Course Number

MA1101

Course Credit

(L-T-P-C)                

3-1-0-4

Course Title                  

Calculus and Linear Algebra

Learning Mode           

Lectures and Tutorials

Learning Objectives

To provide the essential knowledge of basic tools of Differential Calculus, Integral Calculus, Vector spaces and Matrix Algebra.

Course Description    

This course provides a foundation for Calculus and Linear Algebra. Topics related to properties of single and two variable functions along with their applications will be discussed. In addition fundamentals of linear algebra and matrix theory with applications will also be discussed.

Course Content         

Differential Calculus (12 Lectures): Limit and continuity of one variable function (including ε-δ definition). Limit, continuity and differentiability of functions of two variables, Tangent plane and normal, Change of variables, chain rule, Jacobians, Taylor’s Theorem for two variables, Extrema of functions of two or more variables, Lagrange’s method of undetermined multipliers.

Integral Calculus (10 Lectures): Riemann integral for one variable functions, Double and Triple integrals, Change of order of integration. Change of variables, Applications of Multiple integrals such as surface area and volume.

Vector Spaces (12 Lectures): Vector spaces (over the field of real numbers), subspaces, spanning set, linear independence, basis and dimension. Linear transformations, range and null space, rank-nullity theorem, matrix of a linear transformation.

Matrix Algebra (8 Lectures): Elementary operations and their use in getting the rank, inverse of a matrix and solution of linear simultaneous equations, Orthogonal, symmetric, skew-symmetric, Hermitian, skew-Hermitian, normal and unitary matrices and their elementary properties, Eigenvalues and Eigenvectors of a matrix, Cayley-Hamilton theorem, Diagonalization of a matrix.

Learning Outcome     

Students completing this course will be able to:

1. Understand various properties of functions such as limit, continuity and differentiability.

2. Learn about integrations in various dimension and their applications.

3. learn about the concept of basis and dimension of a vector space.

4. define Linear Transformations and compute the domain, range, kernel, rank, and nullity of a linear transformation.

5. compute the inverse of an invertible matrix.

6. solve the system of linear equations.

7. Apply linear algebra concepts to model, solve, and analyze real-world problems.

Assessment Method

Quiz /Assignment/ MSE / ESE

Course Number

CS1101

Course Credit

3-0-3-4.5

Course Title

Foundations of Programming

Learning Mode

Offline

Learning Objectives

·       To understand the fundamental concepts of programming 

·       To develop the basic problem-solving skills by designing algorithms and implementing them.

·       To learn about various data types, control statements, functions, arrays, pointers, and file handling.

·       To achieve proficiency in debugging and testing a C program

Course Description

This introductory course provides a solid foundation in programming principles and techniques. Designed for students with little to no prior programming experience, it covers fundamental concepts such as variables, data types, control structures, functions, and basic data structures. Students will learn to write, debug, and execute programs using a high-level programming language. Emphasis is placed on developing problem-solving skills, logical thinking, and the ability to write clear and efficient code. By the end of the course, students will be equipped with the essential skills needed to pursue more advanced studies in computer science and software development.

Course Outline

Introduction and Programming basics, 

Expressions

Control and Iterative statements,

Functions, Arrays, 

Recursion vs. Iteration

Pointers, 

2D-Array with pointers, 

Structures, 

String,

Dynamic memory allocation,

File handling, 

Contemporary programming languages, and applications

Practical component: Lab to be conducted on a 3-hour slot weekly. It will be conducted with the theory course so the topics for problems given in the lab are already initiated in the theory class.

Learning Outcome

·       Understanding of Basic Syntax and Structure in C language

·       Proficiency in Data Types, Operators, and Control Structures

·       Function Implementation and learn to use them appropriately

·       Efficient Use of Arrays and Strings

·       Pointer Utilization

·       Ability to perform dynamic memory allocation and deallocation using malloc (), calloc (), realloc (), and free () functions.

·       Structured data management with structures and unions

·       Exposure of file Handling

·       Learning debugging and error Handling

Assessment Method

Internal (Quiz/Assignment/Project), Mid-Term, End-Term

Course Number          

PH1101/PH1201

Course Credit                

3-1-3-5.5

Course Title                  

Physics

Learning Mode           

Lectures and Tutorials

Learning Objectives

Complies with Program Goals 1 and 2

Course Description    

This course deals with fundamentals in Classical mechanics, Waves and Oscillations and Quantum Mechanics. As a prerequisite, the mathematical preliminaries such as coordinate systems, vector calculus etc will be discussed in the beginning.  

Course Outline         

Orthogonal coordinate systems (Plane polar, Spherical, Cylindrical), concept of generalised coordinates, generalised velocity and phase space for a mechanical system, Introduction to vector operators, Gradient, divergence, curl and Laplacian in different co-ordinate systems.

Central force problem and its applications.

Rigid body rotation, vector nature of angular velocity, Finding the principal axes, Euler's equations; Gyroscopic motion and its application; Accelerated frame of reference, Fictitious forces.

