Curriculum/Syllabi

of
B.Tech. Program
in
Mathematics and Computing

Indian Institute of Technology Indore

1
 2nd Year B.Tech. (Mathematics and Computing)
Semester III
Course Code Course Title Weekly Contact Credits
Hours (L-T-P)
ZZ xxx Course-I for Minor Program X-X-X 3
MA 205 Complex Analysis 3-1-0 (1/2 semester) 2
MA 207 Differential Equations-II 3-1-0 (1/2 semester) 2
MA 209 Foundations of Mathematical Analysis 2-1-0 3
MA 215 Probability and Statistics 2-1-0 3
MA 211 / CS 201 Discrete Mathematical Structures 2-1-0 3
MA 213 / CS 203 Data Structures and Algorithms 2-1-0 3
MA 253 / CS 253 Data Structures and Algorithms Lab 0-0-3 1.5
MA 2xx Department Elective (DE-1) x-x-x 3
Total 20.5/23.5

Semester IV
Course Code Course Title Weekly Contact Credits
Hours (L-T-P)
ZZ XXX Course-II for Minor Program X-X-X 3
MA 204N Numerical Methods 2-0-2 3
MA 202 Multivariate Calculus and Measure Theory 2-1-0 3
MA 206 Mathematical Logic and Theory of Computation 2-1-0 3
MA 208 /CS 204 Design and Analysis of Algorithms 2-1-0 3
MA 254 /CS 254 Design and Analysis of Algorithms Lab 0-0-3 1.5
MA 2xx Department Elective (DE-2) x-x-x 3
ZZ xxx Institute Elective-1 x-x-x 3
Total 19.5 /22.5

3rd Year B. Tech. (Mathematics and Computing)

Semester V
Course Code Subject Name Weekly Contact Credits
Hours (L-T-P)
ZZ XXX Course-III for Minor Program X-X-X 3
MA 301 Matrix Computations 2-0-2 3
MA 305 Data Science 2-0-2 3
MA 307 / CS 307 Optimization Algorithms and Techniques 2-1-0 3
MA 303 / CS 303 Operating Systems 2-1-0 3
MA 313 / CS 313 Computer Networks 2-0-2 3
MA 357 / CS 357N Optimization Algorithms and Techniques Lab 0-0-2 1
MA 353 / CS 353N Operating Systems Lab 0-0-2 1
MA 3xx Department Elective (DE-3) x-x-x 3
ZZ xxx Institute Elective-2 x-x-x 3
Total 23/26

Semester VI
Course Code Subject Name Weekly Contact Credits
Hours (L-T-P)
ZZ xxx Course-IV for Minor Program X-X-X 3
MA 302 Statistical Inference 2-0-2 3
MA 306 Monte-Carlo Simulation 2-0-2 3
MA 308 Parallel Computing Methods 0-1-2 2
MA 304 /CS 304N Computational Intelligence 2-1-0 3
MA 354 /CS 354N Computational Intelligence Lab 0-0-3 1.5
MA xxx Department Elective (DE-4) x-x-x 3
MA xxx Department Elective (DE-5) x-x-x 3
ZZ xxx Institute Elective-3 x-x-x 3
Total 21.5/24.5

2
 4th Year B. Tech. (Mathematics and Computing)
Semester VII

Course Code Subject Name Weekly Contact Credits

Hours (L-T-P)
ZZ xxx Course-V for Minor Program x-x-x 2
MA 493 B. Tech. Project (BTP) 0-0-32 16
MA 495 Internship-I x-x-x 1
MA 497 Internship-II x-x-x 1
Total 18/20

Semester VIII
Course Code Subject Name Weekly Contact Credits
Hours (L-T-P)
MA 4xx Department Elective (DE-6) x-x-x 3
MA 4xx Department Elective (DE-7) x-x-x 3
ZZ xxx Institute Elective-4 x-x-x 3
ZZ xxx Institute Elective-5 x-x-x 3
ZZ xxx Institute Elective-6 x-x-x 3
Total 15

List of the Elective Courses

Semester Course Code Course Title Weekly Contact Credits
Hours (L-T-P)
III MA 217 Linear Programming 2-1-0 3
(DE-1) MA 219 Introduction to Dynamical Systems 2-0-2 3
IV MA 210 Elementary Number Theory and Algebra 2-1-0 3
(DE-2) MA 212 Regression Analysis 2-1-0 3
V MA 309 Numerical Methods for Partial Differential 2-0-2 3
(DE-3) Equations
MA 311 Statistical Distribution Theory 2-1-0 3
VI MA 310 Algorithmic Techniques and Applications of Data 2-1-0 3
(DE-4,5) Science
MA 314 Random Matrices 2-1-0 3
VIII MA 452/ MA 652 Theory of Transforms 2-1-0 3
(DE-6,7) MA 407/ MA 607 Nonlinear Dynamics and Computations 2-0-2 3
MA 454/ MA 654 Mathematical Modeling and Simulations 2-0-2 3
MA 405/ MA 605 Differential Equations in Population Dynamics 2-0-2 3
MA 402 Industrial Statistics 2-1-0 3
MA 404 Foundation of Approximation Theory 2-1-0 3
MA 406 Graph Theory 2-1-0 3
MA 408 Mathematical Theory of Waves 2-1-0 3
MA 414 Time Series Analysis 2-1-0 3
MA 416 Integral Equations 2-1-0 3

3
 Syllabi
of
B. Tech. in Mathematics and Computing
(From AY 2023-24 onwards)
Department Core in Semester-III

Course Code MA 205

Title of the Course Complex Analysis

Course Category Institute Core

Credit Structure L-T- P-Credits
3-1-0-2 (half semester)
Name of the Mathematics
Concerned
Department
Pre-requisite, if None
any
Objective of the This is a foundation course on complex analysis for UG students.
Course
Course Outcomes Students will understand the concepts, like analytic functions, harmonic functions, Cauchy’s
theorem, residue formula and their applications.
Course Syllabus ● Definitions and properties of analytic functions.
● Cauchy-Riemann equations, harmonic functions.
● Power series and their properties. Elementary functions.
● Cauchy’s theorem and its applications, Taylor series and Laurent expansion.
● Residues and Cauchy’s residue formula, Evaluation of improper integrals.

Suggested Books Text Books:

1. E. Kreyszig, Advanced Engineering Mathematics, John Wiley & Sons, 2020,
ISBN: 9781119455929.
2. R.V. Churchill and J.W. Brown, Complex Variables and Applications,
McGraw-Hill Inc. New York, 2014, ISBN: 9780073383170.

Reference Books:

3. J.M. Howie, Complex Analysis, Springer-Verlag, Berlin, 2012, ISBN:

9781447100270.
4. M.J. Ablowitz and A.S. Fokas, Complex Variables: Introduction and
Applications, Cambridge University Press, 2008, ISBN: 9787506291804.

4
Course Code MA 207
Title of the Course Differential Equations-II
Course Category Institute Core

Credit Structure L-T- P-Credits

3-1-0-2 (half semester)
Name of the Mathematics
Concerned
Department
Pre-requisite, if None
any
Objective of the This is a foundation course on differential equations for UG students.
Course
Course Outcomes ● Students will be trained to solve various types of higher ordinary differential
equations and partial differential equations.
● Students will also be exposed to the real-life applications of Laplace, wave, and
heat equations.
Course Syllabus ● Review of power series and series solutions of ODEs.
● Regular singular points, method of Frobenius, Bessel equation and Bessel
function.
● Legendre equation and Legendre Polynomials.
● Strum-Liouville problems, Fourier series.
● Classification of linear second order PDEs in two variables, D'Alembert solution
to the wave equations, Laplace, Wave, and Heat equations with applications.
Suggested Books Text Books:
1. E. Kreyszig, Advanced Engineering Mathematics, John Wiley & Sons, 2020,
ISBN: 9781119455929.
2. W.E. Boyce and R. Diprima, Elementary Differential Equations, John Wiley &
Sons, 2022, ISBN: 9781119820512.

Reference Books:
3. R.V. Churchill and J.W. Brown, Fourier Series and Boundary Value Problems,
McGraw-Hill Inc., 2019, ISBN: 9787560381251.
4. G. Simmons, Differential Equations with Applications and Historical Notes,
Taylor & Francis, 2017, ISBN: 9781498702591.

5
Suggested Course Code MA 209

Title of the Course Foundations of Mathematical Analysis

Course Category Department Core

Credit Structure L-T- P-Credits

2-1-0-3
Name of the Concerned Mathematics
Department

Pre-requisite, if any Basic knowledge of calculus and linear algebra

Objective of the Course Students will have fundamental knowledge and problem-solving skills in analysis in
metric space and convergence criteria in sequences and series of functions.

Course Outcomes ● Students will have knowledge of different topologies on Euclidean spaces.
● They will have an understanding of the space of continuous functions.

Course Content • Review of calculus and highlights of its applications

• Introduction to metric space, Finite-dimensional normed space (𝑅𝑛 , ‖. ‖𝑝 ) as
𝑙𝑝𝑛 with 𝑙𝑝 -norms, real word implication of 𝑙𝑝 norms, illustration of unit balls
in 𝑙𝑝𝑛 , Finite-dimensional inner product space
• Topology on 𝑙𝑝𝑛 : Uniform continuity, convergence and completeness in 𝑙𝑝𝑛 ,
properties of compact sets in 𝑙𝑝𝑛 , Extreme Value Theorem and approximation
result for closest point, Intermediate Value Theorem on a connected subset
of 𝑙𝑝𝑛 , Cantor set
• p-norm on C[0,1], sequence, series and their convergence in C[0,1],
Weierstrass theorem, topological properties of C[0,1], Nowhere
differentiable function

Suggested Books Text Books:

1. N. L. Carothers, Real Analysis, Cambridge University Press, 2009, ISBN:
0521497566.
2. W. Rudin, Principles of Mathematical Analysis, McGrawHill, 1983, ISBN:
0-07-054235-X.

Reference Books:
3. K. R. Davidson and A. P. Donsig, Real Analysis with Real Applications,
Prentice Hall, 2002, ISBN: 978-0-387-98097-3.
4. T. M. Apostol, Calculus: Volumes 1 and 2, Wiley Eastern, 1980, ISBN: 978-
0-471-00005-1.
5. T. M. Apostol, Mathematical Analysis, Narosa Publishers, 2002, ISBN:
9788185015668.
6. S. Kumaresan, Topology of Metric Spaces, Narosa Publishers, 2011, ISBN:
978-8184870589.

