Four year Degree Program of

Computational Mathematics

BS
(Computational Mathematics)

DEPARTMENT OF MATHEMATICS
UNIVERSITY OF KARACHI

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 DEPARTMENT OF MATHEMATICS
UNIVERSITY OF KARACHI
BS Computational Mathematics
Total Credit Hours: 140

Credit Course
Course No. Course Title
Hours Type
300.1 (E) English – I 2+0 Gen Ed
300.1 (I. S) Islamic Studies OR Ethics (Non-Muslim) 2+0 Gen Ed
SEMESTER - I

300.1 (Civ/Com) Civics and Community Engagement 2+0 Gen Ed

Everyday Science, Astronomy, Physics, Chemistry, Earth
300.1 (N. Sc) 3+0 Gen Ed
Science or Biology
301STA Stats-I 2+1 Int Disc
301PHY Phy-I 2+1 Int Disc
YEAR - 1

CM301 Calculus 3+0 Major

Total Credit Hours 18

300.2 Ideology & Constitution of Pakistan/Pakistan Studies 2+0/2+0 Gen Ed

300.2 Functional English 3+0 Gen Ed
SEMESTER - II

300.2 (Entr) Entrepreneurship 2+0 Gen Ed

Intro to Soc. Sc., Urdu, Economics, History, Geography or
300.2 (Soc. Sc) 2+0 Gen Ed
Psychology.
302STA Stats-II 2+1 Int Disc
302PHY Phy-II 2+1 Int Disc
CM302 Multivariable Calculus and Geometry 3+0 Major
Total Credit Hours 20

Credit Course
Course No. Course Title
Hours Type
400.1 (Q. Reas) Quantitative Reasoning-I 3+0 Gen Ed
SEMESTER-III

400.1 (E. Writ) Expository Writing 3+0 Gen Ed

401STA Stats-III 2+1 Int Disc
CM401 Data Structure & Algorithms 2+1 Int Disc
CM403 Linear Algebra 3+0 Major
YEAR - 2

CM405 Number Theory 3+0 Major

Total Credit Hours 18

400.2 (Q. Reas) Quantitative Reasoning-II 3+0 Gen Ed

SEMESTER-IV

400.2 (ICT) Application of Inf. & Comm. Technologies 3+0 Gen Ed

402STA Stats-IV 2+1 Sub
CM402 Introduction to Database 2+1 Sub
CM404 Mechanics 3+0 Major
CM406 Discrete Mathematics 3+0 Major
Total Credit Hours 18

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 Credit Course
Course No. Course Title
Hours Type
CM501 Real Analysis 3+0 Major
SEMESTER-V CM503 Algorithm Design 2+1 Major
CM505 Ordinary Differential Equations 3+0 Major
CM507 Fluid Dynamics-I 3+0 Major
CM509 Object Oriented Programming in Python 2+1 Major
YEAR - 3

Total Credit Hours 15

CM502 Complex Analysis 3+0 Major

SEMESTER-VI

CM504 Essential Software 2+1 Major

CM506 Numerical Analysis-I 3+0 Major
CM508 Fluid Dynamics-II 2+1 Major
CM510 Object Oriented Programming in C/C++ 3+0 Major

Total Credit Hours 15

Credit Course
Course No. Course Title
Hours Type
CM601 Numerical Analysis-II 3+0 Major / (Opt)
SEMESTER - VII

CM603 Abstract Algebra 3+0 Major / (Opt)

Optional-I 3+0 Major / (Opt)
Optional-II 3+0 Major / (Opt)
Optional-III 3+0 Major / (Opt)
YEAR - 4

CM600.1 Field Experience / Internship 0+3 Major / (Opt)

Total Credit Hours 18

CM602 Partial Differential Equations 3+0 Major / (Opt)

SEMESTER - VIII

CM604 Stochastic Processes 3+0 Major / (Opt)

Optional-I 3+0 Major / (Opt)
Optional-II 3+0 Major / (Opt)
Optional-III 3+0 Major / (Opt)
CM600.2 Capstone Project 0+3 Major / (Opt)
Total Credit Hours 18

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 List of Elective Courses
Semester-VII Semester-VIII
CM641 Modeling & Simulation (3+0) CM642 Cryptography (3+0)
CM643 Perturbation Methods (3+0) CM644 Fuzzy Mathematics (3+0)
CM645 Operations Research – I (3+0) CM646 Operations Research – II (3+0)
CM647 Computational Fluid Dynamics – I (2+1) CM648 Computational Fluid Dynamics– II (2+1)
CM649 Big Data Analytics- I (3+0) CM650 Big Data Analytics-II (3+0)
CM651 Machine Learning (3+0) CM652 Artificial Intelligence (3+0)
CM653 Optimization Theory (3+0) CM654 Scientific Computing (2+1)
CM655 Numerical Linear Algebra (2+1) CM606 Wavelets (3+0)

(Computational Mathematics)
First Year
Credit Course
Course No. Course Title
Hours Type
300.1 (E) English – I 2+0 Gen Ed
300.1 (I. S) Islamic Studies OR Ethics (Non-Muslim) 2+0 Gen Ed
SEMESTER - I

300.1 (Civ/Com) Civics and Community Engagement 2+0 Gen Ed

Everyday Science, Astronomy, Physics, Chemistry, Earth
300.1 (N. Sc) 3+0 Gen Ed
Science or Biology
301STA Stats-I 2+1 Int Disc
301PHY Phy-I 2+1 Int Disc
YEAR - 1

CM301 Calculus 3+0 Major

Total Credit Hours 18

300.2 Ideology & Constitution of Pakistan/Pakistan Studies 2+0/2+0 Gen Ed

300.2 Functional English 3+0 Gen Ed
SEMESTER - II

300.2 (Entr) Entrepreneurship 2+0 Gen Ed

Intro to Soc. Sc., Urdu, Economics, History, Geography or
300.2 (Soc. Sc) 2+0 Gen Ed
Psychology.
302STA Stats-II 2+1 Int Disc
302PHY Phy-II 2+1 Int Disc
CM302 Multivariable Calculus and Geometry 3+0 Major
Total Credit Hours 20

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 First Semester
CM-301 Calculus ( 3 + 0 )
Limits & Continuity: Limits, Continuity, Tangent lines & Rate of Change, Sequence and Series: Sequence and Their
Divergence and Convergence Test, Introduction to Infinite Series, Taylor and Maclaurin Series, Convergence and
Divergence Test for Series: Limit comparison test, Ratio test, Root test, Derivatives: Techniques of differentiation,
Chain rule and implicit differentiation, derivatives of Inverse functions, hyperbolic functions, inverse trigonometric
& hyperbolic functions, Applications of differentiation, Maxima and Minima of a function of single variable, Marginal
analysis and approximations using increments, Indeterminate forms and L’ Hospital Rule, The Integral: Riemann
integral, Integration techniques, Integration by substitution, differentiation & integration of logarithmic & exponential
function, Integrals of inverse trigonometric & hyperbolic function, Integration of Power of sine, cosine, secant and
tangent, by parts, trigonometric substitution, Improper integrals, Beta and gamma integrals, Differential Equations:
Differential equations, formation and solution, equations of first order, initial and boundary value problems, various
methods of solving first order differential equations: Separable, Exact & Homogeneous equation, integration factor
and orthogonal trajectories. Non-Linear First Order Equations, Envelopes and Singular solutions
Recommended Books:
1. Anton, H. and C. Rorres,. (2001), Calculus, 7th Edition, Wiley.
2. Hoffmann K, (2007), Calculus for Business, Economics and the social and the life sciences, 10th Edition,
McGraw Hill.
3. Kreyszig, E., (2005), Advanced Engineering Mathematics, 9th Edition, John Wiley.
4. Morris T., & Harry.P., (2012), Ordinary Differential Equations, Dover Publications, Incorporated.
5. Thomas, G. B., & R. L. Finney, (2005), Calculus and Analytic Geometry, Addision Wesley Publishing
Company.
Second Semester
CM-302 Multivariable Calculus and Geometry ( 3 + 0 )
Polar Coordinates: Polar Coordinate & Sketching the graph of polar coordinates, Slope of tangent line and arc length
for parametric and polar curve, Area in polar Coordinates, Introduction to Vectors, Line and Plane: Product of vectors,
Projection of vectors, Parametric equation of line, Plane in three spaces, Quadratic surfaces, Cylindrical & Spherical
coordinate, Derivatives of function of two variables: Partial derivative, Tangent plane, Euler’s theorem with
applications, Total differential for function of two variables, Directional derivatives and gradient for function of two
variables, Maxima and minima for the function of two variables and Jacobians, The Integral: Introduction of double
and triple integrals and their application.
Recommended Books:
1. Dineen S,(2001), Multivariate calculus and geometry, Springer.
2. Larson, R. & Edwards.B.H., (2013), Multivariable calculus, Cengage Learning.
3. Lax, P. D., & M. S. Terrell., (2017), Multivariable calculus with applications, Springer.
4. Marsden, J. E., (1993), Basic multivariable calculus, Springer.
5. Walschap, G., (2015), Multivariable calculus and differential geometry, Walter de Gruyter GmbH & Co.

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 Second Year
Credit Course
Course No. Course Title
Hours Type
SEMESTER-III 400.1 (Q. Reas) Quantitative Reasoning-I 3+0 Gen Ed
400.1 (E. Writ) Expository Writing 3+0 Gen Ed
401STA Stats-III 2+1 Int Disc
CM401 Data Structure & Algorithms 2+1 Int Disc
CM403 Linear Algebra 3+0 Major
YEAR - 2

CM405 Number Theory 3+0 Major

Total Credit Hours 18

400.2 (Q. Reas) Quantitative Reasoning-II 3+0 Gen Ed

SEMESTER-IV

400.2 (ICT) Application of Inf. & Comm. Technologies 3+0 Gen Ed

402STA Stats-IV 2+1 Sub
CM402 Introduction to Database 2+1 Sub
CM404 Mechanics 3+0 Major
CM406 Discrete Mathematics 3+0 Major
Total Credit Hours 18

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 Third Semester
400.1 (Q.Reas) Quantitative Reasoning-I (3+0)
Numeric Reasoning: Number system, basic arithmetic equations, units and conversions, dimensions, rates, ratios,
percentage, scientific notation, computation with real number, operations of integers, exponent, square root,
measurement scales.