Potential energy and concept of equilibrium, Lennard-Jones and double-well potentials, Small oscillations, Harmonic oscillator, damped and forced oscillations, resonance and its different examples, oscillator states in phase space, coupled oscillations, normal modes, longitudinal and transverse waves, wave equation, plane waves, examples two- and three-dimensional waves.

Michelson-Morley experiment, Lorentz transformation, Postulates of special theory of relativity, Time dilation and length contraction, Applications of special theory of relativity.  

Learning Outcome     

Complies with PLO 1a, 2a, 3a

Assessment Method

Quiz, Assignments and Exams

Course code       

CE1101/CE1201

Course Credit

(L-T-P-C)                                 

1-0-3-2.5

Course Title                  

Engineering Graphics

Learning Mode           

Lectures and Practical

Learning Objectives

Complies with PLO-1a

1.     The course on engineering drawing is designed to introduce the fundamentals of technical drawing as an important form of conveying information.

2.     Apply principles of engineering visualization and projection theory to prepare engineering drawings, using conventional and modern drawing tools.

3.     Practice drawing orthographic projections, isometric views, and sectional views, of simple and combined solids in different orientations.

Course Description    

This course will introduce drawing as a tool to represent a complex three-dimensional object on two-dimensional paper through methods of projections. The course explains the use of different drafting tools and the importance of conventions for uniformity and standardization of the interpretation of the drawings. 

Course Outline         

Fundamental of engineering drawing, line types, dimensioning, and scales. Conic sections: ellipse, parabola, hyperbola; cycloidal curves.

Principle of projection, method of projection, orthographic projection, plane of projection, first angle of projection, Projection of points, lines, planes and solids.

Section of solids: Sectional views of simple solids- prism, pyramid, cylinder, cone, sphere; the true shape of the section. Methods of development, development of surfaces.

Isometric projections: construction of isometric view of solids and combination of solids from orthographic projections.

Introduction to AutoCad and solving isometric problems.

Learning Outcome     

After attending this course, the following outcomes are expected:

a)     The student will understand the basic concepts of engineering drawing.

b)     The student will be able to use basic drafting tools, drawing instruments, and sheets.

c)     The student will be able to represent three-dimensional simple and combined solid objects on two-dimensional paper.

d)     The student will be able to visualize and interpret the orientation of simple and combine solid objects.

Assessment Method

Laboratory Assignments (30%), Mid-semester examination (25%) and End-semester examination (45%).

Course Number 

EE1101/EE1201

Course Credit 

3-0-3-4.5 

Course Title 

Electrical Sciences     

Learning Mode 

Lectures and Experiments  

Learning Objectives 

Complies with Program goals 1, 2 and 3 

Course Description 

The course is designed to meet the requirements of all B. Tech programmes. The course aims at giving an overview of the entire electrical engineering domain from the concepts of circuits, devices, digital systems and magnetic circuits. 

Course Outline 

Circuit Analysis Techniques, Circuit elements, Simple RL and RC Circuits, Kirchoff’s law, Nodal Analysis, Mesh Analysis, Linearity and Superposition, Source Transformations, Thevenin’s and Norton’s Theorems, Time Domain Response of RC, RL and RLC circuits, Sinusoidal Forcing Function, Phasor Relationship for R, L and C, Impedance and Admittance, Instantaneous power, Real, reactive power and power factor. 

Semiconductor Diode, Zener Diode, Rectifier Circuits, Clipper, Clamper, UJT, Bipolar Junction Transistors, MOSFET, Transistor Biasing, Transistor Small Signal Analysis, Transistor Amplifier and their types, Operational Amplifiers, Op-amp Equivalent Circuit, Practical Op-amp Circuits, Power Opamp, DC Offset, Constant Gain Multiplier, Voltage Summing, Voltage Buffer, Controlled Sources, Instrumentation Amplifier, Active Filters and Oscillators. 

Number Systems, Logic Gates, Boolean Theorem, Algebraic Simplification, K-map, Combinatorial Circuits, Encoder, Decoder, Combinatorial Circuit Design, Introduction to Sequential Circuits. 

Magnetic Circuits, Mutually Coupled Circuits, Transformers, Equivalent Circuit and Performance, Analysis of Three-Phase Circuits, Power measurement in three phase system, Electromechanical Energy Conversion, Introduction to Rotating Machines (DC and AC Machines). 

Laboratory: 

Experiments to verify Circuit Theorems; Experiments using diodes and bipolar junction transistor (BJT): design and analysis of half -wave and full-wave rectifiers, clipping and clamping circuits and Zener diode characteristics and its regulators, BJT characteristics (CE, CB and CC) and BJT amplifiers; Experiment on MOSFET characteristics (CS, CG, and CD), parameter extraction and amplifier; Experiments using operational amplifiers (op-amps): summing amplifier, comparator, precision rectifier, Astable and Monostable Multivibrators and oscillators; Experiments using logic gates: combinational circuits such as staircase switch, majority detector, equality detector, multiplexer and demultiplexer; Experiments using flip-flops: sequential circuits such as non-overlapping pulse generator, ripple counter, synchronous counter, pulse counter and numerical display; Power Measurement by two Wattmeter method; Open and Short Circuit Tests of Transformer. 