6
Course Code MA 215

Title of the Course Probability and Statistics

Course Category Department Core

Credit Structure L-T- P-Credits

2-1-0-3

Name of the Concerned Mathematics

Department
Pre-requisite, if any Nil

Objective of the Course This is a foundation course on probability and statistics for UG students.
Course Outcomes ● understand the techniques of data collection, analysis, and interpretation, enabling
them to make informed decisions in diverse fields,
● learn a solid foundation in probability and statistics, empowering them to analyze
data, and draw meaningful conclusions.
Course Content • Descriptive Statistics: Data collection techniques, organizing and presenting data,
frequency distributions, measures of central tendency, variation, skewness, and
kurtosis.
• Probability and Random Variable: Axiomatic definition of probability,
conditional probability and Bayes rule, random variables, cumulative distribution
function, and its properties, histogram density estimation and bootstrap, discrete
random variables, probability mass function, continuous random variables,
probability density function, functions of random variables, expectation and
moment of a random variable, moment generating function, probability integral
transform.
• Probability Distributions: Bernoulli, binomial, geometric, negative binomial,
hypergeometric, Poisson, exponential, gamma, Weibull, beta, Cauchy, normal.
• Random Vectors: Joint distributions, marginal and conditional distributions,
independence of random variables, covariance and correlation.
• Inequalities and Limit Theorems: Markov’s inequality, Chebyshev’s inequality,
Jensen’s inequality, convergence in probability and convergence in distribution,
weak law of large numbers and central limit theorem.

Suggested Books Text Books:

1. S. M. Ross, Introductory Statistics, Academic Press, USA, 2017, ISBN: 978-
0-12-804317-2.
2. D. C. Montgomery and G. C. Runger, Applied Statistics and Probability for
Engineers, Wiley, 2016, ISBN: 978-8126562947.

Reference Books:
3. S. M. Ross, Introduction to Probability and Statistics for Engineers and
Scientists, Academic Press, 2004, ISBN: 9780123704832.
4. J. A. Rice, Mathematical Statistics and Data Analysis, Duxbury Press, 2006,
ISBN: 0-534-39942-8.
5. I. R. Miller, J.E. Freund, R. Johnson, Probability and Statistics for Engineers,
Prentice-Hall (I) Ltd, India, 2011, ISBN: 9788177581843.

7
Suggested Course code MA 211 / CS 201

Title of the course Discrete Mathematical Structures

Course category Department Core

L - T - P – Credits
Credit Structure
2-1-0-3

Name of the Concerned

Mathematics / Computer Science and Engineering
Department

Pre-requisite, if any Basic courses on mathematics

This course will introduce the basic concepts of discrete mathematics and its
Objective of the Course
applications.

● Students will learn about discrete mathematical structures like sets,

relations, functions, groups, graphs, etc.
Course Outcome
● They will also learn about proof techniques and how to apply them to
prove lemmas, theorems, etc.

● Elementary counting techniques

● Propositions and predicates, proofs and proof techniques.
● Sets, relations and functions, cardinality
Course Syllabus
● Posets and lattices: Dilworth`s theorem, inversion and distributive lattices
● Graph theory basics: paths, cycles, trees, connectivity
● Group theory: Lagrange`s theorem, homomorphisms, applications

Textbooks:
1. K. H. Rosen, Discrete Mathematics and Its Applications, Mc Graw
Hill, 2019, ISBN: 9781259676512
Suggested Books
Reference books:
2. R. P Grimaldi, Discrete and Combinatorial Mathematics, Pearson,
2017, ISBN: 9788177584240

8
Suggested Course code MA 213/ CS 203

Title of the course Data Structures and Algorithms

Course Category Department Core

L - T - P - Credits
Credit Structure
2-1-0-3

Name of the Concerned

Mathematics / Computer Science and Engineering
Department

Pre-requisite, if any Computer Programming

● This Course is designed to provide an introduction to the theory

Objective of the Course
and practice of different data structures.
● This course will also provide familiarity with the algorithms for
those data structures.

Students will learn the uses of data structures to make efficient

Course Outcomes
algorithms

● Introduction to data structures, Abstract data types, Analysis of

algorithms, Introduction to complexity analysis and measures.
● Arrays – operations and addressing, Linked list (singly, doubly, and
circular), Stack ADT and its applications in expression evaluation
and recursion, Queue ADT and its variants such as circular queues
and double-ended queues. Hashing and hash tables, Recursion.
Course Syllabus ● Tree ADT, Binary trees – properties and traversals, Binary search
trees, Height balanced trees -- AVL trees, Binary heaps, and priority
queues.
● Graph ADT, Graph representation, Graph traversal – breadth-first
search, depth-first search, and topological ordering, Connected
components, cut-vertices, 2-connected components
● Algorithms and data structures for sorting and searching, Order
statistics.

Textbooks:
1. S. Sahni, Data structures, algorithms, and applications in C++,
McGraw-Hill, 1998, ISBN: 978-0929306322
2. T. H. Cormen, C. E. Leiserson, R. L. Rivest, and C. Stein,
Introduction to Algorithms, (3rd Edition), Prentice Hall, 2009.
ISBN: 978-81-203-4007-7
Suggested Books
Reference Books:
3. D. E. Knuth, The Art of Computer Programming: Fundamental
Algorithms, Vol. 1 (3rd Edition, 1997) and Vol 3, (2nd Edition,
1998), Addison-Wesley Professional. ISBN: 978-0137935109
4. M.T. Goodrich, R. Tamassia, and D. Mount, Data Structures
and Algorithms in C++, 2nd Edition, Wiley, ISBN: 978-0-470-
38327-8

9
Suggested Course code MA 253/ CS 253

Title of the course Data Structures and Algorithms Lab

Course Category Department Core

L - T - P - Credits
Credit Structure
0-0-3-1.5

Name of the Concerned

Mathematics/Computer Science and Engineering
Department

Pre-requisite, if any Computer Programming

This Course is designed to provide

Objective of the Course ● an introduction to the theory and practice of different data structures
● familiarity with the algorithms for those data structures

Course Outcomes Students will learn uses of data structures to make efficient algorithms.

● Implementation of array, linked list, stack, and queue

● Implementation of tree and graph data structure
Course Syllabus
● Implementation of sorting and searching,
● Implementation of Hash and hash tables and order statistics.

Textbooks:
1. T. H. Cormen, C. E. Leiserson, R. L. Rivest, and C. Stein,
Introduction to Algorithms, (3rd Edition), Prentice Hall, 2009.
ISBN: 978-81-203-4007-7
Suggested Books Reference Books:
2. D. E. Knuth, The Art of Computer Programming: Fundamental
Algorithms, Vol. 1 (3rd Edition, 1997) and Vol 3, (2nd Edition,
1998), Addison-Wesley Professional. ISBN: 978-0137935109
3. M.T. Goodrich, R. Tamassia, and D. Mount, Data Structures and
Algorithms in C++, 2nd Edition, Wiley. ISBN: 978-0-470-38327-8

10
 Department Core in Semester-IV
Course Code MA 204N
Title of the Course Numerical Methods
Course Category Institute Core
Credit Structure L-T- P-Credits
2-0-2-3
Name of the Mathematics
Concerned Department
Pre-requisite, if any None
Objective of the This is a foundation course on numerical methods for UG students.
Course
Course Outcomes Students will be trained to evaluate integration and differentiation, and to solve
numerically system of linear equations and differential equations.

Course Syllabus ● Interpolation by polynomials, divided differences, error of the interpolating

polynomial.
● Solution of a system of linear equations, Cholesky's method, Gauss-Seidel
methods, partial pivoting, row echelon form, norms, ill-conditioning.
Eigen-value problem, power method.
● Solution of a nonlinear equation, bisection and secant methods, Newton's
method, rate of convergence, solution of a system of nonlinear equations.
● Numerical integration, composite rules, error formulae.
● Numerical solution of ordinary differential equations, Euler and Runge-
Kutta methods, multi-step methods, predictor-corrector methods, order of
convergence.
● Finite difference methods, numerical solutions of elliptic, parabolic, and
hyperbolic partial differential equations.

Suggested Books Text Books:

1. S. S. Sastry, Introductory Methods of Numerical Analysis, PHI Learning,
ISBN-978-81-203-4592-8, 2012.
2. E. Kreyszig, Advanced Engineering Mathematics, John Wiley & Sons,
2020, ISBN: 9781119455929.
3. S. D. Conte and Carle de Boor, Elementary Numerical Analysis - An
Algorithmic Approach, SIAM, 2018, ISBN: 9781611975208

Reference Books:
4. B. Bradie, A Friendly Introduction to Numerical Analysis, Pearson
Prentice Hall, 2007, ISBN: 8131709426.
5. W. Cheney, D. Kincaid, Numerical Mathematics and Computing,
Cengage Learning, 2020, ISBN: 9780357670842.
6. D. Watkinson, Fundamentals of Matrix Computations, Wiley Inter
Science, 2010, ISBN: 9780470528334.

11
Course Code MA 202

Title of the Course Multivariate Calculus and Measure Theory

Course Category Department Core

Credit Structure L-T- P-Credits

2-1-0-3

Name of the Mathematics

Concerned
Department

Pre-requisite, if any Basic knowledge of calculus and linear algebra

Objective of the First part of this course introduces basic concepts and results related to continuity
Course and differentiability in the finite dimensional setting. The second part introduces
concepts related to Lebesgue integral and some of their important properties.
Course Outcomes The student is able to generalize all the results and techniques learned in the first
year calculus course and their applications.

Course Content • Functions of several variables - Continuity and differential calculus for
functions from 𝑅𝑛 to 𝑅𝑚 Jacobian matrix, Mean Value Theorem, higher order
derivatives, Taylor series for function from 𝑅𝑛 to R, inverse function theorem,
implicit function theorem.
• Lebesgue measure and integral - sigma-algebra of sets, measure space,
Lebesgue measure, measurable functions, Lebesgue integral, Fatou’s lemma,
dominated convergence theorem, monotone convergence theorem, Lp spaces.

Suggested Books Text Books:

1. T. M. Apostol, Mathematical Analysis, Narosa Publishers, 2002, ISBN:
978-8185015668.
2. R. G. Bartle, The Elements of Integration and Lebesgue Measure, Wiley,
1995, ISBN: 0471042226.

Reference Books:
3. W. Rudin, Principles of Mathematical Analysis, McGraw Hill, 1983,
ISBN: 0-07-054235-X.
4. M. Capinski and E. Kopp, Measure, Integral and Probability, Springer,
2007, ISBN: 9781852337810.
5. G. de Barra, Measure Theory and Integration, New Age International,
1981, ISBN: 9788122435023.