Algebraic and Geometric Reasoning: Basics of geometry, line, angle, circle, polygon, area, perimeter, volume,
surface etc., introduction of set, properties and operation, functions, types of functions, graphical representation of
functions, relations, types of relations, simplifying algebraic expressions exponents, factorization, algebraic solutions
of linear and quadratic equations.

Logical and critical reasoning: Logic, proposition, propositional equivalence, truth table, Conjunction, disjunction,
negation, propositions, logical fallacies, tautologies and contradictions, logical equivalence, Venn diagram,
components of critical thinking, observation, analysis, interpretation, reflection, evaluation, inference, scientific
reasoning.

Mathematical Modelling and Analysis: Introduction to deterministic models, linear and non-linear functions, system
of linear equations, application of derivatives, linear and exponential growth decay model.

Recommended Books:

1. Alan F. Beardon. (2005). Algebra and Geometry, 1st edition, Cambridge University Press.

2. Eric Zaslow. (2020). Quantitative Reasoning, 1st edition, Cambridge University Press.

3. Forest Jim. (2020). Introduction to Statistics: An Intuitive Guide for Analyzing Data and Unlocking
Discoveries, Jim Publishing.

4. Rosen, K. H. (2018). Discrete Mathematics and its Applications, 7 th edition, McGraw Hill.

5. Sevilla. A & Somers K. (2008). Quantitative Reasoning: Tools for Today's Informed Citizen, 1 st edition,
Wiley.

6. Bennett.J & Briggs.W. (2018). Using & Understanding Mathematics: A Quantitative Reasoning
Approach, 7th edition, Pearson.

7. Frank S Budnick. (1993). Applied Mathematics for Business, Economics, and the Social Sciences, 4th
edition, McGraw Hill.

8. William Fox. (2017). Mathematical Modeling for Business Analytics, 1st edition, CRC Press.

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CM-401 Data Structure & Algorithms (2+1)
Elementary Data Structures: Simple array-based data structures: arrays, matrices, stacks, queues, Linked lists,
Introduction to Trees, Logical construction and traversing of Binary Trees, Implementation of Binary Trees (Insertion
and Traversing), Searching and deletion in Binary Trees, Binary Search Tree, Introduction to Balanced and AVL
Trees., Algorithm Specification: The Role of Algorithms in Computing, Properties of Algorithm, examples,
performance, complexity analysis, measurement, and Big Oh notation, Abstract data types (ADTs): Array and
Polynomial as an ADT, Sparse Matrices, and Representation of Arrays., Stack ADT, Linked lists and array
implementations, Expressions, Postfix Notation, and Infix to postfix conversion.
Recursion and Queue: Recursive Definition and Processes, Writing Recursive Programs, analyzing recursive
algorithms, Queue ADT, Linked and array implementations of queues, circular and double ended queue, dequeuer,
priority queues, Self Referencing Classes: Dynamic Memory Allocation, garbage collection. Linked List: Singly
Linked Lists, Circular Lists, Linked Stacks and Queues (Double Ended List), Doubly Linked Lists, Sorting and Order
Statistics: Heaps and Heaps as Priority Queues, Double Ended Priority Queue. Searching: Linear Search, Binary
Search, and Types of Indexing. Hash Functions, Division, Overflow Handling, Chaining. B-Trees, Generalized List,
etc. Divide and conquer algorithms, Sorting, selection, insertion, merge, quick, bubble, heap, shell, radix, bucket.
Labs:
Implement basic operations on arrays and matrices.
Perform insertion, deletion, and traversal of array elements.
Implement stacks and queues using arrays and linked lists.
Perform stack operations: push, pop, and peek.
Implement singly linked lists, circular linked lists, and doubly linked lists.
Perform insertion, deletion, and traversal of linked list elements.
Implement binary trees and binary search trees.
Perform insertion, deletion, and traversal (in-order, pre-order, post-order) of binary trees.
Analyze the performance of recursive algorithms.
Implement and compare different sorting algorithms: selection sort, insertion sort, merge sort, quicksort, bubble sort,
heap sort, shell sort, radix sort, and bucket sort.
Analyze the time and space complexity of each sorting algorithm.
Implement linear and binary search algorithms.
Analyze the performance of different hash functions.
Implement classic divide and conquer algorithms: merge sort, quicksort.
Analyze the performance and efficiency of divide and conquer algorithms.

Recommended Books

1. Adam B. Drozdek, (2012), Data Structure and Algorithm in C++, 4th Edition, Cengage Learning.
2. Conger S. (2021), Hands-on Database: An Introduction to Database Design and Development, 2 nd Edition,
Springer.
3. Horowitz.E, Sahni.S, & Mehta.D, (1995), Fundamentals of Data Structures in C++, 2nd Edition, Computer
Science Press.
4. Rocca.M.L.,(2021), Advanced Algorithms and Data Structures, Manning Publication.
5. Wengrow.J, (2020), A Common-Sense Guide to Data Structures and Algorithms, 2nd Edition, Pragmatic
Bookshelf.

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CM-403 Linear Algebra ( 3 + 0 )
Linear systems, Vector equations, Row reduction and echelon forms, The matrix equation Ax = b, Solution sets of
linear systems, Applications of linear systems, Linear independence, Linear transformations, Matrix of a linear
transformation, Linear models in business, science, and engineering, Matrix operations, Inverse of a matrix,
Characterization of invertible matrices, Matrix factorization, Introduction to determinants, Properties of determinants,
Cramer’s rule, volume and linear transformations, Vector spaces and subspaces, Null spaces, column spaces, and
linear transformations, Linearly independent sets; bases, Coordinate system, The dimension of a vector space, Rank,
Change of basis, Eigenvectors and eigenvalues, The characteristic equation, Diagonalization, Diagonalization of
symmetric matrices, Eigenvectors and linear transformations, Review of complex numbers, Complex eigenvalues,
Applications to Markov chains, Applications to differential equations, Inner product, length and orthogonality,
Orthogonal sets, Orthogonal projections, The Gram–Schmidt process, Least-squares problems, Application to linear
models in Finance, Inner product spaces, The singular value decomposition.

Recommended Books:
1. Anton, H., & C. Rorres, (2010), Elementary Linear algebra: applications version, 7th Edition, John
2. Wiley & Sons.
3. David C. L, Steven R. L, & Judi J. M, (2014), Linear Algebra and Its Applications, 7th Edition, Pearson
Education.
4. Cheney.E.W, & Kincaid.D.R, (2009), Linear Algebra, Theory and Applications, Jones & Bartlett Publishers.
5. Johnson.L.W, Riess.R.D, & Arnold.J.T, (2015), Introduction to Linear Algebra, 6th Edition, Pearson
Education.
CM-405 Number Theory (3+0)
Introduction to Set theory operations with fundamental concepts, Divisibility, Linear Diophantine Equations, Unique
Factorization, Applications of Unique Factorization, Congruences, Fermat, Euler, Wilson, Cryptographic
Applications, Order and Primitive Roots, More Cryptographic Applications, Quadratic Reciprocity, Primality and
Factorization, Sums of Squares, Arithmetic Functions, Continued Fractions, Recent Developments, Prime
Factorization, The Sequence of Prime Numbers, The Ring of Integers Modulo n, Congruences Modulo n, The Chinese
Remainder theorem, Primality testing, Public key cryptosystem, The RSA cryptosystem, Continued fraction system,
Finite continued fractions, The continued fractions of exponent (e).
Recommended Books:
1. Boulagouaz M., & Tignol J.P, (1999), Algebra and Number Theory, 1st Edition, Chapman and Hall/CRC.
2. Hardy .G.H, & Wright.E.M, (2008), An Introduction to the Theory of Numbers Oxford University Press.
3. Kraft JS, & Washington LC, (2014), Elementary Number Theory, 1st Edition, Chapman and Hall/CRC.
4. Stein William, (2008), Elementary Number Theory: Primes, congruence and Secrets, Springer.
5. Vazzana.A, Erickson.M, & Garth.D, (2007), Introduction to Number Theory, 1st Edition, Chapman and
Hall/CRC

Page 9 of 27
 Fourth Semester
400.2 (Q.Reas) Quantitative Reasoning-II (3+0)

Fundamental Statistical Concepts: Population and sample Interpretation of Tabular and Graphical form of data
(Grouped and ungrouped). Summarizing data; Measures of central tendency, dispersion and Quantiles.
Combinatorial Analysis: Rules of counting (multiplicative, permutation and combination); Venn diagram
Basic concept of probability: Axioms of Probability. Introduction to probability models for continuous and discrete
variables; Normal and Binomial distribution with simple applications.
Bivariate Data analysis: Scatter plots; Pearson correlation; Simple linear regression with simple application
Fundamental Concepts of Inference: Basic ideas of test of significance and testing of hypothesis. Concepts of level
of significance and degree of freedom.
Quantitative reasoning exercises using fundamental statistical concepts

Recommended Books:
Bennett, J., & Briggs, W. (2019). Using & understanding mathematics: a quantitative reasoning approach. Pearson.
Mann, P. S. (2010). Introductory statistics. John Wiley & Sons.
Chatfield, C. (2018). Statistics for technology: a course in applied statistics. Routledge.
Lock, R. H., Lock, P. F., Morgan, K. L., Lock, E. F., & Lock, D. F. (2020). Statistics: Unlocking the power of data.
John Wiley & Sons.
Peck, R., Short, T., & Olsen, C. (2020). Introduction to statistics and data analysis. Cengage Learning.