Learning Outcomes 

Complies with PLO 1a, 2a and 3a 

Assessment Method 

Quiz, Assignments and Exams 

Course Number

HS1101

Course Credit

L-T-P-W: 2-0-1-2.5

Course Title

English for Professionals

Learning Mode

Offline

Learning Objectives

This course aims to help the students (a) attain proficiency in written English through the construction of grammatically correct sentences, utilization of subject-verb agreement principles, mastery of various tenses, and effective deployment of active and passive voice to ensure coherent and impactful written expression; (b) enhance oral communication skills by honing public speaking abilities, acquiring strategies to deliver persuasive presentations, and cultivating a polished telephone etiquette, enabling confident and articulate verbal communication; (c) foster active listening capabilities by recognizing different types of listening, and applying proven methods and strategies to improve active listening skills; (d) strengthen reading skills, including comprehension, interpretation, and critical analysis, to grasp diverse written materials and derive meaning from various types of texts encountered in academic and professional contexts; (e) develop adeptness in written communication for business purposes, encompassing the understanding of essential writing elements, mastery of appropriate writing styles thereby enhancing prospects for successful job

interviews and subsequent professional endeavors.

Course Description

This academic course on communication skills aims to equip students with fluency in spoken and written English for effective expression in both academic and professional settings. By focusing on essential communication principles and providing practical experiences, students develop clarity, precision, and confidence in their communication. Through interactive discussions and exercises, students enhance critical thinking and adaptability in diverse contexts. Upon completion, students will excel in formal presentations, group discussions,

and persuasive writing, enhancing their overall communication proficiency.

Course Outline

Unit I: Introduction to professional communication – LSRW - Phonetics and phonology

Sounds in English Language – production and articulation – rhythm and intonation – connected speech - Basic Grammar and Advanced Vocabulary

Sounds in English Language – production and articulation – rhythm and intonation – connected speech – persuading and negotiating – brevity and clarity in language.

Unit II: Characteristics of Technical Communication: Types of communication and forms of communication - Formal and informal communication Verbal and non-Verbal Communication – Communication barriers and remedies Intercultural communication – neutral language

Unit III: Comprehension and Composition – summarization, precis writing Business Letter Writing CV/ Resume – E-Communication

Unit IV: Statement of Purpose, Writing Project Reports, Writing research proposal, writing abstracts, developing presentations, interviews – combating nervousness

Tutorial: Listening Exercises, Speaking Practice (GDs, and Presentations), and Writing Practice

Learning Outcome

·       Attain proficiency in written English, enabling the construction of grammatically correct sentences and coherent written expression through the use of appropriate grammar, tenses, and voice.

·       Enhance oral communication skills, including public speaking, persuasive presentation, and polished telephone etiquette, fostering confident and articulate verbal expression.

·       Cultivate active listening abilities, recognizing different listening types, overcoming obstacles, and employing strategies for attentive and effective communication.

·       Develop proficient written communication skills for business purposes, demonstrating understanding of essential writing elements, appropriate styles, and the creation of reports, notices, agendas, and minutes that effectively convey information.

Assessment Method

Class test + Quiz = 20%; Mid-semester = 25%; Assignment = 15%; End semester = 40%

Course Number

MA1201

Course Credit

(L-T-P-C)                

3-1-0-4

Course Title                  

Probability Theory and Ordinary Differential Equations

Learning Mode           

Lectures and Tutorials

Learning Objectives

To introduce the basic concepts of probability, statistics, and Differential equations.

Course Description    

This course aims to cover basic concepts of probability, statistics and ordinary differential equations. In particular, popular distributions, random sampling, various estimators and hypothesis testing will be discussed. Students will also get exposure to the linear ordinary differential equations and their solution techniques.

Course Content         

Probability (12 Lectures): Random variables and their probability distributions, Cumulative distribution functions, Expectation and Variance, probability inequalities, Binomial, Poisson, Geometric, negative binomial distributions, Uniform, Exponential, beta, Gamma, Normal and lognormal distributions.

Statistics (10 Lectures):  Random sampling, sampling distributions, Parameter estimation, Point estimation, unbiased estimators, maximum likelihood estimation, Confidence intervals for normal mean, Simple and composite hypothesis, Type I and Type II errors, Hypothesis testing for normal mean.

Ordinary Differential Equations (20 Lectures): First order ordinary differential equations, exactness and integrating factors, Picard's iteration, Ordinary linear differential equations of n-th order, solutions of homogeneous and non-homogeneous equations (Method of variation of parameters). Systems of ordinary differential equations,

Power series methods for solutions of ordinary differential equations. Legendre equation and Legendre polynomials, Bessel equation and Bessel functions.

Learning Outcome     

Students will get exposure and understanding of:

1.     Random variables and their probability distributions

2.     Understand popular distributions and their properties

3.     Sampling, estimation and hypothesis testing

4.     Solution of ordinary differential equations

5.     Solution of system of ordinary differential equations

6.     Special functions arising as power series solutions of ordinary differential equations

Assessment Method

Quiz /Assignment/ MSE / ESE

Course Number

CS1201

Course Credit

3-0-3-4.5

Course Title

Data Structure

Learning Mode

Offline

Learning Objectives

·       Understand the principles and concepts of data structures and their importance in computer science.