12
Course Code MA 206

Title of the Course Mathematical Logic and Theory of Computation

Course Category Department Core

Credit Structure L-T- P-Credits
2-1-0-3
Name of the Mathematics
Concerned
Department
Pre-requisite, if any Discrete mathematical structures

Objective of the At the end of the course, students should be exposed to fundamental knowledge in
Course mathematical Logic and theory of computations.

Course Outcomes ● Exhibit a strong foundation in formal computation, mathematical logic, formal
reasoning, and formal semantics.
● Distinguish various computing languages, and effectively engage in logical
argumentation, discussion, and communication of essential logic concepts in the
context of computer science.

Course Content • Propositional Logic: Language of propositional logic, Tautological consequence

• First Order Logic: A language for arithmetic, First order languages, Examples of
first-order languages for some mathematical structures, Tarski’s definition of truth.
• Automata and Language Theory: Finite automata, Regular expressions, Push-
down automata, Context-free grammars, Pumping lemmas.
• Computability Theory: Turing machines, Church-Turing thesis, Decidability,
Halting problem, Reducibility.

Suggested Books Text Books:

1. H. R. Lewis and C. H. Papadimitriou, Elements of Theory of Computation,
Prentice-Hall, 2nd Edition, Englewood, New Jersey, 1997, ISBN: 0-13-
26247&-8.
2. R. E. Hodel, An Introduction to Mathematical Logic, PWS Publishing
Company, Boston, 1995, ISBN: 9780534944407.

Reference Books:
3. J. Hopcroft, R. Motwani, and J. Ullman, Introduction to Automata Theory,
Language, and Computation, Pearson Education, 2nd Edition, 2001.
ISBN:0201441241.
4. M. Sipser, Introduction to the Theory of Computation, Cengage India
Private Limited, 3rd Edition, 2014, ISBN: 8131771865.

13
Suggested Course code MA 208 /CS 204

Title of the Course Design and Analysis of Algorithms

Course Category Department Core

L - T - P - Credits:
Credit Structure
2-1-0-3

Name of the Concerned

Mathematics/Computer Science and Engineering
Discipline

Pre-requisite, if any Knowledge of Data Structures and Algorithms

Objective of the Course This is an introductory course in the field of computer algorithms.

At the end of the course, students will know the basics of

 algorithm analysis,
Course Outcomes
 algorithm design, and
 different problem classes.

• Algorithm Analysis: Time and Space Complexity; Computational

Tractability (Best, Average & Worst Cases), Asymptotic Bounds (Lower,
Upper & Tight Bounds).
• Algorithm Design: Divide and Conquer; Greedy, Dynamic Programming,
Course Syllabus
Branch and Bound.
• Problem Classes: Reducibility and Intractability, P, NP, PSPACE, NP-
Complete, and NP-Hard.

Textbooks:
1. T. H. Cormen, C. E. Leiserson, R. L. Rivest, and C. Stein, Introduction
to Algorithms (Eastern Economy Edition), 3rd Edition, PHI Learning
Suggested Books
Pvt. Ltd. (Originally MIT Press), 2010. ISBN: 978-8120340077
Reference books:
2. J. Kleinberg and E. Tardos, Algorithm Design, 2nd Edition, Pearson
Education, 2022. ISBN: 978-0132131087

14
Suggested Course code MA 254/CS 254

Title of the Course Design and Analysis of Algorithms Lab

Course Category Department Core

L - T - P - Credits:
Credit Structure
0-0-3-1.5

Name of the Concerned

Mathematics/Computer Science and Engineering
Discipline

Pre-requisite, if any Knowledge of Data Structures and Algorithms

Objective of the Course This is an introductory course in the field of computer algorithms.

At the end of the course, students will know the basics of

Course Outcomes  algorithm analysis and design
 different problem classes.

● Runtime analysis of different sorting algorithms and linked lists in best-case,

worst-case, and average-case.
● Implementation and analysis of algorithms based upon the following design
techniques:
○ Divide and Conquer Strategy (Closest Pair of Points, Integer
Course Syllabus
Multiplication, Matrix Multiplication, Fast Fourier Transform etc.).
○ Greedy Strategy (Interval Partitioning, Dijkstra's Algorithm, Minimum
Spanning Tree etc.).
● Dynamic Programming Strategy (Weighted Interval Scheduling, Sequence
Alignment, Bellman-Ford Algorithm etc.).

Textbooks:
1. T. H. Cormen, C. E. Leiserson, R. L. Rivest, and C. Stein, Introduction to
Algorithms (Eastern Economy Edition), 3rd Edition, PHI Learning Pvt. Ltd.
(Originally MIT Press), 2010. ISBN: 978-8120340077
Suggested Books

Reference books:
2. J. Kleinberg and E. Tardos, Algorithm Design, 2nd Edition, Pearson
Education, 2022. ISBN: 978-0132131087

15
 Department Core in Semester-V

Course Code MA 301

Title of the Course Matrix Computations

Course Category Department Core

Credit Structure L-T- P-Credits
2-0-2-3
Name of the Concerned Mathematics
Department
Pre-requisite, if any Basic knowledge of calculus and linear algebra
Objective of the Course This course is aimed at understanding the theoretical and computational aspects of
important algorithms and techniques of scientific computing.

Course Outcomes • To solve application problems involving matrix computation algorithms and
understanding the relationships between the computational effort and the
accuracy of these algorithms.
• Knowledge of effect of errors in computations.

Course Syllabus • Review of basic linear algebra, minimal polynomials, Cayley-Hamilton

Theorem, triangulation, diagonalization, Invariant subspace, Rational canonical
form, Jordan canonical form.
• Linear least-squares problems: Rotation and reflections, QR factorization,
Gram-Schmidt orthogonalization, SVD and Moore-Penrose pseudoinverse, low-
rank approximation by SVD, solution of least-squares problems by normal
equation, QR method. Eigenvalue problems: Eigenvalues and eigenvectors,
Schur theorem, Inner product space, spectral theorems for Hermitian and normal
matrices, power and inverse power methods, QR algorithm for eigenvalue
problems. Iterative methods for linear systems: SOR, and CG methods.

Suggested Books Text Books:

1. D. S. Watkins, Fundamentals of Matrix Computations, Wiley, 2010, ISBN:
9780470528334.
2. G. Strang, Linear Algebra and Its Applications, Academic Press, 2006, ISBN:
978-8131501726.
3. C. T. Kelley, Iterative Methods for Linear and Nonlinear Equations, SIAM,
1995, ISBN: 9780898713527.

Reference Books:
4. G. H. Golub, C. F. Van Loan, Matrix Computations, The Johns Hopkins
University Press, 2013, ISBN: 9781421407944.
5. L. N. Trefethen, D. Bau, Numerical Linear Algebra, SIAM, 1997, ISBN:
9780898713619.
6. J. W. Demmel, Applied Numerical Linear Algebra, SIAM, 1997, ISBN:
9780898713893.

16
Course Code MA 305

Title of the Course Data Science

Course Category Department Core

Credit Structure L-T- P-Credits
2-0-2-3

Name of the Concerned Mathematics

Department

Prerequisite, if any Basics of linear algebra, probability and statistics

Objective of the Course This is a foundation course on data science for UG students.

Course Outcomes The students will understand the fundamental concepts of data science,
supervised/unsupervised learning and their applications to industrial problems.
Course Syllabus • Concept of data science, data editing, missing data and logical operators,
data management with repeats, sorting, ordering, and lists, statistical
functions for handling data through graphics, programming and
illustration with examples.
• Overview of concepts: Bias/variance, overfitting and train/test splits of
data, confusion matrix, accuracy metrics, receiver operator
characteristics (ROC) curve, unbalanced datasets, types of machine
learning-supervised (regression and classification), unsupervised
(clustering), classification and regression algorithms - K-Nearest
neighbors, support vector machines (SVM) for classification and
regression problems, kernel based SVM and their generalization ability.
• Principal component analysis in high dimension - rank and covariance
estimation, graph, networks and clustering, k-means and spectral
clustering, introduction to diffusion maps of point clouds and
relationship to spectral clustering, semi-supervised learning -
introduction.
• Data science applications such as weather forecasting, stock market
prediction, credit card fraud detection, object recognition, real time
sentiment analysis, disease diagnosis, etc.

Suggested Books Text Books:

1. A. Blum, J. Hopcroft, and R. Kannan, Foundations of Data Science,
Cambridge University Press, 2020, ISBN: 9781108485067.
2. J. A. Rice, Mathematical Statistics and Data Analysis, Cengage,
Boston, 2013, ISBN: 9788131519547.

Reference Books:
3. S. Marsland, Machine Learning-An Algorithmic Perspective, CRC
Press, Taylor & Francis, Boca Raton, 2015, ISBN: 9781138583405.
4. M. P. Deisenroth, A. A. Faisal, and C. S. Ong, Mathematics for
Machine Learning, Cambridge University Press, 2020, ISBN:
9781108455145.
5. T. T. Soong, Fundamentals of Probability and Statistics for
Engineers, John Wiley & Sons, 2004, ISBN: 0470868147.
6. P. Teetor, R Cookbook, O’Reilly Media, Inc., 2011, ISBN:
9780596809157.

17
Suggested Course
MA 307 / CS 307
code

Title of the Course Optimization Algorithms and Techniques

Course Category Department Core

L-T-P-Credits
Credit Structure
2–1–0-3

Name of the
Mathematics/Computer Science & Engineering
Concerned Discipline

Pre-requisite, if any Knowledge of Data Structures and Algorithms

Objective of the
This is an introductory course in the field of mathematical optimization.
Course

At the end of the course, students will know

● The Basics of Optimization,
Course Outcomes
● Unconstrained and Constrained Optimization, and
● Linear and Quadratic Programming.

● Introduction to Optimization and Math Foundation: Type of Problems,

Examples, Formulations, Applications, Notations, and Convexity.
● Unconstrained Optimization: Necessary and Sufficient conditions for a Minima;
Linear Search and Trust Region Methods; Multi-dimensional Minimization -
Steepest descent, Newton, Gauss Newton, Quasi Newton; One-Dimensional
Course Syllabus minimization - Dichotomous, Quadratic & Cubic Interpolation.
● Constrained Optimization: Conversion to Unconstrained, Lagrange Multipliers,
Necessary and Sufficient Conditions for Minima (KKT), and Duality.
● Linear Programming: Necessary and Sufficient Conditions for a Minima for a
Linear Program, Derivation and Implementation of Simplex, Starting Simplex,
and Interior-Point Methods.