CM-402 Introduction to Database (2+1)

Introduction to Database Systems, Why databases, File systems versus DBMS, Roles of the database management
system (DBMS),Types of database management systems, Description, data requirements and transaction
requirements, Introduction to Database Design, DBMS architecture and data independence, The process for designing
a database in industry, Database Languages, Data Definition Language (DDL), Data Manipulation Language (DML),
Relational Model, Historical perspective: hierarchical and network models, Relational data structure, Relational
algebra, Logical design of the application, Conceptual design of the application, Modeling relationships in the data,
Entity Relationship (ER) and Extended Entity Relationship (EER) modeling concepts, Conceptual design with ER
and EER modeling, Logical database design: ER to Relational Mapping, Database Application Development,
Normalization of database, Integrity constraints, Tuning the database design

Labs: Generate a database application (DA) from an existing database, based on a real-world scenario, Write detailed
specifications for the DA, Write data requirements for the DA Write transaction requirements for the DA, Design a
conceptual model of the database application using ER and EER models, Complete logical design of the database
application--ER to relational schema mapping, Tune the model using normalization, Implement the database
application that includes, Fabricating substantial amount of data for the DA, Build a user interface for the A, Design
an advanced application using cursors, triggers, stored procedures.
Recommended books
1. C.J. Date, (2003), an Introduction to Database Systems, 8 th Edition, Pearson.
2. Conger S. (2021). Hands-on Database: An Introduction to Database Design and Development, 2 nd Edition,
Springer.
3. Peter Lake, Paul Crowther (auth.), (2013), Concise Guide to Databases: A Practical Introduction, 2nd Edition,

4. SatinderBal Gupta, Aditya Mittal, (2017), Introduction to DatabaseManagement System, 2nd Edition, Laxmi
Publications Pvt Ltd
5. Wengrow.J, (2020), A Common-Sense Guide to Data Structures and Algorithms, 2nd Edition, Pragmatic
Bookshelf.

Page 10 of 27
CM-404 Mechanics ( 3 + 0 )
Vectors: Differentiation of vectors and vector fields, Gradient, divergence and curl of a vector field, Vector
integration, Applications of Green’s, Stoke’s and divergence theorems.
Statics: Composition of forces, equilibrium problems, moments and couples, centre of mass and gravity, friction,
virtual work, flexible cables, Catenaries.
Dynamics: Galilean-Newtonian principle, inertial frames, Galilean transformations, kinematics, rectilinear motion
with variable accelerations, simple harmonic motion, methods of dynamics, principles of energy and momentum,
Motion of a projectile, orbital motion, moment of inertia, motion of a rigid body, plane impulsive motion Compound
pendulum.
Recommended Books:
1. Chorlton, F., (1970), Mechanics, Van Nostrand, Reinhold.
2. Ghori, Q. K., (1971), Introduction to Mechanics, West Pakistan Publishing Co.
3. Kleppner D., (2013), An Introduction to Mechanics, 2nd Edition, McGraw-Hill.
4. Meirovitch L., (2007), Methods of Analytical Dynamics, 1st Edition, McGraw Hill, New York.
5. Meriam, J. L., & Kraige.L.G, (2012), Engineering mechanics: dynamics, John Wiley & Sons.
CM-406 Discrete Mathematics (3+0)
Logic: Propositions and Truth Values, Logical Connectives and Truth Tables, Tautologies and Contradictions, Logical
Equivalence and Logical Implication, The Algebra of Propositions, Arguments, Formal Proof of the Validity of
Arguments, Predicate Logic, Arguments in Predicate Logic
Mathematical Proof: The Nature of Proof, Axioms and Axiom Systems, Methods of Proof, Mathematical Induction
Sets: Sets and Membership, Subsets, Operations on Sets, Counting Techniques, The Algebra of Sets, Families of Sets,
The Cartesian Product, Types and Typed Set Theory
Relations: Relations and Their Representations, Properties of Relations, Intersections and Unions of Relations,
Equivalence Relations and Partitions, Order Relations, Hasse Diagrams, Relational Databases
Functions: Functions, Composite Functions, Injections and Surjections, Bijections and Inverse Functions, More on
Cardinality, Functional Dependence and Normal Forms
Boolean Algebra: Introduction, Properties of Boolean Algebras, Boolean Functions, Switching Circuits, Logic
Networks, Minimization of Boolean Expressions
Graph Theory: Introductions and types, Paths and Cycles, Isomorphism of Graphs, Planar Graphs, Directed Graphs,
Trees and applications of trees
Applications of Graph Theory: Rooted Trees, Sorting, Searching Strategies, Weighted Graphs, The Shortest Path
and Traveling Salesman Problems, graph colouring, Networks and Flows
Recommended Books:

1. J. Gallier, Discrete Mathematics, Springer, 2011

2. K. H. Rosen, Handbook of Discrete and Combinatorial Mathematics, 1999 Chapman and Hall/CRC
3. R. Garnier, J. Taylor, Discrete Mathematics: Proofs, Structures and Applications, CRC Press (3rd Edition),
2009
4. S. Govindarajan, A. Maheshwari, Algorithms and Discrete Applied Mathematics, Springer, 2016
5. W. Conradie, V. Goranko, Logic and Discrete Mathematics: A Concise Introduction, Wiley, 2015

Page 11 of 27
 Third Year
Credit Course
Course No. Course Title
Hours Type
CM501 Real Analysis 3+0 Major
SEMESTER-V CM503 Algorithm Design 2+1 Major
CM505 Ordinary Differential Equations 3+0 Major
CM507 Fluid Dynamics-I 3+0 Major
CM509 Object Oriented Programming in Python 2+1 Major
YEAR - 3

Total Credit Hours 15

CM502 Complex Analysis 3+0 Major

SEMESTER-VI

CM504 Essential Software 2+1 Major

CM506 Numerical Analysis-I 3+0 Major
CM508 Fluid Dynamics-II 2+1 Major
CM510 Object Oriented Programming in C/C++ 3+0 Major

Total Credit Hours 15

Fifth Semester
CM-501 Real Analysis (3+0)
Algebra of sets; partition and equivalent classes; partially ordered sets and Axiom of Choice, Canonical decomposition
of functions, Rn, n >= 1; Euclidean metric space, Completeness, Functions Convergence of sequences and
completeness, Functions of several real variables; their continuity and differentiability Implicit and Inverse Function
Theorems, Jacobians and emotional dependence, Taylor’s Theorems, Jacobians and Minima: Language's method of
undetermined multipliers, Riemann and Riemann-Stieltjes integrals, Differentiation under integral sign.
Uniform and absolute convergence of sequences and series of functions, Uniform convergence and continuity: Term
by term differentiation and integration, Improper integrals and their convergence; their absolute and uniform
convergence.

Recommended Books

1. Browder, A. (2012). Mathematical analysis: an introduction, 2 nd Edition, Springer Science & Business Media.
2. Canuto, C., &Tabacco, A. (2015). Mathematical Analysis II (Vol. 85). Springer.
3. Johnsonbaugh, R., & Pfaffenberger, W. E. (2012). Foundations of mathematical analysis. Courier
Corporation.
4. Robdera, M. A. (2011). A concise approach to mathematical analysis, 3 rd Edition, Springer Science &
Business Media.
5. Schröder, B. S. (2007). Mathematical analysis: a concise introduction, 2 nd Edition, John Wiley & Sons.

Page 12 of 27
CM-503 Algorithm Design (2+1)
Algorithm design paradigms - motivation; concepts of algorithmic efficiency; run-time analysis of algorithms, the
Landau notation, Divide-and-Conquer: Structure of divide-and-conquer algorithms; example applications from Binary
Search, Integer Multiplication, Nearest Neighbors. Analysis of divide-and-conquer run-time recurrence relations,
Dynamic Programming, Form of dynamic programming algorithms; differences between dynamic programming and
Divide-and-Conquer; example applications from: shortest path in graphs; ordering of matrix multiplications; longest
common subsequence, Greedy Methods: Overall view of greedy paradigm. Example of exact optimization solution
(Minimum spanning tree) and approximation solution (Integer Knapsack), Graph Searching and
traversal: Pervasiveness of graph models in applications and notion of search, combinatorial search (e.g. Knight's
Tour); graph traversal methods: depth-first and breadth-first search, s: does an algorithmic solution exist? does
an efficient algorithmic solution exist? Models of algorithmic process and their universality: Church-Turing
hypothesis, Introduction to Computability: The existence of problems with no algorithmic solution; an example and
proof that a specific computational problem has no algorithmic solution, Computational Complexity: Quantification
of resources used by algorithms: Time and Space; Complexity measures and Classes; Polynomial versus Non-
Polynomial time complexity; the class P and motivation for viewing this as the set of tractable computational
problems, NP-completeness, Combinatorial search and optimisation problems, informal view of the case NP as
problems with efficient checking algorithms; approaches to tackling the question of P = NP - informal review of NP-
completeness, Cook's Theorem (without proof).
Labs:
 Write programs to perform Binary Search, Integer Multiplication, and Nearest Neighbors. Analyze their run-
time recurrence relations and compare the efficiencies.
 Implement algorithms to find the shortest path in graphs (e.g., Dijkstra's or Floyd-Warshall), optimize the
ordering of matrix multiplications, and find the longest common subsequence. Compare these with
corresponding divide-and-conquer approaches.
 Implement the Minimum Spanning Tree (using Prim's or Kruskal's algorithm) and solve the Integer Knapsack
problem using a greedy approximation approach. Analyze the exactness and efficiency of these algorithms.
 Implement depth-first search (DFS) and breadth-first search (BFS) algorithms. Apply these methods to solve
problems like the Knight's Tour and explore their efficiencies in different scenarios.
 Implement algorithms for combinatorial search and optimization problems. Conduct experiments to classify
problems into P and NP, and perform an informal review of NP-completeness with examples such as the
Cook's Theorem.
Recommended Books

1. Thomas H C, Charles E L, Ronald L R, & Clifford S., (2009), Introduction to Algorithms, 3rd Edition, MIT
Press
2. Jon K., & Eva T., (2005), Algorithm Design, 1st Edition, Pearson.
3. M.A. Weiss., (1993), Data Structures and Algorithm Analysis in ADAl, Benjamin Cummings Publishing.
4. Michael T. G., & Roberto,. (2016). Algorithm Design and Applications, 1st Edition, Wiley.
5. P.E. Dunne., (1991) Computability Theory - concepts and applications, 3rd Edition, Ellis Horwood Ltd.