·       Learn to implement various data structures and understand how different algorithms works. 

·       Develop problem-solving skills by applying appropriate data structures to different computational problems.

·       Achieving proficiency in designing efficient algorithms.

Course Description

This course provides a comprehensive study of data structures and their applications in computer science. It focuses on the implementation, analysis, and use of various data structures such as arrays, linked lists, stacks, queues, trees, and graphs. Through theoretical concepts and practical programming exercises, this course aims to develop problem-solving and algorithmic thinking skills essential for advanced topics in computer science and software development.

Course Outline

·       Introduction to Data Structure,

·       Time and space requirements, Asymptotic notations

·       Abstraction and Abstract data types 

·       Linear Data Structure: stack, queue, list, and linked structure

·       Unfolding the recursion

·       Tree, Binary Tree, traversal

·       Search and Sorting, 

·       Graph, traversal, MST, Shortest distance 

·       Balanced Tree

Practical component: Lab to be conducted on a 3-hour slot weekly. It will be conducted with the theory course so the topics for problems given in the lab are already initiated in the theory class.

Learning Outcome

·       Understand Data Structure Fundamentals

·       Implement Basic Data Structures using a programming language

·       Analyse and Apply Algorithms

·       Design and Analyse Tree Structures

·       Understand the usage of graph and its related algorithms

·       Design and Implement Sorting and Searching Algorithms

·       Debug and Optimize Code

Assessment Method

Internal (Quiz/Assignment/Project), Mid-Term, End-Term

Course Number          

CH1201/CH1101

Course Credit                

3-1-3-5.5

Course Title                  

Chemistry

Learning Mode           

Offline

Learning Objectives

The course aims to lay a foundation for all three branches of chemistry, viz. Organic, Inorganic, and Physical Chemistry. The course aims to nurture knowledge to appreciate the interface of chemistry with other science and Engineering branches by combining theoretical concepts and experimental studies.

Course Description    

This course introduces basic organic chemistry, inorganic chemistry and Physical chemistry to understand fundamental laws that governs various reactions, reaction rates, equilibrium, and their applications in daily life through relevant experimentation.

Course Outline         

Module 1: Thermodynamics: The fundamental definition and concept, the zeroth and first law. Work, heat, energy and enthalpies. Second law: entropy, free energy and chemical potential. Change of Phase. Third law. Chemical equilibrium. Conductance of solutions, Kohlrausch’s law-ionic mobilities, Basic Electrochemistry.

Module 2: Coordination chemistry: Crystal field theory and consequences color, magnetism, J.T distortion. Bioinorganic chemistry: Trace elements in biology, heme and non-heme oxygen carriers, haemoglobin and myoglobin; Organometallic chemistry.

Module 3: Stereo and regio-chemistry of organic compounds, conformational analysis and conformers, Molecules devoid of point chirality (allenes and biphenyls); Significance of chirality in living systems, organic photochemistry, Modern techniques in structural elucidation of compounds (UV–Vis, IR, NMR).

Module 4 (Lab Component): Experiments based on redox and complexometric titrations; synthesis and characterization of inorganic complexes and nanomaterials; synthesis and characterization of organic compounds; experiments based on chromatography; experiments based on pH and conductivity measurement; experiment related to chemical kinetics and spectroscopy.

Learning Outcome     

Students will be able to
1. identify organic and inorganic molecules and relate them to daily life applications through experiments.

2. understand important hypothesis, laws and their derivations to intercept physical phenomenon of chemical reactions and apply them in hands-on experiments.

3. understand the importance of organic and inorganic molecules in our body and environment.

4. know important analytical techniques to intercept chemical entity.

5. approach organic and inorganic synthesis as a skillset for drug manufacturing, calculate limiting reagents and yields, use various analytical tools to characterize organic compounds, interpret and ascertain data related to Physical chemistry aspects and know laboratory safety measures, risk factors and scientific report writing skills.

Assessment Method

Theory: 20% Quiz and assignment, 30% Mid sem and 50% End semester exams for theory part (4 credits).

Lab: 60% lab report, lab performance and assignment, 20% End semester exam for practical part, 20% viva/quiz (1.5 credits).

Overall Weightage: Theory (70%), Lab (30%).

Course Number          

ME1201/ME1101

Course Credit                

0-0-3-1.5

Course Title                  

Mechanical Fabrication

Learning Mode           

Fabrication work – hands on fabrication work in Workshop

Learning Objectives

Complies with PLOs 3-4.

·       This course aims to develop the concepts and skills of various mechanical fabrication methods.

·       Fabrication of metallic and non-metallic components, fabrication using bulk and sheet metals, subtractive and additive manufacturing methods, and assemble the parts

Course Description    

This course is designed to fulfil the need of hand on experience about various approaches (conventional and CNC, subtractive and additive) of mechanical fabrication approaches.

Prerequisite: NIL

Course Outline         

The jobs for various shops should be planned such that they are the parts of an assembled item. The student groups will fabricate different parts in various shops which will involve some amount of their creativeness/input particularly in design and/or planning.