Textbooks:
1. J. Nocedal and S. J. Wright, Numerical Optimization, 1st Edition, Springer,
2006. ISBN: 781493937110
Suggested Books
Reference books:
2. A. Antoniou and W.-S.g Lu, Practical Optimization: Algorithms and
Engineering Applications, 2nd Edition, Springer, 2021. ISBN: 9781071608432

18
Course Code MA 303/ CS 303

Title of the Course Operating Systems

Course Category Department Core

Credit Structure L-T- P-Credits

2-1-0-3

Name of the Concerned Mathematics / Computer Science and Engineering

Department
Pre-requisite, if any NIL

Objective of the Course This course will introduce the basic components of operating systems and
functionalities.
Course Outcomes Understanding basic functionalities of operating system for efficient performance
of the processes
Course Syllabus • Introduction: Overview of important features of computer architectures for
OS operation; Service and system performance
• Multiprogramming: Concurrency and parallelism; Processes and threads;
Process synchronization; Process deadlocks
• Memory management: Paging; Segmentation; Virtual memory
• File systems: File operations. File protection
• Case Studies: Case studies of contemporary operating systems

Suggested Books Text books:

1. A. Silberschatz, P.B. Galvin, and G. Gagne, Operating System
Principles, 7th edition, John Wiley, 2005, ISBN: 9788126509621.
Reference books:
2. A. Silberschatz, P.B. Galvin, and G. Gagne, Operating System
Concepts, 9th edition, Wiley, 2018, ISBN: 9781118063330.
3. W. Stallings, Operating Systems: Internals and Design Principles, 5th
edition, Pearson Education, 2005, ISBN: 9780134670959.

19
 MA 313 / CS 313
Suggested Course code

Title of the course Computer Networks

Course Category Department Core

L - T - P - Credits
Credit Structure
2-0-2-3

Name of the Concerned

Mathematics / Computer Science and Engineering
Department

Knowledge of data structures and algorithms, programming skills in

Pre-requisite if any
C/C++/python

This course will introduce computer networking protocols and performance

Objective of the Course
analysis of networks.

Course outcome Understanding the basic functionalities of computer networks

● Network Architecture and protocols. History of networking–Circuit

switching and packet switching. Network performance metrics–
Throughput and delay
Course Syllabus ● Application layer–HTTP, DNS, CDN, SMTP, P2P etc.,
● Transport layer–UDP and TCP, Reliability and congestion control in TCP.
● Socket programming, Introduction to Network Layer. Routing protocols.
Interdomain routing–BGP
● Link layer and physical layer, Performance analysis of networks. Router
Architecture, Resource allocation, and QoS, Network simulation version 3
(NS3).
● Introduction to next-generation networks.
● Practical components:
○ Experimental study of application protocols such as HTTP, FTP,
SMTP, using network packet sniffers and analyzers
○ Socket programming - Small exercises in socket programming in
C/C++/Java.
○ Experiments with packet sniffers to study the TCP protocol.
○ Introduction to ns3 (network simulator) and small simulation
exercises to study TCP behavior under different scenarios.
○ Setting up a small IP network in ns3
○ Experiments with ns3 to study Ethernet and 802.11 wireless LAN.
○ Programming with pcap

Suggested Books
Textbooks:
1. J. Kurose and K. Ross, Computer Networking, A Top-Down
Approach, Pearson Education, 8th Ed. 2022. ISBN: 978-9356061316
Reference books:
2. L. Peterson and B. Davie, Computer Networks, A Systems Approach,
Morgan Kaufmann Publishers Inc, 6th ed. 2021, ISBN: 978-
0128182000
3. W. R. Stevens, Unix Network Programming: The Sockets
Networking API, Pearson Education, 3rd ed. 2017, ISBN: 978-
9332549746
4. Bertsekas and Gallager, Data Networks, Pearson Education 2nd ed.,
2015. ISBN:978-9332550476

20
Course Code MA 357/ CS 357N

Title of the Course Optimization Algorithms and Techniques Lab

Course Category Department Core

Credit Structure L-T- P-Credits

0-0-2-1

Name of the Concerned Mathematics/Computer Science and Engineering

Department

Pre-requisite, if any Knowledge of Data Structures and Algorithms

Objective of the Course This is an introductory course in the field of mathematical optimization.

Course Outcomes At the end of the course, students will know

● The Basics of Optimization,
● Unconstrained and Constrained Optimization, and
● Linear and Quadratic Programming.

Course Syllabus • Understanding of Matlab/ Scilab via implementation of Newton's

method for solving non-linear system of equations as well as
numerical integration.
• Analyzing convexity of functions numerically.
• Implementation and analysis of Multi-dimensional Unconstrained
Optimization algorithms (Steepest Descent, Newton, Gauss-
Newton, Quasi-Newton, Conjugate Gradients etc.).
• Implementation and analysis of One-dimensional Unconstrained
Optimization algorithms (Dichotomous, Quadratic Interpolation,
Cubic Interpolation etc.).
• Implementation and analysis of Simplex and Interior Point Methods
for Linear Program.
• Implementation and analysis of Sequential Quadratic Program for
solving general Constrained Optimization problem.
Suggested Books Textbooks:
1. J. Nocedal and S. J. Wright, Numerical Optimization, 1st
Edition, Springer, 2006. ISBN: 78-1-4939-3711-0

Reference books:
2. A. Antoniou and W.-S.g Lu, Practical Optimization:
Algorithms and Engineering Applications, 2nd Edition,
Springer, 2021. ISBN: 978-1-0716-0843-2

21
Course Code MA 353/ CS 353N
Title of the Course Operating Systems Lab

Course Category Department Core

Credit Structure L-T- P-Credits

0-0-2-1
Name of the Mathematics / Computer Science and Engineering
Concerned
Department
Pre-requisite, if any NIL

Objective of the This course will introduce the basic components of operating systems and
Course functionalities.
Course Outcomes Understanding basic functionalities of operating system for efficient performance of
the processes
Course Syllabus ● OS Programming prerequisites: Familiarities with IPC facilities, IPC
identifiers, IPC keys, Message queues and their internal and user data
structures, System calls related to IPC, Semaphore and Shared memory.
● CPU scheduling: Simulation programs for long-term, short-term and medium
term schedulers, Simulation for the maintenance of various scheduling queues
such as ready, I/O, blocked etc., Implementations of different scheduling
algorithms such as FCFS, SJF, Priority scheduling (preemptive and non-
preemptive), Round robin, multilevel feedback queue scheduling and their
performance evaluations.
● Concurrent Processing and Concurrency Control: Simulation of updating
processe PCBs with shared memory, Implementation of interprocess
communication using simulated semaphore through (i) shared memory, (ii)
synchronized producer-consumer problem, (ii) Pipes and message passing
(asynchronous and synchronous). Concurrence control with pipes socket for
iterative and concurrent servers
● File Systems Implementation: creating, removing, accessing, protecting and
error handling of EXT2 FS, Registering the virtual file system in Kernel,
accessing superblock information.
Suggested Books Textbooks:
1. A. Silberschatz, P.B. Galvin, and G. Gagne, Operating System Principles,
7th edition, John Wiley, 2005. ISBN: 9788126509621
Reference books:
2. A. Silberschatz, P.B. Galvin, and G. Gagne, Operating System Concepts,
9th edition, Wiley, 2018. ISBN: 978-1-118-06333-0
3. W. Stallings, Operating Systems: Internals and Design Principles, 5th
edition, Pearson Education, 2005. ISBN: 978-0-13-467095-9

22
 Department Core in Semester-VI

Course Code MA 302

Title of the Course Statistical Inference

Course Category Department Core

Credit Structure L-T- P-Credits

2-0-2-3

Name of the Concerned Mathematics

Department
Pre-requisite, if any Probability and Statistics

Objective of the Course This course aims to describe the methods of estimation and testing of
hypotheses. The course will help to apply statistical methodologies in data
science and other fields of study.
Course Outcomes ● Understanding the estimation theory and testing of statistical hypotheses
and applying these techniques to real-life problems.

Course Syllabus • Review of random variables and associated probability distributions,

sampling distributions, order statistics, distribution of order statistics.
• Principles of Data Reduction: Sufficient statistics, minimal
sufficiency, Fisher’s factorization theorem, ancillary statistics,
completeness.
• Point and Interval Estimation: Concept of estimation, unbiased
estimation, uniformly minimum variance unbiased estimator, Rao-
Blackwell and Lehmann-Scheffe theorems and their applications,
Cramer-Rao inequality, method of moments, method of maximum
likelihood estimation, confidence intervals for mean, difference of
means, and proportions, Bayesian estimation.
• Testing of Hypothesis: Elements of testing of hypothesis, the most
powerful test, uniformly most powerful test, tests for one sample and
two sample problems for normal populations, tests for proportions.
Suggested Books Text Books:
1. G. Casella and R. L. Berger, Statistical Inference, Cengage Learning,
Delhi. (Duxbury Advanced Series), 2002, ISBN: 9788131503942.
2. V. K. Rohatgi and A. K. Md. E. Saleh, An Introduction to Probability and
Statistics, Wiley, 2001, ISBN: 9788126519262.

Reference Books:
3. J. A. Rice, Mathematical Statistics and Data Analysis, Duxbury Press,
2006, ISBN: 0534399428.
4. R. V. Hogg, J. McKean, and A. T. Craig, Introduction to Mathematical
Statistics, Pearson Education, 2019, ISBN: 9789332519114.

23
Course Code MA 306

Title of the Course Monte-Carlo Simulation

Course Category Department Core

Credit Structure L-T- P-Credits

2-0-2-3

Name of the Concerned Mathematics

Department

Pre-requisite, if any Basic knowledge of calculus, probability and statistics

Objective of the Course This course supply all the basic tools and theory for understanding the Monte-
Carlo simulation and demonstrate its applications in mathematics and finance.
Course Outcomes • The student will learn how to generate random numbers and its usage in
Monte-Carlo simulation.
• The students will be able to evaluate integrals, finding roots, maximum-
likelihood estimation using Monte-Carlo simulation.

Course Content • Uniform random number generation, apparent randomness of pseudo-

random number generators, generating random numbers from nonuniform
continuous distributions, generating random numbers from discrete
distributions.
• Random samples associated with Markov chains, variance reduction for
one-dimensional Monte-Carlo integration, errors in numerical integration.
• Theory of low-discrepancy sequences, finding a root, maximization of
functions, maximum-likelihood estimation, estimating derivatives, the
score function estimator.