CM-505 Ordinary Differential Equations (3+0)

The course must cover linear equations of the first order; linear equations with constant coefficients; the general linear
equation; Modeling with higher-order, variation of parameters; undetermined coefficients; linear independence; the
Wronskian; Solving Higher order Differential equations by using Reduction of Order, With one known solution.
Higher order differential equation which do not contain x directly, higher order equations which do not contain y
directly, solution of higher order differential equations by changing independent variable, Laplace transforms;
existence and uniqueness of solutions; solution by power series; Modelling of Electrical Circuits. Systems of
Differential Equations, oscillation and comparison theorems, Laplace transform, and systems of linear first-order
differential equations, transform methods.
Recommended Books

1. Brannan, J. R., & Boyce, W. E. (2015). Differential equations: An introduction to modern methods and
applications, 3rd Edition, John Wiley & Sons.
2. Hassani, S. (2013). Mathematical physics: a modern introduction to its foundations,2 nd Edition, Springer
Science & Business Media.
3. Kreyszig, E. (2019). Advanced Engineering Mathematics, 10 th Edition, John Wiley & Sons.
4. O'neil, P. V. (2017). Advanced engineering mathematics, 8 th Edition, Cengage learning.
5. Zill, D. G. (2016). Differential equations with boundary-value problems, 9th Edition, Cengage Learning.

Page 13 of 27
CM-507 Fluid Dynamics-I (3+0)
Introduction to fluid mechanics, real and ideal fluids, steady, unsteady, uniform, non-uniform, one, two, three
dimensional, compressible, incompressible, rotational, irrotational flows etc., Differentiation following the motion of
fluid particles, Langrangian and Eulerian methods, Equations of motion and continuity for incompressible inviscid
fluids, Velocity potentials and stokes stream functions Properties of stream function, Bernoulli’s equation with
application to flow along curve paths, Kinetic energy: kinetic induced by a moving body, induced mass, Sources,
sinks, doubles in 2- and 3- dimensions, limiting stream lines, Images and rigid planes.
Recommended Books

1. Bernard, P. S. (2015). Fluid Dynamics, 5 th Edition, Cambridge University Press.

2. Frank, M. (2017). Fluid Mechanics, 4th Edition, McGraw-Hill.
3. Kambe, T. (2007). Elementary fluid mechanics, World Scientific.
4. Rieutord, M. (2014). Fluid dynamics: an introduction, Springer.
5. Young, D. F., Munson, B. R., Okiishi, T. H., &Huebsch, W. W. (2010). A brief introduction to fluid
mechanics. 5th Edition, John Wiley & Sons.

CM-509 Object Oriented Programming in Python (2+1)

Intro and Overview, Principle of Software Engineering and Reusing and Extending Code, Review of Fundamentals
of Procedural Programming, Objects, Data Abstraction, Information Hiding & Encapsulation, Constructors,
destructors, and object creation, Name space and references, Class Methods, Methods Overloading, Inheritance,
Polymorphism, Abstract Classes, Exceptions, Exception Handling, Templates, Example translations of concepts in
Python to Java, Practical Example: Data Science Classes, Student final project presentations.
Labs: Relevant problem on each topic of Python Programming using Python
Recommended books

1. Ayeva, K., & Kasampalis, S. (2018). Mastering Python Design Patterns: A guide to creating smart, efficient,
and reusable software, 2nd Edition, Packt Publishing.
2. Charles R. Severance. (2016). Python for Everybody: Exploring Data in Python 3, University of Michigan
3. Goldwasser, M. H., &Letscher, D. (2008). Object-oriented Programming in Python, Pearson Prentice Hall.
4. Lott, S. F. (2019). Mastering Object-Oriented Python: Build powerful applications with reusable code using
OOP design patterns and Python 3.7, 2nd Edition: Packt Publishing.
5. Lott, S. F., & Phillips, D. (2021). Python Object-Oriented Programming: Build robust and maintainable
object-oriented Python applications and libraries, 4th Edition: Packt Publishing.

Page 14 of 27
 Sixth Semester
CM-502 Complex Analysis (3+0)
Complex numbers and functions, complex limits and differentiability, elementary examples, analytic functions and
power series, complex line integral, Cauchy’s theorem and the Cauchy integral formula, Taylor’s theorem, zeros of
homomorphic functions, Schwarz Lemma, automorphisms of the ball, the plane and Riemann sphere, isolated
singularities and their classifications, Laurent series, the Residue theorem, calculation of definite integrals and
evaluation of infinite series using residues, Riemann Mapping Theorem.
Recommended Books

1. Alpay, D. (2015). An Advanced Complex Analysis Problem Book, 1 st Edition, Springer.

2. Boas, R. P. (2020). Invitation to complex analysis (Vol. 20). American Mathematical Soc.
3. Marsden, J. E., Hoffman, M. J., & Marsden, T. (1999). Basic complex analysis, 3 rd Edition, Macmillan.
4. Mathews, J., & Howell, R. (2012). Complex analysis for mathematics and engineering, 3 rd Edition, Jones &
Bartlett Publishers.
5. Zill, D. G., & Shanahan, P. D. (2013). Complex analysis: A first course with applications. 3 rd Edition, Jones
& Bartlett Publishers.

CM504 Essential Software (2+1)

Working with the MATLAB user interface, entering commands and creating variables, analyzing vectors and
matrices, visualizing vector and matrix data, working with data files, working with data types, automating commands
with scripts, writing programs with branching and loops, writing functions
Labs: Relevant problems on each topic of theory using MATLAB software
Recommended Books

1. Attaway, S. (2013). Matlab: a practical introduction to programming and problem solving, 3 rd Edition.
Butterworth-Heinemann.
2. Gilat, A. (2004). MATLAB: an introduction with applications, John Wiley & Sons.
3. Kattan, P. I. (2008). Matlab for Beginners: A gentle approach, 3 rd Edition, Petra books.
4. Valentine, D. T., & Hahn, B. (2016). Essential MATLAB for engineers and scientists, Academic Press.

CM-506 NUMERICAL ANALYSIS-I (3+0)

Preliminaries of Computing, Error analysis, Numerical Solution of Nonlinear Equation: Bisection method, fixed-point
iteration, Newton’s method, Secant Method, Interpolation and polynomial Approximation: Newton’s Method,
Lagrange Polynomial, Divided differences, Hermite Interpolation, Spline Interpolation., Direct Method for Solving
System of Linear Equations: LU decomposition method, numerical factorizations, Eigen value problems,
Approximating Eigen values, Power method, House holder’s method, Indirect Method for Solving System of Linear
Equations: Gauss Siedel Method, Jacobi’s Method, Relaxation Method, Numerical Integration: Trapezoidal Rule,
Simpsons Rules, Gaussian quadrature method, Numerical solution of Ordinary Differential Equation: Euler Method,
Modified Euler, Taylor’s series, Runge-Kutta method, Software/ Language: Relevant problem on each topic of
Numerical Analysis using software.
Recommended Books

1. Burden, R. L., Faires, J. D., & Burden, A. M. (2015). Numerical Analysis, Cengage Learning.
2. Epperson, J. F. (2013). An Introduction to Numerical Methods and Analysis, 3 rd Edition, Wiley.
3. Gerald, C. F. (2004). Applied numerical analysis, 5 th Edition, Pearson Education India.
4. Mathews, J. H., & Fink, K. D. (2004). Numerical methods using MATLAB (Vol. 4), Pearson prentice hall
Upper Saddle River, NJ.
5. Süli, E., &Mayers, D. F. (2003). An introduction to numerical analysis, Cambridge university press.

Page 15 of 27
CM-508 FLUID DYNAMICS-II (3+0)
Introduction of incompressible viscous fluid, Navier-Stokes and energy equations for viscous incompressible fluids,
Dynamical similarity and Reynolds number, Steady one-dimensional flow of viscous fluid, Two-dimensional flow
and small disturbance theory, Radial flow between plane walls, Open channel flow, axi-symmetric jets, Inviscid
compressible flow, energy equation and compressibility effect, Unsteady one-dimensional flow, Equations of motion
for some specific types of flow and ensuring solutions, gas dynamics.
Recommended Books

1. Cengel, Y., & Cimbala, J. (2013). EBOOK: Fluid Mechanics Fundamentals and Applications (SI units). 3rd
Edition, McGraw Hill.
2. E. George (2015), Analytical Fluid Dynamics. 3 rd Edition, CRC Press.
3. Kundu, P. K., Cohen, I. M., & Dowling, D. R. (2015). Fluid mechanics. 4 th Edition, Academic press.
4. Spurk, J., &Aksel, N. (2008). Fluid mechanics. 2nd Edition, Springer Science & Business Media.
5. White, F. M., &Majdalani, J. (2006). Viscous fluid flow (Vol. 3, pp. 433-434). 2nd Edition, McGraw-Hill.
New York.