Various components as required for the assembled part can be made using the following shops: 

Sheet Metal Working:

Development, sheet cutting and fabrication of designated job using sheet metal (ferrous/nonferrous); Joining of required portions by soldering, in case part is desired to be made leak proof.

Pattern Making and Foundry:

Making of suitable pattern (wood); making of sand mould, melting of non-ferrous metal/alloy (Al or Al alloys), pouring, solidification. Observation/identification of various defects appeared on the component.

Joining:

Butt/lap/corner joint job fabrication as required  of low carbon steel plates; weld quality inspection by dye-penetration test (non-destructive testing approach)of the component made. Demonstration of semi-automatic Gas Metal Arc welding (GMAW).

Conventional machining:

Operations on lathe and vertical milling to fabricate the required component. The fabrication of the component should cover various lathe operations like straight turning, facing, thread cutting, parting off etc., and operations using indexing mechanism on vertical milling.

CNC centre:

Fundamentals of CNC programming using G and M code; setting and operations of job using CNC lathe or milling, tool reference, work reference, tool offset, tool radius compensation to fabricate the component with a designed profile on Al/Al-alloy plate.

3D printing (Fused Filament Fabrication): (2 weeks)

Create the model, select appropriate slicing and path for fabrication of a 3D job by layer deposition (additive manufacturing approach) using polymeric material. Demonstration on pattern fabrication using 3D printing.

Learning Outcome     

·       This course would enable the students to develop the concept of design, fabrication (subtractive and additive) for various engineering applications. Fabrication of components and assemble them.

·       The practical skill and hands on experience for various fabrication methods from bulk, sheet metal using conventional as well as CNC machines.

Assessment Method

Fabrication of components in each of the shops required for assembly of the given part; submission of reports for each shop, and quiz assessment.

Course Number

ME1202/ ME1102

Course Number

Engineering Mechanics

L-T-P-C

3-1-0-4

Pre-requisites

Nil

Semester

Spring

Learning Mode

Lectures

Learning Objectives

Complies with PLOs 1, 4

·       The objective of this first course in mechanics is to enable engineering students to analyze basic mechanics problems and apply vector-based approach to solve them.

Course Outline

1.       Rigid body statics: Equivalent force system. Equations of equilibrium, Free body diagram, Reaction, Static indeterminacy.

2.       Structures: 2D truss, Method of joints, Method of section. Beam, Frame, types of loading and supports, axial force, Bending moment, Shear force and Torque Diagrams for a member.

3.       Friction: Dry friction (static and kinetic), wedge friction, disk friction (thrust bearing), belt friction, square threaded screw, journal bearings, Wheel friction, Rolling resistance.

4.       Centroid and Moment of Inertia

5.       Introduction to stress and strain: Definition of Stress, Normal and shear Stress. Relation between stress and strain, Cauchy formula.

Stress in an axially loaded member and stress due to torsion in axisymmetric section

Learning Outcomes:

Following learning outcomes are expected after going through this course.

·       Learn and apply general mathematical and computer skills to solve basic mechanics problems.

·       Apply the vector-based approach to solve mechanics problems.

Assessment Method

Mid semester examination, End semester examination, Class test/Quiz, Tutorials

Course Number

CS2101

Course Credit

(L-T-P-C)

3-0-3-4.5

Course Title

Algorithm

Learning Mode

Offline

Learning Objectives

This course aims to help the students

(a) to understand and explain fundamental concepts of computational complexity, including time and space complexity, and analyses the efficiency of algorithms;

(b) to apply various algorithm design paradigms such as divide-and-conquer, dynamic programming, greedy algorithms, and backtracking to solve computational problems;

(c) to develop and implement common algorithms for tasks such as sorting, searching, and graph traversal, and utilize well-known algorithms like Dijkstra's and Kruskal's;

(d) to utilize fundamental data structures, including arrays, linked lists, stacks, queues, trees, and graphs, selecting and implementing the most appropriate one for specific problems; and

(e) to evaluate the performance and scalability of algorithms and data structures, conducting empirical analysis to understand their practical performance, and enhancing problem-solving skills through theoretical knowledge application in practical scenarios.

Course Description

The course introduces the basics of computational complexity analysis and various algorithm design paradigms. The goal is to provide students with solid foundations to deal with a wide variety of computational problems, and to provide a thorough knowledge of the most common algorithms and data structures.

Course Outline

Unit I

Role of algorithms in computing and elementary data structures.

Unit II
Analysis framework: Asymptotic notations, Analysis & Master Theorem

Unfolding of recursion: review of sorting and searching algorithms, Huffman Encoding, String matching, hashing, Trees, Subset sum

Unit III 
Algorithm design paradigm:

·       Brute force algorithms- Exhaustive search

·       Greedy algorithms

·       Divide and conquer algorithms, Branch-and-bound

·       Backtracking

·       Dynamic programming: Matrix Chain Multiplication, 0/1 Knapsack problem

Unit IV
Graph based algorithm: MST, Shortest distance, colouring, Vertex cover, TSP

Unit V
Reducibility:  P, NP, NP complete, and NP hard

Unit VI
Elements of Randomized and approximation Algorithms

Practical component: Lab to be conducted on a 3-hour slot weekly. It will be conducted with the theory course so the topics for problems given in the lab are already initiated in the theory class.