Suggested Books Text Books:

1. G. S. Fishman, Monte Carlo Concepts, Algorithms, and Applications,
Springer, 1996, ISBN: 9780387945279.
2. I. T. Dimov, Monte Carlo Methods for Applied Scientists, World
Scientific, 2008, ISBN: 9789812779892.

Reference Books:
3. C. Robert, G. Casella, Monte Carlo Statistical Methods, Springer, 2013,
ISBN: 9781475730715.
4. W. Wang, Monte Carlo Simulation with Applications to Finance,
Chapman and Hall/CRC, 2019, ISBN: 9780367381356.
5. D. L. McLeish, Monte Carlo Simulation and Finance, Wiley, 2005,
ISBN: 9780471677789.

24
Course Code MA 308

Title of the Course Parallel Computing Methods

Course Category Department Core

Credit Structure L-T- P-Credits

0-1-2-2

Name of the Concerned Mathematics

Department

Pre-requisite, if any Basic knowledge of linear algebra

Objective of the Course To demonstrate the parallel computing techniques to solve mathematical
problems.

Course Outcomes Understanding major benefits and limitations of parallel computing.

Course Content • Concept of parallelism, scope of parallel computing, sources of overhead in

parallel programs.
• Performance metrics for parallel systems, scalability of parallel systems,
asymptotic analysis of parallel programs, matrix-vector multiplication,
matrix-matrix multiplication.
• Solving a system of linear equations, sequential search algorithms, search
overhead factor, parallel depth-first search, parallel best-first search.

Suggested Books Text Books:

1. A. Grama, A. Gupta, G. Karypis, and V. Kumar, Introduction to
Parallel Computing, Addison Wesley, 2003, ISBN: 0201648652.
2. M. J. Quinn, Parallel Computing: Theory and Practice, Tata McGraw
Hill, 2002, ISBN: 9780070512948.

Reference Books:
3. W. P. Petersen, and P. Arbenz, Introduction to Parallel Computing,
Oxford Texts in Applied and Engineering Mathematics, 2004, ISBN:
019 8515766.
4. P. S. Pacheco, An Introduction to Parallel Programming, Morgan
Kaufmann, 2011, ISBN: 9780123742605.
5. D. B. Kirk and W. W. Hwu, Programming Massively Parallel
Processors: A Hands-on Approach, Morgan Kaufmann, 2016, ISBN:
9780128119860.

25
Course Code MA 304/ CS 304N

Title of the Course Computational Intelligence

Course Category Department Core

Credit Structure L-T- P-Credits
2-1-0-3
Name of the Concerned Mathematics / Computer Science and Engineering
Department
Pre-requisite, if any Computer Programming, Data structure, and Design
and Analysis of Algorithm
Objective of the Course Basics of machine learning techniques
Course Outcomes Understanding of machine learning techniques and implementation
Course Syllabus ● Introduction: Overview, Basics of Problem solving as an Artificial
Intelligence problem, Computational Intelligence, Applications.
Intelligent Search techniques, Knowledge representation,
● Methodologies: Computational intelligence methodologies; Learning,
adaptation: Artificial neural networks: feed-forward, recurrent and multi-
layer architectures; Supervised and unsupervised learning; Characteristics:
adaptability, fault tolerance, generalization; limitations of neuro-
computing.
● Different learning algorithms: Perceptron, Back propagation, Hopefield,
Kohenen networks. Uncertainty treatment: Fuzzy sets - Basic Definition;
Fuzzy-set- theoretic Operations – Member Function Formulation and
Parameterization – Fuzzy Rules and Fuzzy Reasoning, Fuzzy If-Then
Rules Hybrid computational learning : Fuzzy Neural Networks and
Evolutionary Algorithms
● Detailed Discussion from Example Domains: Industry, Language,
Medicine, Verification, Vision, Knowledge Based Systems etc.

Suggested Books Textbooks:

1. S. Russell and P. Norvig, Artificial Intelligence: A Modern Approach,
Pearson, 2010. ISBN: 978-0136042594
2. E. Rich and K. Knight, Artificial Intelligence, McGraw Hill Education,
2017. ISBN: 978-0070087705
Reference books:
3. J.S.R.J ang, C.T. Sun and E. Mizutani, Neuro-Fuzzy and Soft
Computing, Prentice Hall of India and Pearson Education, 2004. ISBN:
978-9332549883
4. D.E. Goldberg, Genetic Algorithms: Search, Optimization and
Machine Learning, Addison Wesley, 1989. ISBN: 9781584883883
5. S. Rajasekaran and G.A.V. Pai, Neural Networks, Fuzzy Logic and
Genetic Algorithms, Prentice Hall, 2003. ISBN: 9788120321861
6. R. Eberhart, P. Simpson and R. Dobbins, Computational Intelligence -
PC Tools, AP Professional, 1996. ISBN: 978-0122286308

26
Course Code MA 354/ CS 354N

Title of the Course Computational Intelligence Lab

Course Category Department Core

Credit Structure L-T- P-Credits
0-0-3-1.5

Name of the Concerned Mathematics/ Computer Science and Engineering

Department

Pre-requisite, if any Computer Programming, Data structure, Discrete Structure, Design and
Analysis of Algorithm
Objective of the Course Basics of machine learning techniques
Course Outcomes Understanding of machine learning techniques and implementation
Course Syllabus ● AI programming: Prolog, LISP, Experiments to support the associated
theory course that demonstrate the different applications of Neural,
fuzzy, evolutionary and hybrid model;
● Implementation: Minor project based on real life applications such as
Functional approximation; Time-series prediction; Pattern recognition;
Data compression; Control applications, Optimization etc.
Suggested Books Textbooks:
1. S. Russell and P. Norvig, Artificial Intelligence: A Modern Approach,
Prentice Hall Series in AI, 1995. ISBN: 978-9332543515
2. E. Rich and K. Knight, Artificial Intelligence, Tata McGraw Hill,
1992. ISBN: 978-0-07-067816-3
Reference books:
3. J.S.R.J ang, C.T. Sun and E. Mizutani, Neuro-Fuzzy and Soft
Computing, Prentice Hall and Pearson Education, 2004. ISBN: 978-
9332549883
4. D.E. Goldberg, Genetic Algorithms: Search, Optimization and
Machine Learning, Addison Wesley, 1989. ISBN: 9781584883883
5. S. Rajasekaran and G.A.V. Pai, Neural Networks, Fuzzy Logic and
Genetic Algorithms, Prentice Hall, 2003. ISBN: 9788120321861
6. R. Eberhart, P. Simpson and R. Dobbins, Computational Intelligence
- PC Tools, AP Professional, 1996. ISBN: 978-0122286308

27
 Department Elective in Semester-III

Suggested Course code MA 217

Title of the course Linear Programming

Course Category Department Elective

L-T-P-Credits
Credit Structure
2-1-0-3

Name of the Concerned

Mathematics
Department

Pre-requisite, if any Basics linear algebra and coordinate geometry

This course aims to develop basic understanding of linear programming

Objective of the Course
problems.

Students will learn basics of linear programming, solution methods, essence

Course Outcomes
of duality and applications
Course Syllabus ● Introduction to linear programming, formulating a linear program,
feasibility and optimality, solution space, some practical examples on
feasibility, optimality and sensitivity.
● Graphically solving linear programming problems (LPP) with two
variables, canonical and standard form of LPP, formalizing the
graphical method, problems with alternate optimal solutions, no
solutions, and unbounded feasible regions.
● Simplex method: Computational procedure, use of artificial variables,
Big M method, applications of simplex algorithm.
● Duality: Primal-dual pair, formulating a dual problem, duality
theorems, complementary slackness theorem.
● Solving linear programming with MATLAB/R, applications to
industrial problems.

Suggested Books Text Books:

1. H. A. Taha, Operations Research: An Introduction, Pearson
Education, 2022, ISBN: 9780137625819.
2. S. Bazaraa, J. J. Jarvis and H. D. Sherali, Linear Programming and
Network Flows, Wiley, 2011, ISBN: 9781118211328.

Reference Books:
3. N. S. Kambo, Mathematical Programming Techniques, Revised
Edition, Affiliated East-West Press, 2008, ISBN: 9788185336473.
4. G. Murty, Linear Programming, Wiley, 1983, ISBN:
9780471892496.

28
Suggested Course code MA 219

Title of the course Introduction to Dynamical Systems

Course Category Department Elective

L-T-P-Credits
Credit Structure
2-0-2-3
Name of the Concerned
Mathematics
Department

Pre-requisite, if any Basic calculus and ordinary differential equations

Objective of the Course
This course introduces relevant tools and techniques used in analysing
dynamic equations applied to modelling real-world problems.

Course Outcomes ● Formulating models of electrophysiology, chemical reactions, dynamics of

the human heart, etc.
● Analyzing slow-fast dynamics and implement it for the population models.

Course Syllabus
● Introduction to linear and nonlinear autonomous systems, complete
solutions, flows, blow-up, equilibrium and local stability, asymptotic
stability, quasi-stability, exponential stability, Hartman-Grobman theorem.
● Oscillation theory, weakly perturbed linear oscillators, multiple time scale
analysis, relaxation oscillations and multiple limit cycles, Stuart–Landau
oscillator networks.
● Introduction to monotone dynamical systems, Metzler matrices, Kamke’s
condition, Ji-Fa’s theorem, Smillie’s theorem, dynamics of cooperative and
competitive systems, application to the Ribosome flow model and
electrophysiology.
● Numerical simulations and applications: Modelling electric circuits, enzyme
kinetics, chemical oscillators and the Belousov-Zabitinsky reaction,
population models, dynamics of neurons and human heart.

Text Books:
Suggested Books
1. R. C. Hilborn, Chaos and Nonlinear Dynamics, Oxford University
Press, 2000, ISBN: 978-0198507239.
2. H. L. Smith, Monotone Dynamical Systems: An Introduction to the
Theory of Competitive Cooperative Systems, American Mathematical
Society, 2008, ISBN: 978-0821844878.

Reference Books:
3. S. H. Strogatz, Nonlinear Dynamics and Chaos, Westview Press, 2015,
ISBN: 978-0-8133-4910-7.
4. D. W. Jordon, P. Smith, Nonlinear Ordinary Differential Equations:
An Introduction for Scientists and Engineers, Oxford University Press,
2007, ISBN: 978-0199208258.

29
 Department Elective in Semester-IV

Course Code MA 210

Title of the Course Elementary Number Theory and Algebra

Course Category Department Elective

Credit Structure L-T- P-Credits

2-1-0-3

Name of the Concerned Mathematics

Department

Pre-requisite, if any Basic knowledge of linear algebra

Objective of the Course To expose the students to the basic ideas of algebra. At the end of the course,
students should be exposed to fundamental knowledge and problem-solving skills
in number theory and groups.