CM-510 OBJECT ORIENTED PROGRAMMING C/C++ (2+1)

Introduction to basic C++ Programming (variables, data types, conditions, operators, loops, functions etc.), What is
an Object, Benefits of OOP; Object Oriented Environment; Class Object; Object Oriented Programming (from C to
C++); Constructor; Destructor; Program Style; Functions; Inheritance, I/O streams, Overloading operations,
Programming Examples.
Labs: Relevant problem on each topic of theory using C++ language.
Recommended Books

1. Das, A. Object Oriented Programming With C++: Vikas Publishing House.

2. Deitel, P. J., &Deitel, H. M. (2017). C++ how to Program, 4th Edition, Pearson.
3. Doyle, B. (2013). C# Programming: From Problem Analysis to Program Design, Cengage Learning.
4. Malik, D. S. (2017). C++ Programming: From Problem Analysis to Program Design, 8 th Edition, Cengage
Learning.
5. Weisfeld, M. (2019). The Object-Oriented Thought Process, 5th Edition, Addison Wesley Professional.

Page 16 of 27
 Fourth Year
Credit Course
Course No. Course Title
Hours Type
CM601 Numerical Analysis-II 3+0 Major / (Opt)

SEMESTER - VII
CM603 Abstract Algebra 3+0 Major / (Opt)
Optional-I 3+0 Major / (Opt)
Optional-II 3+0 Major / (Opt)
Optional-III 3+0 Major / (Opt)
YEAR - 4

CM600.1 Field Experience / Internship 0+3 Major / (Opt)

Total Credit Hours 18

CM602 Partial Differential Equations 3+0 Major / (Opt)

SEMESTER - VIII

CM604 Stochastic Processes 3+0 Major / (Opt)

Optional-I 3+0 Major / (Opt)
Optional-II 3+0 Major / (Opt)
Optional-III 3+0 Major / (Opt)
CM600.2 Capstone Project 0+3 Major / (Opt)
Total Credit Hours 18

Seventh Semester
CM-601 Numerical Analysis II (3+0)
Difference Equations, formation, Solutions and applications, Initial Value Problems (ODE-IVPs): Analytic Solutions
of Linear ODE-IVP, Taylor series based and Runge-Kutta methods, Multi-step (predictor-corrector) approaches;
Milnes Method, Adams Method, stability of ODE-IVP solvers, choice of step size and stability envelops, stiffness and
variable step, size implementation, Introduction to the solutions of differential algebraic equations (DAEs), Boundary
Value Problems (ODE-BVPs): Single shooting method, Finite difference Method for solving ODE-BVPs. Orthogonal
Collocations method for solving ODE-BVPs, least square approximation, Gauss Newton Method, Method of least
squares for solving ODE-BVP, Gelarkin’s method and generic equation forms arising in problem discretization, Errors
in Discretization, Solving Partial Differential Equation: Problem Discretization Using Approximation Theory,
Weierstrass theorem and polynomial approximations, Taylor series approximation, Newton’s Method for solving non-
linear algebraic equation as an application of multivariable Taylor series, Introduction to polynomial interpolation,
polynomial and function interpolations, Boundary Value Problems (PDE-BVPs): Finite difference Method for solving
PDE-BVPs; Heat Equation, wave Equation, Laplace Equation.
Software/ Language: Relevant problem on each topic of Numerical Analysis using software.
Recommended Books

1. Ackleh, A. S., Allen, E. J., Kearfott, R. B., &Seshaiyer, P. (2009). Classical and modern numerical analysis:
theory, methods and practice, Crc Press.
2. Argyros, I. K., Cho, Y. J., &Hilout, S. (2012). Numerical methods for equations and its applications, CRC
Press.
3. Butcher, J. C. (2004). Numerical Methods for Ordinary Differential Equations 4 th Edition, Wiley.
4. Isaacson, E., & Keller, H. B. (2012). Analysis of numerical methods, Courier Corporation.
5. Linz, P. (2019). Theoretical Numerical Analysis, 3 rd Edition, Dover Publications.

Page 17 of 27
CM-603 Abstract Algebra (3+0)
Group Theory: Groups, Subgroups, cyclic groups, normal subgroups, quotient groups, examples. Homomorphism
of groups, the fundamental theorem of homorphism, Isomorphism of groups, the isomorphism theorems, Direct
product of groups, Internal and external direct products, Finitely generated Abelian groups, Generators and torsion,
The fundamental theorem of F.G. Abelian groups, Applications, Group action on a fixed sets and isotropy subgroups,
orbits, Sylow theorems, p-groups, First, second and third Sylow theorems, Application of the Sylow theory,
RING THEORY: Rings, Integral domain, The characteristic of a ring, Fermat’s and group algebra, Quotient rings,
ideals, maximal and prime ideals, Ring homomorphism: Definition, properties, prime fields, Fundamental theorems
of homorphism and isomorphism, Polynomial rings, the evaluation modules, ideals, Isomorphism theorem, Near rings,
subnear rings, near ring modules, isomorphism theorem.
Recommended Books

1. Fraleigh, J. B., & Katz, V. J. (2003). A First Course in Abstract Algebra, 7th Edition, Pearson.
2. Landin, J. (2012). An Introduction to Algebraic Structures, Dover Publications.
3. Nicholson, W. K. (2012). Introduction to Abstract Algebra, 6 thEdition, Wiley.
4. Pinter, C. C. (2010). A Book of Abstract Algebra: Second Edition, Dover Publications.
5. Rauf Querashi M.A., Foundation of Abstract Algebra, 1 st Edition, 2018.
6. Warner, S. (2019). Abstract Algebra for Beginners: A Rigorous Introduction to Groups, Rings, Fields, Vector
Spaces, Modules, Substructures, Homomorphisms, Quotients, Permutations, Group Actions, Polynomials, and Galois
Theory, Get 800.
CM-600.1 Field Experience / Internship (0+3)

Students are required to complete a supervised field experience or internship at an appropriate organization. This
practical component provides students with the opportunity to apply their computational mathematics knowledge to
real-world challenges, develop professional competencies, and gain valuable industry exposure.

Page 18 of 27
 Eight Semester

CM-602 Partial Differential Equations (3+0)

Ordinary differential equation in more than one variable, partial differential equation (PDEs) of first order, Nonlinear
PDEs of first order and its application, partial differential equation with variable coefficients reducible to constant
coefficients, Second order Partial differential equation with variable coefficients, mathematical modeling of heat,
Laplace and wave equation and classification of second order PDEs, boundary and initial conditions, reduction to
canonical form and is solutions, Techniques of separation of variable for the solution of PDEs with special emphasis
on Heat, Laplace and wave equation and Laplace transform, Difference equations, Elliptic equations. Dirichlet’s
problem, harmonic functions, the maximum principle, Poisson’s formula, Green functions and integral
representations, The heat kernel, Partial differential equations in higher dimensions.
Recommended Books

1. Haberman, R. (2018). Applied Partial Differential Equations with Fourier series and Boundary Value
Problems (Classic Version), Pearson.
2. Jang, C. L. (2011). Partial Differential Equations: Theory, Analysis and Applications, 6 th Edition, Nova
Science Publishers.
3. Picard, R., & McGhee, D. (2011). Partial Differential Equations: A unified Hilbert Space Approach, De
Gruyter.
4. Pinchover, Y., & Rubinstein, J. (2005). An Introduction to Partial Differential Equations, 1 st Edition,
Cambridge University Press.
5. Pinsky, M. A. (2011). Partial Differential Equations and Boundary-Value Problems with Applications,
American Mathematical Society.
6. Strauss, W. A. (2007). Partial differential equations: An introduction, John Wiley & Sons.

CM-604 Stochastic Processes (3+0)

Stochastic Modeling, Probability Review, The Major Discrete and Continuous Distributions, Conditional Probability
and Conditional Expectation, Conditioning on a Continuous Random Variable, Martingales, Stochastic Processes,
Markov Chains: Chapman-Kolmogorov Equations, Classification of States of a Markov Chain, Long-Run, Properties
of Markov Chains, First Passage Times, Absorbing States, Markov Decision Processes, Optimal Policies, Policy
Improvement Algorithm for Finding Optimal Policies, Discounted Cost Criterion, Poisson Processes, The Poisson
Distribution and the Poisson Process, The Law of Rare Events, Distributions Associated with the Poisson Process,
The Uniform Distribution and Poisson Processes, Spatial Poisson Processes, Compound and Marked Poisson
Processes., Continuous Time Markov Chains: Pure Birth Processes, Pure Death Processes, Birth and Death Processes,
The Limiting Behavior of Birth and Death Processes, Birth and Death Processes with Absorbing States, Finite State
Continuous Time Markov Chains.
Recommended Books

1. Taylor H.M., Karlin S. (1998), An Introduction to Stochastic Modeling, 3rd Edition, Academic Press.
2. Karlin S., Pinsky M. (2010). An Introduction to Stochastic Modeling, 4 th Edition, Academic Press.
3. Cinlar, E. (2013). Introduction to Stochastic Processes, Dover Publications, IncorporatEdition
4. Kao, E. P. (2019). An introduction to stochastic processes, Courier Dover Publications.
5. Lindgren G. (2012). Stationary Stochastic Processes Theory and Applications, CRC Press.
6. Jones P.W., Smith P. (2017 ) Stochastic Processes, An Introduction, 3 rdEdition, Chapman and Hall/CRC.

Page 19 of 27
CM-600.2 Capstone Project (0+3)
Students will undertake an in-depth capstone project to apply their computational mathematics expertise to a complex
problem or innovative solution. This culminating experience involves rigorous research, development, and
documentation, culminating in a comprehensive report and presentation. The project is designed to foster critical
thinking, problem-solving, and the ability to translate theoretical knowledge into practical applications.