Learning Outcome

·       Describe how efficiency affects the practical usage of algorithms and data structures.

·       Identify different algorithmic techniques for running programs at scale.

·       Construct programs that apply computational concepts as a tool in other domains.

·       Discuss how computer science interacts with and affects the world.

Assessment Method

Internal(Quiz/Assignment/Project), Mid-Term, End-Term

Course Number

CS2102

Course Credit

(L-T-P-C)

3-0-3-4.5

Course Title

 Digital Logic and Computer Organization

Learning Mode

Offline

Learning Objectives

This course targets to cover the different number systems, designing of combinational and sequential logic circuits.  This course will also expose students to the basic architecture of processing, memory and i/o organization in a computer system.

Course Description

The course covers foundation of digital logic and Computer organization that including number systems, Boolean algebra, optimizing logic gates. Besides this it covers designing of different combinational and sequential circuits, computer organization  

Course Outline

Number System and Codes; Combinational logic circuits: Sequential logic circuits; Finite State machines.

Basic computer organization and design, Operational concepts, Instruction codes, Computer Registers, Computer Instructions   Familiarization with assembly language programming; Execution of a complete instruction.

Memory organization:  concept of hierarchical memory organization  

I/O devices – Programmed Input/output -Interrupts – Direct Memory Access – Buses, I/O devices and processors.

 Practical component: Lab to be conducted on a 3-hour slot weekly. It will be conducted with the theory course so the topics for problems given in the lab are already initiated in the theory class.

Learning Outcome

 The student will be able to:

·       Demonstrate an understanding of how data is represented within a computer system.

·       Appreciate understanding of the basic blocks, key terminology in digital logic and Computer organization

·       Demonstrate classic components of a computational system (i.e. input, output, memory, data path, control) and understanding their functionality.

Assessment Method

Internal(Quiz/Assignment/Project), Mid-Term, End-Term

Course Number

 CS2103

Course Credit

(L-T-P-C)

 2-0-2-3

Course Title

Artificial Intelligence Concepts

Learning Mode

Offline

Learning Objectives

This course aims to help the students (a) grasp the fundamental principles and subfields of Artificial Intelligence (AI) and Data Science.(b) Gain expertise in the stages of Data Science from data collection to model evaluation.(c) proficiency in applying supervised and unsupervised learning algorithms.(d) introduced to Deep Learning architectures and their applications.

Course Description

This course offers a comprehensive exploration of foundational principles and advanced techniques in Artificial Intelligence (AI), Data Science, Machine Learning (ML), and Deep Learning (DL). Students will delve into the ethical implications, applications, and future trends of AI, understanding its societal impacts and responsible deployment. The curriculum covers the evolution and stages of Data Science, emphasizing mastery of data collection, pre-processing, exploratory analytics, and rigorous model development and evaluation across various domains. In Machine Learning, students will gain proficiency in supervised and unsupervised learning algorithms, feature selection, dimensionality reduction, and a variety of classification and clustering techniques. Deep Learning concepts will be introduced, focusing on neural networks, Convolutional Neural Networks (CNNs) for image analysis, Recurrent Neural Networks (RNNs) for sequential data processing, attention mechanisms, and training Generative Adversarial Networks (GANs). Through theoretical lectures, practical exercises, and hands-on projects, students will acquire the skills necessary to apply these technologies effectively in solving real-world problems and advancing their careers in AI and Data Science.

Course Outline

Historical evolution of AI, Conceptualization of AI, related terms, and subfields with applications.

Practical component: Lab to be conducted on a 2-hour slot weekly. It will be conducted with the theory course so the topics for problems given in the lab are already initiated in the theory class. 

Learning Outcome

·       Understand the basic concept of AI.

·       Analysis of Data using Data science and data Analytics.

·       Explore state-of-the-art techniques and applications in machine learning

·       Compare and contrast various multiple deep learning architectures 

Assessment Method

Internal(Quiz/Assignment/Project), Mid-Term, End-Term

Course Number

CS2104

Course Credit

(L-T-P-C)

3-0-0-3

Course Title

Discrete Mathematics

Learning Mode

Offline

Learning Objectives

The objective of the course is to introduce the fundamental concepts in discrete mathematics with emphasis on their applications to computer science. 

Course Description

This course covers Fundamentals of logic (the laws of logic, rules of inferences, quantifiers, proofs of theorems), Fundamental principles of counting (permutations, combinations), set theory, relations and functions, graphs, shortest path and minimal spanning trees algorithms. Monoids and Groups.

Course Outline

·       Logic and proofs

·       Elementary set theory

·       Relations and functions

·       Recurrence relations

·       Counting & Combinatorics

·       Induction and Recursion

·       Modular arithmetic

·       Graph theory

·       Elementary probability theory

Learning Outcomes

·       Mathematical formalism of complex computer science problem and identifying their effective solutions.

·       Improving critical thinking, and recognize valid, logical, mathematical arguments and construct valid arguments/proofs.