Course Outcomes Making students familiar with groups, ring and fields which will help them in
cryptography and coding theory.

Course Content • Number theory: Integers, divisibility in integers, GCD, LCM, Bezout’s
identity, modular arithmetic, Chinese remainder theorem, Fermat’s little
theorem, Euler Phi-function.
• Group theory: Cyclic, dihedral, symmetric, matrix groups, normal subgroups
and quotient groups, conjugacy classes, isomorphism theorems, group
automorphisms, symmetric group and alternating group, class equations,
Cauchy’s theorem (without proof), rings, integral domains, ideals, quotient
rings, prime and maximal ideals, ring homomorphisms, polynomial rings,
factorization in polynomial rings, fields, characteristic of a field, field
extensions.

Suggested Books Text Books:

1. N. Herstein, Topics in Algebra, John Wiley & Sons, 2005, ISBN:
997151253X.
2. D. Burton, Elementary Number Theory, McGraw Hill Education, 2017,
ISBN: 9355325126.

Reference Books:
3. D. S. Dummit and R.M. Foote, Abstract Algebra, John Wiley & Sons,
2003, ISBN: 812651776X.
4. M. Artin, Algebra, Prentice Hall of India, 1999, ISBN: 8184956754.
5. I. Niven, H. S. Zuckerman, and H. L. Montgomery, An Introduction to
the Theory of Numbers, John Wiley & Sons, 1991, ISBN:
9788126518111.

30
Course Code MA 212

Title of the Course Regression Analysis

Course Category Department Elective

Credit Structure L-T- P-Credits

2-1-0-3
Name of the Concerned Mathematics
Department
Pre-requisite, if any Probability and Statistics

Objective of the Course Understanding of data modelling and forecasting concepts. It has several
applications in the fields of machine learning and data science.

Course Outcomes ● understand and apply regression techniques to model and analyse the
relationship between variables,
● interpret the coefficients of regression models, and predict the new
observations.
Course Syllabus ● Simple Linear Regression: Least-squares and maximum likelihood
estimation of the parameters, hypothesis testing on the slope and intercept,
interval estimation, prediction of new observations, coefficient of
determination, regression through the origin.
● Multiple Linear Regression: Estimation of the model parameters, hypothesis
testing, confidence intervals, prediction of new observations.
● Model Adequacy Checking: Residual analysis, methods for scaling residuals,
residual plots, detection and treatment of outliers, lack of fit of the regression
model.
● Model Inadequacies Corrections: Variance-stabilizing transformations,
transformations to linearize the model, box–cox method, generalized and
weighted least squares.
● Multicollinearity, variance inflation factors, ridge regression, variable
selection and model building, logistic regression models, Poisson regression.
Suggested Books Text Books:
1. D. C. Montgomery, E. A. Peck, G. G. Vining, Introduction to Linear
Regression Analysis, Wiley, India, 2012, ISBN: 978-0470542811.
2. M. H. Kutner, C. J. Nachtsheim, J. Neter, W. Li, Applied Linear Statistical
Models, McGraw-Hill, Irwin, 2005, ISBN: 0-07-238688-6.

Reference Books:
3. N. R. Draper, H. Smith, Applied Regression Analysis, Wiley, 1998,
ISBN: 978-0471170822.

31
 Department Elective in Semester-V

Course Code MA 309

Title of the Course Numerical Methods for Partial Differential Equations

Course Category Department Elective

Credit Structure L-T- P-Credits

2-0-2-3

Name of the Concerned Mathematics

Department
Pre-requisite, if any Basic knowledge of differential equations

Objective of the Course The course will introduce some numerical techniques for solving partial
differential equations that are used for modelling many practical problems and
the theories behind them.

Course Outcomes Students will be able to choose suitable methods to solve different types of
differential equations numerically.
Course Syllabus • Finite difference method: Explicit and implicit schemes; consistency,
stability and convergence, maximum principle, Lax's equivalence theorem;
FTCS, ADI methods, Lax-Wendroff method, upwind scheme, CFL
conditions.
• Finite element method: Variational methods, method of weighted residuals,
finite element analysis of one- and two-dimensional problems.
• Finite volume schemes, conservation properties, multigrid methods and
boundary integral methods.
• Recent progresses on numerical PDEs arising in the applicable field will
be discussed and demonstrated through computations.

Suggested Books Text Books:

1. P. Knabner, L. Angermann, Numerical Methods for Elliptic and
Parabolic Partial Differential Equations, Springer, 2003, ISBN:
038795449X.
2. G. D. Smith, Numerical Solutions of Partial Differential Equations,
Calrendorn Press, 1985, ISBN: 9780198596509.

Reference Books:
3. G. F. Pinder, Numerical Methods for Solving Partial Differential
Equations: A Comprehensive Introduction for Scientists and
Engineers, 2018, John Wiley and Sons, Inc, ISBN: 9781119316114.
4. M. S. Gockenbach, Partial Differential Equations Analytical and
Numerical Methods, SIAM, 2002, ISBN: 0898715180.
5. M. M. Hafez, J. J. Chattot, Innovative Methods for Numerical
Solutions of Partial Differential Equations, World Scientific, 2002,
ISBN: 9810248105.
6. R. J. LeVeque, Finite Volume Methods for Hyperbolic Problems,
Cambridge University Press, 2002, ISBN: 9780521009249.

32
Course Code MA 311

Title of the Course Statistical Distribution Theory

Course Category Department Elective

Credit Structure L-T- P-Credits

2-1-0-3
Name of the Concerned Mathematics
Department
Pre-requisite, if any Probability and Statistics

Objective of the Course This course deals with multivariate distributions and their applications. The
concept of copula function will be introduced for measuring the dependence
between multivariate random variables.

Course Outcomes ● understanding the multivariate probability distributions.

● apply statistical techniques involving two or more dependent variables
using copula functions.
Course Syllabus ● Review of standard univariate distributions, distribution of function of
random variable, Jacobians of transformation technique, random sample
generation from univariate distributions.
● Bivariate distributions, conditional distributions, conditional expectation
and variance, independence of random variables, covariance, Pearson and
Spearman correlations, distributions of functions of random variables,
including sums, means, products and ratios, convolution technique.
● Bivariate and multivariate normal distributions and their properties,
bivariate exponential distribution and their properties, copula function
and their applications, and construction of bivariate distributions using
copula functions.

Suggested Books Text Books:

1. V. K. Rohatgi and A. K. Md. E. Saleh, An Introduction to Probability
and Statistics, Wiley, 2001, ISBN: 9788126519262.
2. G. Casella and R. L. Berger, Statistical Inference, Cengage Learning,
(Duxbury Advanced Series), 2002, ISBN: 9788131503942.

Reference Books:
3. J. A. Rice, Mathematical Statistics and Data Analysis. Duxbury Press,
2006, ISBN: 0534399428.
4. R. V. Hogg, J. McKean, and A. T. Craig, Introduction to Mathematical
Statistics, Pearson Education, 2019, ISBN: 9789332519114.
5. R. B. Nelsen, An Introduction to Copulas, Springer, 2006, ISBN:
9780387286594.

33
 Department Elective in VI Semester

Course Code MA 310

Title of the Course Algorithmic Techniques and Applications of Data Science

Course Category Department Elective

Credit Structure L-T-P–Credits

2-1-0-3
Name of the Concerned Mathematics / Computer Science and Engineering
Department
Pre-requisite, if any Linear Algebra, Probability and Statistics, Discrete Mathematics

Objective of the Course This course will provide fundamentals of algorithmic techniques of data science and
presents different applications wherein such techniques are applied.
Course Outcomes The students will learn the fundamental principles of data science and the
mathematical foundations related to high dimensional space, SVD, random walks, etc.
Course Syllabus • High Dimensional Space: Law of large numbers, geometry of high himensions,
properties of unit ball, generating points, uniformly at random from a ball,
Gaussians in high dimension, random projection and Johnson-Lindenstrauss
lemma.
• Singular Value Decomposition (SVD): SVD applications to discrete
optimization problems.
• Random Walks and Markov Chain: Stationary distribution, Markov Chain
Monte Carlo, Metropolis Hasting algorithm, areas and volumes, convergence of
random walks on undirected graphs, random walks in Euclidean space.
• Foundations of Machine Learning: Perceptron algorithm, kernel functions,
generalizing new data, overfitting and uniform convergence, online learning,
strong and weak learning, stochastic gradient descent.
• Algorithms for Massive Data Problems: Streaming, sketching, sampling.
• Advanced Topics in Data Science: Clustering techniques, linear methods for
regression and classification, basis expansion and regularization, kernel
smoothing methods, model assessment and selection, model inference and
averaging, additive models, logistic regression, trees and related methods,
boosting and additive trees, decision trees, random forests, neural networks,
recurrent neural networks (RNNs).

Suggested Books Text Books:

1. T. Hastie, R. Tibshirani and J. Friedman, Elements of Statistical Learning,
Springer, 2013, ISBN: 9781489905185.
2. A. Blum, J. Hopcroft and R. Kannan, Foundations of Data Science,
Cambridge University Press, 2020, ISBN: 9781108485067.
Reference Books:
3. C. C. Aggarwal and C. K. Reddy, Data Clustering, Algorithms and
Applications., Chapman and Hall, CRC Press, 2013, ISBN: 9781466558229.
4. M. J. Kearns and U. Vazirani, An Introduction to Computational Learning
Theory, The MIT Press, 1994, ISBN: 9780262111935.

34
Course Code MA 314
Title of the Course Random Matrices
Course Category Department Elective
Credit Structure L-T- P-Credits
2-1-0-3
Name of the Concerned Mathematics
Discipline
Pre-requisite, if any Basic knowledge of calculus and linear algebra

Objective of the Course This course introduces random matrices and their applications.

Course Outcomes Students will learn how the different ensembles of random matrices are defined and
their applications in various fields including data science, mathematical Finance, etc.

Course Syllabus • Random matrices in science and applications: Random matrices in statistics,
physics, telecommunications, numerical analysis, community detection in
networks
• Norms of random matrices: Norm of a random symmetric matrix, norms of
rectangular matrices, the moment method, Gaussian processes, Sudakov-
Fernique inequality
• Sample covariance matrices: Concentration inequalities and moment
inequalities for the sample covariance matrices, spectral projectors, principal
component analysis
• Gaussian ensembles of random matrices: Gaussian Unitary Ensemble (GUE),
Gaussian Orthogonal ensemble (GOE), Wishart ensemble, eigenvalues density,
eigenvectors, determinantal structure, spectral statistics, Wigner-Dyson-Gaudin-
Mehta conjecture
• Random vectors in high dimension: Multivariate Gaussian distribution,
distribution of norm of random vector, dimensionality reduction, Johnson-
Lindenstrauss lemma
Suggested Books Text Books:
1. G. Anderson, A. Guionnet and O. Zeitouni, An Introduction to Random
Matrices, Cambridge University Press, 2010, ISBN: 9780521194525.
2. M. L. Mehta, Random Matrices, Academic Press, 2004, ISBN:
9780120884094.