Elective Courses
CM-641 Modelling & Simulation (3+0)
Introduction to modelling: Introduction, model: approximation of real world events, history of modelling and
simulation, properties of useful model, model development process, static and dynamic models, model selection,
model validation, ethics in modeling, Introduction to systems: System boundary, classification of systems, linear
systems, mathematical point of view of linear systems, time varying vs time-interval systems, continuous time and
discrete time systems, deterministic vs stochastic systems, System modelling: Need of system modelling, classification
od models: mathematical vs descriptive models, static vs dynamic models, deterministic vs stochastic models,
continuous discrete models, Mathematical modelling of physical systems, model order reduction, Introduction to
simulation: Advantages of simulations, applications of simulation, Numerical methods for simulation, Nonlinear and
Chaotic systems: Linear vs nonlinear systems, types of nonlinearities, Introduction to chaotic systems, first order
continuous-time systems, bifurcations, second order systems, Discrete Event Modelling and Simulation: Introduction,
some important definitions, discrete event system simulation, input data modelling, random number generation, chi-
square test, Training on Lab View software etc.
Recommended Books

1. Birta, L. G., & Arbez, G. (2013). Modelling and simulation. London: Springer.
2. Chaturvedi, D. K. (2017). Modeling and simulation of systems using MATLAB® and Simulink®. 1 st Edition,
CRC press.
3. Giordano, F. R., Fox, W. P., & Horton, S. B. (2013). A first course in mathematical modeling. 5 th Edition,
Cengage Learning.
4. Mooney, D. D., & Swift, R. J. (2021). A course in mathematical modeling (Vol. 13). American Mathematical
Society.
5. Velten, K. (2009). Mathematical modeling and simulation: introduction for scientists and engineers. John
Wiley & Sons.

CM-642 Cryptography (3+0)

Background and overview: One-time encryption using stream ciphers, Semantic security, block Cipher and its
principles, pseudorandom functions, Chosen plaintext and cipher text security and modes of operation, DES and AES
block cipher, Message integrity, Hash function, CBC-MAC, HMAC, PMAC and CW-MAC, Collision resistant
hashing., Classical Encryption Techniques: Symmetric and asymmetric cipher models, Substitution and Transposition
techniques, Authenticated encryption: CCM, GCM, TLS and IPSec, Key derivation function, Deterministic
encryption, non-expanding encryption and format preserving encryption, fully homomorphic encryption, Basic Key
exchange: Diffie-Hellman, RSA and Merkle puzzles, Computational number theory, Number theoretic hardness
assumptions, Authenticated and TLS key exchange, Public Key Cryptography: Principles of Public Key
Cryptosystem, Public key encryption, Trapdoor permutation and RSA, The ElGamal system and variants, Digital
Signatures and certificate, Identification Protocols, Authentication Protocols, Zero Knowledge Protocols and proof of
knowledge, Privacy Mechanism: Group signatures and credential systems, Private information retrieval and oblivious
transfer, Two Party Computations: Yao’s protocol and its applications, Elliptic curve cryptography (ECC), Quantum
computing, Pairing-based cryptography, Lattice based cryptography, Software/ Language: Usage of different
Encryption and Decryption cipher, Symmetric and asymmetric cipher models, Different private and public key
cryptosystem algorithms, RSA algorithms, Different protocols, Digital signature, Yao’s protocol, Elliptic curve
cryptography (ECC).
Recommended Books

1. Katz, J., &Lindell, Y. (2014). Introduction to Modern Cryptography, Second Edition, Taylor & Francis.
2. Lee, D. T., Shieh, S. P., &Tygar, D. (2005). Computer Security in the 21st Century, Springer US.
3. Paar, C., &Pelzl, J. (2009). Understanding cryptography: a textbook for students and practitioners, Springer
Science & Business Media.
4. Stallings, W. (2016). Cryptography and Network Security: Principles and Practice, 2ndEdition, Pearson
Education.
5. Stanoyevitch, A. (2010). Introduction to Cryptography with Mathematical Foundations and Computer
Implementations, 2nd Edition, Taylor & Francis.
Page 20 of 27
CM-643 Perturbation Methods (3+0)
Dimensional analysis, Gauge functions, asymptotic series, asymptotic expansions and sequences. Quadratic equations,
cubic equations, higher order equations, transcendental equations. Expansion of integral, Integration by parts,
Laplace’s method, the method of stationary phase and the method of steepest descent, Straightforward expansion,
exact solution, the Lindstedt- Poincare technique, method of renormalization, method of multiple scales, variation of
parameters and method of averaging. Linear Damped Oscillator, Self-Excited Oscillator, System with Quadratic and
Cubic Nonlinearities, Duffing Equation, The Mathieu Equations.
Recommended Books

1. Bender, C. M., &Orszag, S. A. (2013). Advanced Mathematical Methods for Scientists and Engineers I:
Asymptotic Methods and Perturbation Theory, Springer Science & Business Media.

2. Kevorkian, J., & Cole, J. D. (2013). Perturbation Methods in Applied Mathematics, Springer New York.
3. Nayfeh, A. H. (2008). Perturbation methods, 2nd Edition, John Wiley & Sons.
4. Nayfeh, A. H. (2011). Introduction to Perturbation Techniques, 3rd Edition, Wiley.
5. Sanders, J. A., &Verhulst, F. (2013). Averaging Methods in Nonlinear Dynamical Systems: Springer New
York.
6. Shivamoggi, B. (2002). Perturbation Methods for Differential Equations, Birkhäuser Boston.

CM-644 Fuzzy Mathematics (3+0)

Set Theory: Crisp set theory, Relation between sets, concept of a fuzzy set, relation between fuzzy sets, operations on
fuzzy sets, properties of standard operations, Crisp vs Fuzzy types of fuzzy sets, membership functions, Fuzzy
Relations: Relations, operation on fuzzy relations, α-cuts of a fuzzy relation, composition of fuzzy relations,
projections of fuzzy relations, Propositional Logic: Introduction, syntax, semantics, semantic properties and properties
satisfied by the connectives, inference rules and derivation.
Predicate Logic: Introduction, syntax, semantics, semantic properties and properties satisfied by the connectives,
inference rules and derivation, Boolean Algebra: Introduction, Boolean algebra, identification, complete disjunctive
normal form (CDNF), Fuzzy Mathematics: Addition, Subtraction, Multiplication and Division, Derivatives and
Integration in Fuzzy Sense, Switching Functions and switching circuits: Introduction, switching functions, disjunctive
normal form, switching circuits, relation between switching functions and switching circuits, equivalence of circuits,
simplification of circuits, Fuzzy Methods in Decision Making: Introduction to decision making, Measures of
Dissonance, Measures of confusion, Measures of Non-specificity, Uncertainty and information, Fuzzy methods in
decision making, Fuzzy numerical analysis and other applications.
Recommended Books

1. Buckley, J. J., &Eslami, E. (2013). An Introduction to Fuzzy Logic and Fuzzy Sets, 2nd Edition, Physica.
2. Dubois, D., &Prade, H. (2012). Fundamentals of Fuzzy Sets, Springer US.
3. Klir, G. J., & Yuan, B. (2015). Fuzzy Sets and Fuzzy Logic: Theory and Applications, Pearson.
4. Lawry, J., Miranda, E., Bugarin, A., Li, S., Gil, M. A., Grzegorzewski, P., &Hryniewicz, O. (2007). Soft
Methods for Integrated Uncertainty Modelling, Springer Berlin Heidelberg.
5. Zimmermann, H. J. (2013). Fuzzy Set Theory and Its Applications, Springer Netherlands.

Page 21 of 27
CM-645 Operations Research-I (3+0)
Introduction to operations research, the Origins and applications of Operations Research, System Modeling Principles,
Linear programming, the Linear Programming Model, The Art of Problem Formulation, Graphical Solution of Linear
Programming Problems, Preparation for the Simplex Method, The Simplex Method, Initial Solutions for General
Constraints, Two-phase simplex method and Big-M technique, Duality and Sensitivity Analysis, Primal-Dual
Relationship, The Dual Simplex Method, Parametric Linear Programming, The Upper Bound Technique, Revised
Simplex method and Computational Efficiency, Guide to Software Tools. The Transportation Problem, a Streamlined
Simplex Method for the Transportation Problem, The Assignment Problem, Hungarian method. Network optimization
models, The Shortest-Path Problem, The Minimum Spanning, Tree Problem, The Maximum Flow Problem, The
Minimum Cost Flow Problem, The Network Simplex Method.
Recommended Books

1. Ficken, F. A. (2015). The simplex method of linear programming, 2nd Edition, Courier Dover Publications.
2. Hillier, F., & Lieberman, G. (2010). Introduction to Operations Research with Student Access Card,
9thEdition, McGraw-Hill Science
3. Maros, I. (2012). Computational Techniques of the Simplex Method (Vol. 61), Springer Science & Business
Media.
4. Murthy, P. R. (2005). Operations research (linear programming). bohem press.
5. Taha, H. A. (2011). Operations research: an introduction (Vol. 790), Pearson/Prentice Hall.

CM-646 Operations Research-II (3+0)

Multiple Objective LP Problems Goal Programming (Pre-emptive, Non pre-emptive), Integer Programming, Binary
Integer Programming (BIP) Applications, Use of Binary Auxiliary Variables, Branch and Bound Technique for BIP,
Mixed Integer Programming (MIP) Branch and Bound Technique for MIP, Introduction to Meta Heuristics, Tabu
Search, Simulated Annealing, Genetic Algorithm, Game Theory Two Person Zero Sum games, Two Person Constant
Sum games, Using LP for Solving Games with Mix Strategies, Dual LP for Column Player Strategies, Prisoners
Dilemma Problems, Decision Analysis, Decision Making under Uncertainty, Expected Monetary Value Criterion
Value of Perfect Information, Decision Making with Experimentation, Value of Information, Posterior Probabilities
Utility Theory in Decision Analysis, Developing Risk Profiles, Simulation Applications of Monte Carlo Simulation
Models, Queuing Theory Queuing Models with multiple servers, Simulation Models for Queuing, Data Envelopment
Analysis (DEA), Inventory Management Economic Order Quantity (EOQ) Inventory Model, Deterministic Periodic-
Review Inventory Model, Deterministic Continuous-Review Inventory Model, Stochastic Continuous-Review
Inventory Model, Aggregation Inventory Models, Forecasting Models, Time Series Models, Exponential Smoothing,
Trend Models, Seasonal Models, Forecasting Errors, Tracking Signals in Forecast.
Recommended Books

1. Antunes, C. H., Alves, M. J., &Clímaco, J. (2016). Multi-objective linear and integer programming. Berlin,
Springer.
2. DinhThe Luc. (2016). Multi- objective linear programming: an introduction, Springer International
Publishing.
3. Nag, B., Hillier, F. S., Lieberman, G. J., &Basu, P. (2017). Introduction to Operations Research, 10 th
Edition, McGraw Hill.
4. Eiselt, H. A., Sandblom, C. L., &Sandblom, C. L. (2007). Linear programming and its applications. Berlin,
Springer.
5. Tadelis, S. (2013). Game theory: an introduction, 3rd Edition, Princeton university press.