·       Understanding the mathematical foundation behind cryptographic solutions in cryptology and others.

Assessment Method

Course Number

CS2105

Course Credit

(L-T-P-C)

 3-0-0-3

Course Title

Optimization Techniques

Learning Mode

Offline

Learning Objectives

·    To gain a thorough understanding principles of linear programming including problem formulation, geometric interpretations, and graphical solutions.

 ·    To explore advanced methods such as the Simplex algorithm, Big M method, and Revised Simplex method for optimizing linear programming problems.

·    To understand duality theory and sensitivity analysis in linear programming, and apply them to real-world scenarios like transportation and assignment problems.

·    To learn integer programming techniques like Branch and Bound and the Gomory cutting plane method for solving integer and mixed integer problems.

To understand game theory concepts such as saddle points, matrix games, and strategies, and apply optimization methods to solve game-theoretic problems effectively.

Course Description

This course provides an exploration of essential methods for solving complex problems across various domains, including operations research, engineering, economics, and artificial intelligence. Beginning with foundational concepts in linear programming, students will delve into problem formulation, geometric interpretations, and graphical solutions, progressing to advanced techniques such as the Simplex algorithm, Big M method, and Revised Simplex method. Duality theory in linear programming is extensively covered, alongside integer programming techniques like Branch and Bound and the Gomory cutting plane method for both integer and mixed integer problems. The course also explores game theory applications, focusing on matrix games and two-person zero-sum games, utilizing graphical and simplex methods to derive optimal solutions. Additionally, students will gain insights into optimization techniques tailored for artificial intelligence and machine learning applications, preparing them to tackle real-world optimization challenges effectively.

Course Outline

Linear programming problem (LLP): Introduction and problem formulation,

Concepts from Geometry, Geometrical aspects of LPP, Graphical solutions, Linear programming in standard form,

Simplex, Big M and Two Phase Methods, Revised simplex method, Special cases of LPP.

Duality theory: Dual simplex method, Sensitivity analysis of LP problems,

Transportation, Assignment, and Traveling Salesman problems.

Integer programming problems: Branch and bound method, Gomory cutting plane method for all integers and for mixed integer LPP.

Theory of games: Saddle point, Linear programming formulation of matrix games, Two-person zero-sum games with and without saddle-points, Pure and mixed strategies, Graphical method of solution of a game, Solution of a game by simplex method.

Basics of optimization techniques for artificial intelligence and machine learning

Learning Outcome

Upon successful completion of this course, students will:

·       Demonstrate proficiency in formulating and solving linear programming problems using advanced methods like the Simplex algorithm and its variants.

·       Apply duality theory and sensitivity analysis to analyze and optimize solutions in linear programming applications, including transportation and assignment problems.

·       Utilize integer programming techniques, such as Branch and Bound and Gomory cutting plane methods, to solve integer and mixed integer linear programming problems effectively.

·       Apply game theory concepts to analyze and solve matrix games using linear programming formulations, employing graphical and simplex methods for optimal strategy determination.

·       Apply optimization techniques relevant to artificial intelligence and machine learning applications, demonstrating the ability to optimize models

Assessment Method

Internal(Quiz/Assignment/Project), Mid-Term, End-Term

Course Number

MA2201 (Core)

Course Credit

(L-T-P-C)                

2-0-2-3

Course Title                  

Introduction to Machine Learning

Learning Mode           

Lectures and Lab

Learning Objectives

In this subject, the students will be trained with the fundamentals of Machine   Learning concepts along with the knowledge of mathematical tools that are required to grasp those skills.

Course Description    

Introduction to Machine Learning, as a basic subject for undergraduate students, provides the initial knowledge of Machine Learning with its applications in various Mathematical and Statistical problems.

Course Content         

Regression: Least Squares, Goodness of Fit, Bias-Variance Trade Off, Linear, Polynomial and Logistic Regression,

Classification: Binary and Multinomial Classification, Naive Bayes Classifier, Neural Networks, K-Nearest Neighbors, Support Vector Machine, Decision Trees, Unsupervised Learning: PCA, K-means clustering, Hiracrhieal Clustering, Density based Clustering.

LAB: problems based on theory lectures using R/Python.

Learning Outcome     

On successful completion of the course, students should be able to:

1. Analyse the role of mathematical tools in Machine Learning.

2. Understand the terminology and basic concepts of Machine Learning

3. Differentiate and apply the Supervised and Unsupervised Learning models.

Assessment Method

Quiz /Assignment/ MSE / ESE

Course Number

MA2202 (Core)

Course Credit

(L-T-P-C)                

3-0-0-3

Course Title                  

Real Analysis and Measure Theory

Learning Mode           

Lectures

Learning Objectives

Students will understand the concept of sequences and series of real numbers as well as functions.

Students also learn various concepts associated with Lebesgue measure and understand the need for Lebesgue integration. Theorems related to Lebesgue integration are discussed to highlight the applications of Lebesgue integration.

Course Description    

This course discusses details of sequences and series of real numbers and real valued functions. Distinction between pointwise convergence and uniform convergence shall be covered in detail and how uniform convergence leads to some important theorems.