Reference Books:
3. T. Tao, Topics in Random Matrix Theory, AMS, 2023, ISBN:
9781470474591.
4. Z. Bai and J. W. Silverstein, Spectral Analysis of Large Dimensional
Random Matrices, Springer, 2010, ISBN: 9781441906601.

35
 Department Elective in Semester-VIII

Course Code MA 452/ MA 652

Title of the Course Theory of Transforms
Course Category Department Elective
Credit Structure L-T- P-Credits
2-1-0-3
Name of the Concerned Mathematics
Department
Pre-requisite, if any Basic knowledge of calculus, complex variable, differential equations
Objective of the Course This course explores properties of integral transforms, applying them to solve initial
and boundary value problems arise from mathematical modelling.
Course Outcomes Understanding the concept of various transform techniques and their applications.
Course Syllabus • Fourier series, Riemann-Lebesgue lemma, Gibbs phenomenon, Fourier sine and
cosine series, Fourier transform, Fourier integral theorem, convolution and
Parseval’s theorem, applications to partial differential equations.
• Laplace transform: Definition and properties, complex inversion, convolution
theorem, Heaviside’s expansion theorem, Bromwich contour integral,
applications to initial and boundary value problems.
• Fundamental theorem of the discrete Fourier transform, cyclical convolution,
and Parseval’s theorem.
• Z-transform: Definition and examples, basic operational properties of Z-
transforms, inverse Z-transform and examples, applications of Z-transforms to
finite difference equations and summation of infinite series.

Suggested Books Text Books:

1. R. J. Beerends, H. G. ter Morsche, J. C. van den Berg, E. M. van de Vrie,
Fourier and Laplace Transforms, Cambridge University Press, 2003,
ISBN: 0521534410.
2. U. Graf, Applied Laplace Transforms and Z-Transforms for Scientists
and Engineers, Birkhauser Verlag, Basel, 2004, ISBN: 3034895933.
Reference Books:
3. L. Debnath, D. Bhatta, Integral Transforms and their Applications,
Chapman & Hall/CRC, 2006, ISBN: 1584885750.
4. G. B. Folland, Fourier Analysis and its Applications, American
Mathematical Society, Providence, 2009, ISBN: 9780821847909.
5. A. Pinkus, S. Zafrany, Fourier Series and Integral Transforms,
Cambridge University Press, 1997, ISBN: 0521597714.

36
Course Code MA 407/ MA 607
Title of the Course Nonlinear Dynamics and Computations
Course Category Department Elective
Credit Structure L-T-P-Credits
2-0-2-3
Name of the Concerned
Mathematics
Department
Pre-requisite, if any Linear Algebra and Ordinary Differential Equations
Objective of the Course Understand the qualitative behaviours of autonomous systems and discrete
maps, and write independent algorithms and coding in exploring complex
dynamics numerically.
Course Outcomes ● Learning the idea of global stability with Lyapunov function.
● Generating Arnold tongue and shrimp structures using numerical
simulation.
Course Syllabus ● Introduction to dynamical systems, flows, phase space analysis, stable
and unstable manifolds, Hartman-Grobman theorem, Lyapunov function
and stability.
● Transcritical, saddle-node, pitch-fork, and Hopf-bifurcations, limit
cycles, index theory, Poincare-Bendixson theorem, homoclinic and
heteroclinic orbits, nonlinear centers.
● Lorenz system, Rössler attractor, Chua’s circuit, Kuramoto oscillator.
● Difference equations, periodic orbits, period-doubling, Feigenbaum
constant, period-bubbling, quasi-periodic, chaos, Lyapunov exponents,
Sharkovskii’s theorem, synchronization, shadowing lemma, routes to
chaos, Ruelle-Takens embedding theorem, reconstructing an attractor,
Smale horseshoe, the renormalization idea, Neimark-Sacker bifurcation,
Henon map.
● Bifurcations in 2D parameter plane: Isoperiodic diagram, Arnold tongue,
shrimp-shaped structure, spiral structure.
● Numerical simulations: Plotting orbits, phase portrait, bifurcation
diagrams, Lyapunov exponents, organized structures, etc. using
computer programming.
Suggested Books Text Books:
1. S. H. Strogatz, Nonlinear Dynamics and Chaos, Westview Press,
2015, ISBN: 9780813349107.
2. K. T. Alligood, T. D. Sauer and J. A. Yorke, Chaos: An Introduction
to Dynamical Systems, Springer, 1996, ISBN: 9780387224923.

Reference Books:
3. M. W. Hirsch, S. Smale and R. L. Devaney, Differential Equations,
Dynamical Systems, and an Introduction to Chaos, Academic
Press, 2012, ISBN: 9780123820105.
4. S. Lynch, Dynamical Systems with Applications using MATLAB,
Springer, 2014, ISBN: 9783319068206.

37
Course Code MA 454 / MA 654
Title of the Course Mathematical Modeling and Simulations
Course Category Department Elective
Credit Structure L-T-P-Credits
2-1-0-3
Name of the Concerned
Mathematics
Department
Pre-requisite, if any Basic knowledge of differential equations and linear algebra
Objective of the Course The Mathematical model plays a significant role providing a quantitative
framework for understanding and solving many real-life problems under
certain conditions.
Course Outcomes ● Students should be exposed to fundamental knowledge of implementing
the models in real-world situations.
● They will get the bright idea about constructing or selecting the
appropriate model, identify the problem, analytically or numerically
computing the solution and test the validity of models.
Course Syllabus • Introduction to mathematical modeling: Characteristics,
classifications, tools, techniques, deterministic and stochastic models,
modeling approaches, compartmental models, introduction to discrete
models and continuous models, dynamical systems and its mathematical
models.
• Models from systems of natural sciences: Population models for a
single species (discrete and continuous-time models), modeling of
population dynamics of two interacting species, analytical tool:
Kolmogorov Theorem, linear stability snalysis, Lotka-Volterra model,
variation of the classical LV model, Leslie-Gower model, prey-predator
model, arms race model, Holling-Tanner model, modified HT model,
applications of Lyapunov functions.
• Modeling of atmospheric, mining and engineering systems: Spatial
models using partial differential equations, modeling with stochastic
differential equations, models of heating and cooling, models for traffic
flow, model for detecting land mines, models in mechanical systems,
models in electronic systems, models for vehicle dynamics, kicked
harmonic oscillator, modeling the ventilation system of a mine.
• MATLAB/MATHEMATICA programs to study the dynamics of the
developed model systems
Suggested Books Text Books:
1. B. Barnes, G. R. Fulford, Mathematical Modeling with Case
Studies, CRC PRESS, Taylor & Francis, 2009, ISBN:
9781420083484.
2. S. Banerjee, Mathematical Modeling, Models, Analysis and
Applications, CRC Press, Taylor & Francis, London, 2014, ISBN:
9781482229165.

Reference Books:
3. E. A. Bender, An Introduction to Mathematical Modeling, Dover
Publications, 2012, ISBN: 9780486137124.
4. R. K. Upadhyay, S. R. K. Iyengar, Introduction to Mathematical
Modeling and Chaotic Dynamics, CRC Press Taylor & Francis,
London, 2014, ISBN: 9781439898871.

38
Course Code MA 405/ MA 605
Title of the Course Differential Equations in Population Dynamics
Course Category Department Elective
Credit Structure L-T-P-Credits
2-0-2-3
Name of the Concerned
Mathematics
Department
Pre-requisite, if any Basic concepts of differential equations and numerical methods
Objective of the Course Theory and computational techniques of differential equations will be applied in
population dynamics.

Course Outcomes ● To know some well celebrated models in population dynamics.

● exploring some ecological phenomenon such as the paradox of enrichment,
ecological resilience, hydra effects, etc.

Course Syllabus • Introduction: Mathematical models: necessity, advantages and limitations;

brief history of population models, different tools and modeling frameworks,
birth and death processes in population models.
• Ordinary differential equations: The Multhus, Verhulst, Lotka-Volterra,
Rosenzweiz-MacArthur and Hestings-Powell models, Routh-Hurwitz
criteria, mean population density in cyclic and chaotic dynamics, population
harvesting, resilience in ecology, hydra effects, population genetic models,
FitzHugh-Nagumo model.
• Partial differential equations: Fisher’s equation, Turing instability, pattern
formation, spatiotemporal chaos, reaction-diffusion in ecological and
chemical systems, diffusion in delayed predator-prey systems.
• Delay differential equations: Discrete and distributed delays in population
dynamics, Hopf-bifurcation and stability switching, delayed harvesting in
Nicholson blowflies model, delayed dispersal in patchy environment,
Mackey-Glass equation.
• Impulsive differential equations: Fixed-time and variable-time impulses,
impulses in biological control theory and epidemic models.
• Computer simulations: Several measures will be quantified in all the
models using numerical methods, and different software will be
implemented to interpret the system dynamics graphically.
Suggested Books Text Books:
1. J. D. Murray, Mathematical Biology: I. An Introduction, Springer,
2002, ISBN: 9780387952239.
2. R. K. Upadhyay, S. R. K. Iyengar, Spatial Dynamics and Pattern
Formation in Biological Populations, Chapman and Hall/CRC, 2021,
ISBN: 9780367555504.
Reference Books:
3. K. Gopalsamy, Stability and Oscillations in Delay Differential
Equations of Population Dynamics, Springer, 1992, ISBN:
9780792315940.
4. V. Lakshmikantham, D. D. Bainov, P. S. Simeonov, Theory of
Impulsive Differential Equations, World Scientific, 1989, ISBN:
9789971509705.

39
Course Code MA 402
Title of the Course Industrial Statistics
Course Category Department Elective
Credit Structure L-T-P-Credits
2-0-2-3
Name of the Concerned
Mathematics
Department
Pre-requisite, if any Probability and Statistics
Objective of the Course Understanding the concepts of quality control and system reliability techniques.