Page 22 of 27
CM-647 Computational Fluid Dynamics – I (2+1)
Introduction: Typical partial differential equations in fluid dynamics, types of second order equations, well posed
problems, properties of linear and Quasilinear equations, physical characters of subsonic and supersonic flows, second
order wave equations, system of first order equations, weak solutions, Finite Difference and Finite Volume
Discretization: Finite difference discretization, discretization of derivatives, consistency, convergence and stability,
finite volume discretization, face area and cell volume, Equation of Parabolic Type: Finite difference scheme for heat
conduction equation, Crank-Nicholson implicit scheme, analogy with schemes for ordinary differential equations, a
note on implicit methods, Leap-frog and DuFrot-Frankel schemes, operator notation, the Alternating Direction
Implicit (ADI) method, Equation of Hyperbolic Type: Explicit scheme, Lax-Wendroff scheme and variants, implicit
schemes, more on upwind schemes, scalar conservation law: Lax-Wenderoff and related schemes, hyperbolic system
of conservation laws, second-order wave equation, method of characteristics for second-order hyperbolic equations,
model convection-diffusion equation, Equation of Elliptic Type: The Laplace equation in two dimension, iterative
methods for solution of linear algebraic systems, solution of the Penta diagonal system, approximate factorization
schemes, grid generation example, body-fitted grid generation using elliptic-type equations some observations of AF
schemes, multi-grid method, Equation of Mixed Elliptic-Hyperbolic Type: Tricomi equation, transonic computations
based on TSP model,
Labs: Usage of partial differential equations in fluid dynamics, solution of Quasilinear equations, Discretization of
face area and cell volume, Lax-Wendroff scheme and its variants, Method of characteristics for second-order
hyperbolic equations, The Laplace equation, TSP model.
Recommended Books

1. Emanuel, G. (2000). Analytical fluid dynamics. 2 nd Edition, CRC press.

2. Tu, J., Yeoh, G. H., & Liu, C. (2018). Computational fluid dynamics: a practical approach. Butterworth-
Heinemann.
3. Wendt, J. F. (Edition). (2008). Computational fluid dynamics: an introduction, 3rd Edition, Springer Science
& Business Media.
4. White, F. M., &Majdalani, J. (2006). Viscous fluid flow, 2nd Edition, New York: McGraw-Hill.
5. Zikanov, O. (2019). Essential computational fluid dynamics, John Wiley & Sons.

CM-648 Computational Fluid Dynamics-II (2+1)

Introduction: Basic conservation principle, unsteady Navier-stokes equations in integral form, Navier-stokes equations
in differential form, Euler equations for inviscid flows, full potential equation, inviscid incompressible irrotational
flow, Grid Generation: Introduction, co-ordinate transformation, differential equation methods, algebraic methods,
transfinite interpolation methods, unstructured grid generation, mesh adaptation, Inviscid Incompressible flow:
Introduction, potential flow problem, panel methods, panel methods for subsonic and supersonic flows, Inviscid
Compressible flow: Introduction, small-perturbation flow, numerical solution of the full potential equation, full
potential solution in generalized coordinates, Euler model, computed examples based on Euler model, supersonic flow
field computation, Viscous Incompressible Flow: Introduction, Incompressible flow computation, stream-function
vorticity approach, primitive variable approach, The MAC method, solution scheme, Case study: separated flow in a
constructed channel.
Viscous Compressible Flow: Introduction, dynamic similarity, Reynolds Averaged Compressible Navier-stokes)
RANS equations, Turbulence modelling, basic computational methods for compressible flow, finite volume
computation in 2D, solution procedure, computational results.
Labs: Solving unsteady Navier-stokes equations, Inviscid incompressible irrotational flow, Numerical solution of the
full potential equation, Euler model, Incompressible flow algorithms, Reynolds Averaged Compressible Navier-
stokes) RANS equations, Finite volume computation in 2D, Turbulence modelling.
Recommended Books
1. Emanuel, G. (2000). Analytical fluid dynamics, 2nd Edition, CRC press.
2. Tu, J., Yeoh, G. H., & Liu, C. (2018). Computational fluid dynamics: a practical approach. Butterworth-
Heinemann.
3. Wendt, J. F. (Edition). (2008). Computational fluid dynamics: an introduction, 3rd Edition, Springer Science
& Business Media.
4. White, F. M., &Majdalani, J. (2006). Viscous fluid flow, 2ndEdition, New York: McGraw-Hill.
5. Zikanov, O. (2019). Essential computational fluid dynamics, John Wiley & Sons.

Page 23 of 27
CM-649 Big Data Analytics-I (3+0)
Overview of MATLAB interface and environment, Basic operations and syntax, Variables, data types, and arrays,
Importing and exporting data, Summarize the central tendency, dispersion, and shape of the dataset.
Visualize data distributions and relationships among variables, Introduction to plotting functions (plot, scatter, bar,
etc.), Functions: scatter, histogram, boxplot, heatmap, scatter3
Customizing plots (titles, labels, legends), Data cleaning techniques (handling missing values), Data Normalization,
Test assumptions about populations and compare groups, Functions, t-test, anova1, chi2, Hypothesis testing (t-tests,
chi-square tests) for inference of multidimensional data, Trend Analysis Test (MK test, MMK).
Satellite Data, Ground-Based Observations, Remote sensing gridded Data, Temporal and Spatial Resolution,
Understanding time series data, Time series plotting and visualization.
Moving averages and smoothing techniques, Pearson’s correlation coefficient, Partial correlation, Linear regression
(LR), generalized linear models (glm).

Recommended Books

1. EMC Education Services. (2015). Data science and big data analytics: discovering, analyzing, visualizing
and presenting data, Wiley.
2. Ghavami, P. (2019). Big data analytics methods. In Big Data Analytics Methods, 1stEdition,DeGruyter.
3. Hair, J. F. (2011). Multivariate data analysis: An overview. International encyclopedia of statistical science,
th
7 Edition, Pearson.,
4. Wilks, D. S. (2011). Statistical methods in the atmospheric sciences (Vol. 100),Academic press.
5. Zhang, Y. (2010). New advances in machine learning. Pearson.

CM-650 Big Data Analytics II (3+0)

Logistic regression, Model relationships between variables and make predictions, Autocorrelation and seasonality
analysis, Group similar data points to identify patterns and structures, Advanced visualization techniques (heatmaps,
3D plots) Arc GIS,
Multivariate Analysis: Identifies underlying relationships between observed variables by modeling them as linear
combinations of potential latent variables, Cluster Analysis, Factor Analysis, Principal Component Analysis,
Canonical Correlation Analysis (CCA), Analyzes the relationships between two multivariate datasets.
Generalized Additive Models (GAM), Time Series Forecasting, ARIMA Models, Fits autoregressive integrated
moving average models to time series data, Neural Networks
Approaches to Analyzing Big Data, The Two Domains of Big, Data Analytics, Introduction to Apache Hadoop and
MapReduce, Apache Spark, Spark programming, (Python and PySpark), Spark - Resilient Distributed Dataset
(RDDs), Spark - RDDs, Data Frames, Spark SQL, PySpark, NumPy, SciPy, Code Optimization, Cluster
Configurations.

Recommended Books

1. EMC Education Services. (2015). Data science and big data analytics: discovering, analyzing, visualizing
and presenting data, 2nd Edition, Wiley.
2. Ghavami, P. (2019). Big data analytics methods. In Big Data Analytics Methods, De Gruyter.
3. Hair, J. F. (2011). Multivariate data analysis: An overview. International encyclopedia of statistical science,
Pearson.
4. Wilks, D. S. (2011). Statistical methods in the atmospheric sciences (Vol. 100), Academic press.
5. Zhang, Y. (2010). New advances in machine learning. Pearson.

Page 24 of 27
CM-651 Machine Learning (3+0)
Machine learning basics, Logistic regression, perceptron, ANN, other ML models (e.g. decision tree and Random
Forest), Deep learning, applications in computer vision, NLP, robotics. Logistic regression, Naive Bayes, Model
selection, Support vector Machine, Tree Models, Model Selection (Practical Consideration, Boosting, Unsupervised
Learning: Clustering, Unsupervised Learning: Principal Component Analysis, Supervised Learning and Linear
Regression, Algorithms and Complexity, Intelligent Robotics, Machine Learning and Intelligent Data Analysis, Robot
vision, Reinforcement Learning.
Recommended Books

1. Barber, D. (2012). Bayesian reasoning and machine learning, Cambridge University Press.

2. Bishop, C. M., & Nasrabadi, N. M. (2006). Pattern recognition and machine learning, Springer.
3. Duda, R. O., & Hart, P. E. (2006).Pattern classification, 1st Edition, John Wiley & Sons.
4. Flach, P. (2012). Machine learning: the art and science of algorithms that make sense of data, Cambridge
university press.
5. Rogers, S., & Girolami, M. (2016). A first course in machine learning. 2nd Edition, Chapman and Hall/CRC.

