Module II 10 hours, Systems of differential equations Existence and uniqueness of solution of systems. Systems of linear Differential equations nth order equations of a first order system. Fundamental matrix Non homogeneous linear systems linear systems with constant. coefficients Eigen values and Eigen vectors,Module III 12 hours.

Boundary value problems for Ordinary differential equations Green s functions. Construction of Green s functions Non homogenous boundary conditions Self Adjoint. Eigenvalue Problems Sturm Liouville Systems Eigen values and Eigen functions. expansion in Eigen functions Stability Stability of linear and non linear systems. Asymptotically stability Critical points Autonomous Systems Lyapunov stability. Books Recommended, Tyn Myint U Ordinary Differential Equations New York Chapters 2 3 3 1 3 5 4 4 1. 4 4 5 5 1 5 6 6 6 1 6 4 7 7 1 7 3 8 8 1 8 5,Reference Books. 1 S D Deo V Lakshmikantham and V Raghavendra Text book of Ordinary differential. equations 2nd edition TMH, 2 Boyce W and R Diprima Elementary Differential Equations and Boundary Value. Problems New York Wiley, Syllabus for 2 Year M Sc Applied Mathematics Admission Batch 2015 16. 15 MMCF 107 DATA STRUCTURE using C 3 0 0, Module I 10 hours Introduction to data structures storage structure for arrays sparse.

matrices Stacks and Queues representation and application Linked lists Single linked. lists linked list representation of stacks and Queues Operations on polynomials Double. linked list circular list, Module II 10 Hours Dynamic storage management garbage collection and. compaction infix to post fix conversion postfix expression evaluation Trees Tree. terminology Binary tree Binary search tree General tree B tree AVL Tree Complete. Binary Tree representation Tree traversals operation on Binary tree expression. Manipulation, Module III 10 Hours Graphs Graph terminology Representation of graphs path. matrix BFS breadth first search DFS depth first search topological sorting. Warshall s algorithm shortest path algorithm Sorting and Searching techniques. Bubble sort selection sort Insertion sort Quick sort merge sort Heap sort Radix sort. Linear and binary search methods Hashing techniques and hash functions. Text Books 1 Gilberg and Forouzan Data Structure A Pseudo code approach with. C by Thomson publication, 2 Data structure in C by Y Kanetkar TMH publication. Reference Books 1 Pai Data Structures Algorithms Concepts Techniques. Algorithms Tata McGraw Hill, 2 Fundamentals of data structure in C Horowitz Sahani Freed Computer Science. 3 Fundamental of Data Structure Schaums Series Tata McGraw Hill 22 BE. Syllabus for 2 Year M Sc Applied Mathematics Admission Batch 2015 16. 15 MMCC 104 ABSTRACT ALGEBRA 3 1 0,Module I 14 hours.

Normal subgroup Isomorphism theorem Automorphisms Permutation group Cyclic. decomposition and Alternating group Structure theorems for groups Direct Product. finitely generated abelian group Structure theorem for groups Invariants of a finite. abelian group Sylows theorem Unique factorization domain Principal ideal domain. Euclidean domains polynomial rings over UFD,Module II 13 hours. Algebraic extension of fields Irreducible polynomials and Einstein criterion Adjunction. of roots Algebraic extension Algebraically closed fields Normal separable extensions. splitting fields normal extensions Normal separable extension Multiple roots Finite. fields Separable extensions,Module III 13hours, Galois Theory Automorphism groups and fixed field s Fundamental theorem of Galois. theory Application of Galois theory to classical problems Roots of unity and Cyclotomic. polynomials Cyclic extensions Polynomials solvable by radicals Symmetric functions. Ruler and compass constructions, P B Bhattacharya S K Jain and S R Nagpaul Basic Abstact Algebra Cambridge. University Press Chapter 5 Art 2 3 7 Art 1 2 8 Art 1 4 11 Art 1 4 15 Art 1 3. 16 Art 1 2 18 1 5,Reference Books, 1 Vivek Sahai and Vikas Bist Algebra Narosa publication House. 2 I S Luthar and I B S Passi Algebra Vol 1 Groups Narosa publication House. 3 I N Herstein Topics in Algebra Wiley Eastern Ltd. 4 Surjit Singh and Quazi Zameeruddin Modern Algebra Vikas Publishing House. 5 S K Jain S R Nagpal Basic Abstract Algebra Cambridge University Press. Syllabus for 2 Year M Sc Applied Mathematics Admission Batch 2015 16. 15 MAMC 105 LINEAR ALGEBRA 3 1 0,Module I 14 hours.

Geometric interpretation of solution of system of equations in two and three variables. matrix notation solution by elimination and back substitution interpretation in terms of. matrices elimination using matrices elementary matrices properties of operations on. matrices Definition and uniqueness non existence in general singular matrices. calculation of inverse using Gauss Jordan elimination existence of one sided inverse. implies invertibility decomposition of a matrix as product of upper and lower triangular. matrices Vector spaces and Subspaces Solving Ax 0 and Ax b Linear Independence. Basis and Dimension The four fundamental Subspaces graph and networks Linear. Transformations,Module II 13 hours, Orthogonal Vectors and Subspaces Cosines and Projections onto Lines Projections and. Least Squares orthogonal Bases and Gram Schmidt The Faster Fourier Transform. Properties of the determinant formulas for the determinant Expansion of determinant. of a matrix in Cofactors Applications of Determinants. Module III 13 hours, Eigen values and eigenvectors Diagonalisation of a Matrix Difference equations and. powers Markov Matrices Differential equations and stability of differential. Course Structure for 2yr M Sc in Applied Mathematics 2015 16 1st Semester 2nd Semester Theory Contact Hours Theory Contact Hours Code Subject L T P Credit Code Subject L T P Credit 15 MMCC101 Real analysis 3 1 0 4 15 MMCC201 Topology 3 1 0 4 15 MMCC103 Discrete Mathematics 3 1 0 4 15 MMCC203 Complex Analysis 3 1 0 4

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