Course Outcomes Techniques to apply these concepts in industrial problems such as pharma,
automotive industry, etc.
Course Syllabus • Statistical Quality Control: Product quality, need for quality control, the
basic concept of process control, process capability and product control,
theory of control charts, operation and uses of control charts, probability
limits, specification limits, tolerance limits, 3-sigma limits, and warning
limits, control charts for variables and attributes, modified control charts,
acceptance sampling plans for attributes inspection, single and double
sampling plans and their properties, and plans for inspection by variables
for one-sided and two-sided specification.
• Reliability Theory: Reliability concepts and measures, components and
systems, coherent systems, reliability of coherent systems, life
distributions, reliability function, hazard rate, mean residual life and mean
time to failure, notions of ageing: IFR, IFRA, DMRL, NBU, and NBUE
classes and their duals, reliability modellings in series/parallel systems and
k-out-of-n systems.

Suggested Books Text Books:

1. D. C. Montgomery, Introduction to Statistical Quality Control,
Seventh edition, Wiley, 2019, ISBN: 9781119399308.
2. J. Navarro, Introduction to System Reliability Theory, Springer, 2022,
ISBN: 9783030869526.

Reference Books:
3. A. J. Duncan, Quality Control and Industrial Statistics, Irwin,
Homewood, 1986, ISBN: 9780256035353.
4. C. D. Lai, and M. Xie, Stochastic Ageing and Dependence for
Reliability. Springer, 2006, ISBN: 0387297421.

40
Course Code MA 404

Title of the Course Foundations of Approximation Theory

Course Category Department Elective

Credit Structure L-T- P-Credits
2-1-0-3
Name of the Concerned Mathematics
Department
Pre-requisite if any Basic knowledge of calculus, linear algebra
Objective of the Course This course introduces the basic terms and techniques of approximation
theory.

Course Outcomes Students would be able to understand the concept of approximations of

functions by polynomials and trigonometric functions.

Course Syllabus • Density theorems: Approximation of periodic function, Weierstrass

Theorem, Stone-Weierstrass Theorem.
• Linear Chebyshev approximation: Approximation in normed linear
space, linear Chebyshev approximation of vector-valued functions,
Chebyshev polynomials, strong uniqueness and continuity of metric
projection, discrete best approximation, approximation by algebraic
polynomials.
• Best approximation in normed linear spaces: Approximative
properties of sets, characterization and duality, continuity of metric
projections.

Suggested Books Text Books:

1. H. N. Mhaskar and D. V. Pai, Fundamentals of Approximation
Theory, CRC Press, 2007, ISBN: 0849309395.
2. M. J. D. Powell, Approximation Theory and Methods, Cambridge
University Press, 1981, ISBN: 0521224721.

Reference Books:
3. K. G. Steffens, The History of Approximation Theory: From Euler
to Bernstein, Birkhauser, Boston, 2006, ISBN: 0817643532.

41
Course Code MA 406
Title of the Course Graph Theory
Course Category Department Elective
Credit Structure L-T-P- Credits
2-1-0-3
Name of the Mathematics
Concerned
Department
Pre-requisite, if any Basic knowledge of linear algebra
Objective of the This course explores the theoretical development of graph theory and mathematical
Course models based on it.

Course Outcomes ● Solving problems arising from computer science using graphs and trees.
● Adapt and demonstrate state-of-the-art algorithms to real-life situations.

Course Syllabus • Graphs and graph models, graph terminology and special types of graphs, path
problems, incidence matrix, adjacency matrix, degree sequence of graphs, graph
isomorphism, trees and its characterizations, spanning trees, algorithms for
minimum weighted spanning trees, matching, perfect matching, augmenting
path, bipartite matching, Hall marriage theorem, matching in general graphs,
Tutte’s theorem, Min-Max theorems, Konig-Egervary theorem.
• Eulerian tour and seven bridges problem, Hamiltonian cycles and travelling
salesman problem, necessary conditions for Hamiltonian graphs, sufficient
conditions for Hamiltonian graphs, vertex coloring, edge coloring, Brook’s
theorem, network flows, max-flow min-cut theorem, Ford-Fulkerson algorithm,
planar graphs, Euler’s Formula, Kuratowski theorem, four color theorem.
Suggested Books Text Books:
1. D. B. West, Introduction to Graph Theory, Pearson Education, 2015,
ISBN: 0130144002.
2. J. A. Bondy, U. S. R. Murty, Graph Theory with Applications, Elsevier
Science Publishing Co., Inc., 1984, ISBN: 0444194517.

Reference Books:
3. T. H. Cormen, C. E. Leiserson, R. L. Rivest, and C. Stein, Introduction to
Algorithms, MIT press, 2009, ISBN: 026204630X
4. R. Diestel, Graph Theory, Springer, 2006, ISBN: 3540261834.
5. A. M. Gibbons, Algorithmic Graph Theory, Cambridge University Press,
1985, ISBN: 0521288819.

42
Course Code MA 408
Title of the Course Mathematical Theory of Waves
Course Category Department Elective
Credit Structure L-T- P-Credits
2-1-0-3

Name of the Concerned Mathematics

Department

Pre-requisite, if any Differential Equations

Objective of the Course To expose the students to the basic ideas that underline linear/non-linear wave
motion. To derive important mathematical tools to deal with problems of
wave theory. To consider simple examples of linear waves on strings, sound
waves and water waves.
Course Outcomes Upon completion of this course, students will know some of the most
interesting wave phenomena that have physical significance, while at the same
time, they will also be introduced to some of the deeper mathematical issues
that are pertaining to wave motion.
Course Syllabus ● Introduction to waves: Classification, terminology, mathematical
representation of waves.
● One-dimensional waves in solids and fluids: Waves in a string (free and
forced vibrations), waves in a rod, steady-state waves, reflection and
transmission of waves, water waves: Surface gravity waves, internal
waves, sinusoidal waves on deep water, ripples, wave patterns, Fourier
analysis of dispersive systems.
● Two-dimensional and three-dimensional waves: Basics of elasticity,
waves in finite, infinite and semi-infinite media, waves in
inhomogeneous media, motion of wave packets, dispersion and
attenuation, phase velocity, group velocity.
● Non-linear waves: General effect of nonlinearity, non-linear Schrodinger
equation, Riemann invariants, Piston problem, discontinues solutions
and shock waves, wave localization phenomena.
Suggested Books Text Books:
1. C. A. Coulson and Alan Jeffrey, Waves: A Mathematical Approach
to the Common Types of Wave Motion, Longman Group Limited,
1977, ISBN: 9780582449541.
2. G. B. Whitham, Linear and Nonlinear Waves, Pure and Applied
Mathematics, Wiley-Interscience, 1999, ISBN: 9780471359425.

Reference Books:
3. R. Knobel, An Introduction to the Mathematical Theory of Waves,
American Mathematical Society, 2000, ISBN: 9780821820391.
4. J. Lighthill, Waves in Fluids, Cambridge Mathematical Library,
Cambridge, 2001, ISBN: 9780521010450.

43
Course Code MA 414

Title of the Course Time Series Analysis

Course Category Department Elective

Credit Structure L-T- P-Credits
2-1-0-3

Name of the Concerned Mathematics

Department

Pre-requisite, if any Probability and Statistics

Objective of the Course To introduce various techniques for modelling and forecasting the time series
data.

Course Outcomes ● Understand the concepts of time series models and their applications in
various fields,
● Apply these models and techniques to real-life problems such as finance
and stock analysis, sales and demand forecasting, weather forecasting etc.
Course Syllabus • Components of time series, tests for randomness, trend and seasonality,
estimation/elimination of trend and seasonality, mathematical formulation
of time series, weak stationary, stationary up to order m.
• Auto-covariance and auto-correlation functions of stationary time series
and its properties, linear stationary processes and their time-domain
properties-AR, MA, ARMA, seasonal, non-seasonal and mixed models,
ARIMA models, invertibility of linear stationary processes.
• Parameter estimation of AR, MA, and ARMA models-least square
approach, estimation based on Yule-Walker for AR, ML approach for AR,
MA and ARMA models, asymptotic distribution of MLE, best linear
predictor and partial auto-correlation function (PACF), model-
identification with ACF and PACF, model order estimation techniques-
AIC, AICC, BIC, etc.

Suggested Books Text Books:

1. P. J. Brockwell and R. A. Davis, Introduction to Time Series and
Forecasting, Springer, 2002, ISBN: 9781493970865.
2. C. Chatfield and H. Xing, The Analysis of Time Series -An
Introduction with R, Chapman and Hall/CRC Press, 2019, ISBN:
9781138066137.

Reference Books:
3. R. H. Shumway, D. S. Stoffer, Time Series Analysis and Its
Applications with R Examples, Springer, 2016, ISBN:
9783319524511.
4. G. E. P. Box, G. Jenkins, and G. Reinsel, Time Series Analysis-
Forecasting and Control, Prentice-Hall International, Inc., 1994,
ISBN: 0130607746.

44
Course Code MA 416

Title of the Course Integral Equations

Course Category Department Elective

Credit Structure L-T- P-Credits

2-1-0-3
Name of the Concerned Mathematics
Department
Pre-requisite, if any Basic knowledge in calculus and differential equations

Objective of the Course The course introduces the classification of integral equations, fundamental
mathematical ideas and techniques that lie at the core of the integral equation
approach of problem solving.
Course Outcomes ● understand the concepts of Volterra and Fredholm integral equations
● apply appropriate integral equation to solve initial and boundary value
problems
Course Syllabus
● Basic concepts, Volterra integral equations, relationship between linear
differential equations and Volterra equations, resolvent kernel, method of
successive approximations, convolution type equations, Volterra equation
of the first kind, Abel’s integral equation.
● Fredholm integral equations, Fredholm equations of the second kind, the
method of Fredholm determinants, iterated kernels, integral equations with
degenerate kernels, eigenvalues and eigen functions of a Fredholm
alternative, construction of Green’s function for BVP.
● Weakly singular integral equations, Cauchy singular integral equations,
hypersingular integral equations.
● Bernstein polynomials, properties and its use in solving integral equations.

Suggested Books Text Books:

1. F. G. Tricomi, Integral Equations, Dover Publications Inc, 1985, ISBN:

9780486648286.
2. N. I. Muskhelishvili, Singular Integral Equations: Boundary Problems of
Functions Theory and Their Applications to Mathematical Physics,
Springer, 2011, ISBN: 9789400999961.

Reference Books:

3. D. Porter and D. S. G. Stirling, Integral Equations: A Practical Treatment,

from Spectral Theory to Applications, Cambridge University Press, 2012,
ISBN: 9781139172028.
4. R. P. Kanwal, Linear Integral Equations: Theory & Technique,
Birkhäuser, 2013, ISBN: 9781461460121.

45