CM-652 Artificial Intelligence (3+0)

Review of Algorithms & Data Structures, An introduction to the basic principles, techniques, and applications of
Artificial Intelligence, Perception and intelligence, Coverage includes knowledge representation, logic, inference,
problem solving, search algorithms, game theory, perception, learning, planning, and agent design. neural networks,
fuzzy logic, robotics, natural language processing (NLP), and computer vision, Algorithms in AI, Humans and AI,
Ethical AI and Biases, Concept of an agent, Structure of an agent, Rationality of an agent, Perfect agents, Task
environments, Designing agents, Simple reflex agent, Model-based reflex agents, What are expert systems?
Representing knowledge, Reasoning with logic, Backward chaining, Advantages and disadvantages of expert systems.

Recommended Books:

1. Akerkar, R. (2014). Introduction to artificial intelligence, PHI Learning Pvt. Ltd.

2. Ertel, W. (2018). Introduction to artificial intelligence, Springer.
3. Finlay, J., & Dix, A. (2020). An introduction to artificial intelligence, 1st Edition, CRC Press.
4. Flasiński, M. (2016). Introduction to artificial intelligence. Switzerland, Springer International Publishing.
5. Stuart, R., & Peter, N. (2016). Artificial intelligence-a modern approach. 3rd Edition, Wiley.

CM653 Optimization Theory (3+0)

Statement of the problem, condition for optimality, concept of direction of search, alternating direction and steepest
descent methods, conjugate direction method, conjugate gradient method, Newton’s method, Quasi-Newton equation,
derivation of updating formulae for Quasi-Newton’s equation, The Gauss-Newton method, The Levenberg-Marquardt
method, The corrected Gauss-Newton method, Methods for large scale problems. Theory of constrained optimization,
methods for minimizing a general function subject to linear equality constraints, active set strategies for linear
inequality constraints, special forms of the objectives functions, Lagrange multiplier estimates, Changes in working
set, Barries function methods, Penalty functions methods, Methods based on Lagrangian functions reduced gradient
and gradient projection methods.
Recommended Books:
1. Gill P.E., Murray E. (1981). Wright, H.H., Practical Optimization, Academic Press
2. Luenberger D.G., (1986) Optimization by Vector Space Methods, John Wiley & Sons, 1986.
3. JoshiM.C. &K.M. Moudgalya. (2004). Optimization: Theory and Practice, 1st Edition, Alpha Science
International
4. Ding-Zhu Du, Panos M. Pardalos & Weili Wu. (2001). Mathematical Theory of Optimization, Springer.
5. Gotfreid B.S., Weisan J., 1973). Introduction to Optimization Theory, Prentice Hall, Englewood Cliffs, NJ,
USA.

Page 25 of 27
CM-654 Scientific Computing (2+1)
C-Programming Primer with MEX-C interface in MATLAB, Structure and semantics of C language, definition of
code blocks using { }, The main function, and important library headers and their declaration, the include statement,
the define statement, Writing a simple Hello World program, The main function, and passing parameters to it, C
language syntax for if, switch case, for, while, loops, The goto statement and how / why to avoid it, Mex-C program
signature, Memory handing in C, and in Mex-C files, Testing and debugging Mex-C codes, Checking stand-alone C-
code for memory leaks using valgrind, Errors in Scientific Computing, Discretization using Finite Difference
Methods, Continuous and discrete boundary value problems, Stencil Notation, Types of PDEs, Grids and
Discretization approaches, Poisson's equation, Matrix Terminology, Eigenvalues of continuous Laplace Operator,
Exercises, Direct Methods The Gaussian Elimination Method, Norms, and Floating point numbers, Error Analysis of
Gaussian Elimination, Pivoting, and iterative improvement, Cholesky decomposition for SPD matrices, Band
Matrices, General Sparse Matrices, Iterative Methods – Basic, Iterative Solvers, Splitting’s Preconditions, Jacobi and
Gauss-Seidel iterative solution methods, Starting vector and termination criteria, convergence of Jacobi and Gauss-
Seidel, Iterative Methods - Krylov-subspace Methods, Method for Systems with an SPD matrix, the Chebyshev
method, the Conjugate Gradient (CG) method, the convergence behaviour of the CG method. Preconditioning of
Krylov Subspace Methods, the Preconditioned Conjugate Gradients (PCG) method. Methods for General Matrices.
Indefinite Symmetric matrices, iterative methods for General matrices, CG applied to the normal equations, BiCG
type methods. GMRES type methods, Choice of iterative method, preconditioning for General matrices
Labs: Usage of MATLAB environment, Functions, Operators, Pseudo-code, flowcharts, and documentation,
Designing an algorithm to find roots, Eigenvalues and solving algebraic equations, Mathematical models for problem
solving, GUI Interface, basic function of MATLAB and its usage to solving ODE, PDE, Direct and Iterative Methods.
Recommended Books:
1. Attaway, S. (2013). MATLAB: A Practical Introduction to Programming and Problem Solving, 3rd Edition,
Butterworth-Heinemann.
2. Quarteroni, Alfio, Saleri, Fausto.(2004).Scientific Computing with MATLAB, Springer.
3. Palm, W. (2010). Introduction to MATLAB for Engineers, 3 rdEdition, McGraw-Hill.
4. Xue D., Chen Y.Q.. (2016). Scientific Computing with MATLAB, 2 ndEdition, CRC Press.
5. Gustafsson, Bertil. (2011).Fundamentals of Scientific Computing, Springer.

CM-655 Numerical Linear Algebra (2 + 1)

Stability of Algorithms and Conditioning of Problems: Introduction, Efficiency of an algorithm, definition and concept
of stability, conditioning of the problem and perturbation analysis, perturbation analysis of the linear system problem,
effect of perturbation on RHS vector b, Effect of perturbation in the Matrix A, effect of perturbation in both Matrix A
and vector B, some well-known ill-conditioned matrices, The condition number and nearness to singularity, example
of ill-conditioned Eigenvalue problems. A computational template in numerical linear algebra, creating zeros in a
vector matrix using elementary matrix, triangularization usingGaussian elimination, Gauss elimination with partial
pivoting, Gaussian stability, Gauss elimination with complete pivoting, of Gaussian elimination, Basic results to
existence and uniqueness, some applications giving rise to linear system problems, solution of Ax=b using LU
factorization, solution Ax=b using factorization MA=U, solution of Ax=b without explicit factorization, solution of
linear system with multiple right hand sides.
Effects of Condition Number on Accuracy of the Computed Solution: Computing and estimating condition number,
component-wise perturbations and the errors, iterative refinement, special systems: positive definite; diagonally
dominant; Hessenberg and tridiagonal, symmetric positive definite systems.
QR Factorization, Singular Value Decomposition, and Projection: Introduction, Householder’s method for QR
factorization, complex QR factorization, classical and Gram –Schmid algorithms for QR factorization, solution of
Ax=b using QR factorization, projections using QR factorization, singular value decomposition and its projection,
SVD of a complex matrix, some practical applications of SVD, geometric mean and generalized triangular
decompositions.
Labs: Efficiency of an algorithm, Perturbation analysis of the linear system problem, Component-wise perturbations,
Numerical solution of Gaussian elimination, Complex QR factorization, Classical and Gram – Schmid algorithms,
Decomposition methods.
Recommended Books:

1.Datta.B.N, .(2010).Numerical Linear Algebra and Applications, SIAM publisher ,2nd Edition, 2010.
2. Gregoire.A, Kaber.M,.(2008). Numerical Linear Algebra, Springer.
3. Sundarapandian.V.(2008). Numerical Linear Algebra, PHI Learning.
4. William Ford. (2014). Numerical Linear Algebra with Applications: Using MATLAB,1st Edition, Academic
Press.
5. William Layton.(2014). Myron.S, Numerical Linear Algebra, Lulu publishers.
Page 26 of 27
CM-606 Wavelets (3 + 0)
Introduction to Wavelets: The Essence of Wavelet Analysis, Beyond the CWT: the Discrete Wavelet Transform,
Review of Fourier Theory and Filters, Fourier Transform of Finite Sequences, Periodized Filters, Orthonormal
Transforms of Time Series, The Projection Theorem, Complex-Valued Transforms, The Orthonormal
Discrete Fourier Transform, The Discrete Wavelet Transform, Qualitative Description of the DWT, The Wavelet
Filter, The Scaling Filter, First Stage of the Pyramid Algorithm, Second Stage of the Pyramid Algorithm, General
Stage of the Pyramid Algorithm, The Partial Discrete Wavelet Transform, Daubechies Wavelet and Scaling Filters:
Form and Phase, Coiflet Wavelet and Scaling Filters: Form and Phase, The Maximal Overlap Discrete Wavelet
Transform, Effect of Circular Shifts on the DWT, MODWT Wavelet and Scaling Filters, The Discrete Wavelet Packet
Transform, Time Shifts for Wavelet Packet Filters.
Haar Wavelet: Haar wavelet and their integrals, Haar matrices, Expanding functions into the Haar wavelet series,
Non-uniform Haar wavelet, Solutions of Differential and Integral, Haar wavelet of Scale two and three.
Recommended Books:
1. Albert Boggess, Francis J. Narcowich, A First Course in Wavelets with Fourier Analysis, Prentice Hall, 2001.
2. Charles K. Chui, An Introduction to Wavelets, Elsevier Science, 2014.
3. Donald B. Percival, Andrew T. Walden, Wavelet Methods for Time Series Analysis Cambridge University Press,
2006.
4. Stephane M, A Wavelet Tour of Signal Processing, Third Edition, The Sparse Way', Academic Press, 2008.
5. Ülo Lepik, Helle Hein, Haar Wavelets, With Applications, Springer, 2014

Page 27 of 27