The concept of Lebesgue integration is introduced by discussing the basics of outer measure, measurable sets and measurable functions. Various interesting theorems associated with the Lebesgue integral shall be covered in detail highlighting their applications.

Course Content         

Sequence and series of real numbers and tests for convergence, Cauchy sequences, Cauchy criterion for convergence, bounded and monotonic sequences, absolute continuity and uniform continuity. Sequences and Series of real valued functions and uniform  convergence, Power series.

Sigma Algebra, Lebesgue outer measure, Measurable sets, Measure space, Complete measure space, Lebesgue measure on R, Properties of Lebesgue measure.

Lebesgue Integration, the integration of non-negative functions, Measurable functions, Fatou's Lemma, Integrable functions and their properties, Lebesgue's dominated convergence theorem (without proof).

Learning Outcome     

On successful completion of the course, students should be able to:

1. Differentiate between uniform convergence and point wise convergence.

2. Differentiate between continuity and uniform continuity.

3. Evaluate the Lebesgue integral of a measurable function.

Assessment Method

Quiz /Assignment/ MSE / ESE

Course Number

MA2203 (Core)

Course Credit

(L-T-P-C)                

3-0-2-4

Course Title                  

Numerical Linear Algebra

Learning Mode           

Lectures and Labs

Learning Objectives

This course answers the fundamental question of choice of suitable matrix computation method for various kind of problems required linear solvers. Hands-on experience with all the methods covered is the most crucial part of this course. All the topics discussed in this course would be accompanied with parallel practical session to reinforce the learning outcome of the course.

Course Description    

Due to increasing complexity in the real world scenarios and recent advances in the area of data science, understanding of numerical linear algebra and large scale matrix computations has become essential for engineers.

Course Content         

Review of basic concepts from linear Algebra; direct methods for solving linear systems; vector and matrix norms; condition numbers; least squares problems;  iterative methods for solving linear systems - Jacobi, Gauss Seidel, SOR and their convergence; projection methods - general projection method, steepest descent, MR Iteration, RNSD method and their convergence; orthogonalization; singular value decomposition; numerical computation of eigenvalues and eigenvectors; Introduction to Krylov subspace methods - Arnoldi’s method, GMRES method, Conjugate gradient algorithm, Lanczos Algorithm  and convergence check for Krylov subspace methods, Preconditioned CG, ILU preconditioner.

Learning Outcome     

On completion of the module, students will be able to

·       do some key matrix factorizations of a matrix,

·       identify suitable technique to solve linear systems of equations, least squares problems, and the eigenvalue problem.

Assessment Method

Quiz /Assignment/ MSE / ESE

Course Number

MA2204 (Core)

Course Credit

(L-T-P-C)                

3-0-3-4.5

Course Title                  

Computer Architecture and Organization

Learning Mode           

Lectures and Lab

Learning Objectives

1. Understand the CPU architecture including registers, instruction execution cycle, addressing modes, and instruction set.

2. Explore CPU control unit design, memory organization, peripheral devices, and their characteristics, while also becoming familiar with assembly language programming.

Course Description    

This course covers the fundamentals of CPU architecture, including registers, instruction execution cycle, and addressing modes. It delves into CPU control unit design, memory organization, cache memory, and peripheral devices. Practical aspects include assembly language programming and case studies on instruction sets of common CPUs.

Course Content         

CPU - registers, instruction execution cycle, RTL interpretation of instructions, addressing modes, instruction set. Case study - instruction sets of some common CPUs; Assembly language programming for some processor; Data representation: signed number representation, fixed and floating-point representations, character representation. Computer arithmetic - integer addition and subtraction, ripple carry adder, carry look-ahead adder, etc. multiplication – shift-and-add, Booth multiplier, carry save multiplier, etc. Division - non-restoring and restoring techniques, floating point arithmetic; CPU control unit design: hardwired and micro-programmed design approaches, Case study - design of a simple hypothetical CPU; Pipelining: Basic concepts of pipelining, throughput and speedup, pipeline hazards; Memory organization: Memory interleaving, concept of hierarchical memory organization, cache memory, cache size vs block size, mapping functions, replacement algorithms, write policy; Peripheral devices and their characteristics: Input-output subsystems, I/O transfers - program controlled, interrupt driven and DMA, privileged and non-privileged instructions, software interrupts and exceptions. Programs and processes - role of interrupts in process state transitions.

Familiarization with assembly language programming; Synthesis/design of simple data paths and controllers, processor design using HDL like verilog/vhdl; Interfacing - DAC, ADC, keyboard-display modules, etc. Development kits as well as Microprocessors/PCs may be used for the laboratory, along with design/simulation tools as and when necessary.

Learning Outcome     

1. Develop a comprehensive understanding of CPU architecture, memory organization, and peripheral devices, along with proficiency in assembly language programming.

2. Apply theoretical concepts to design and analyze simple hypothetical CPUs

Assessment Method

Quiz /Assignment/ MSE / ESE

Course Number

MA2205 (Core)

Course Credit

(L-T-P-C)                

3-0-3-4.5

Course Title                  

Database Management Systems

Learning Mode           

Lectures and Lab

Learning Objectives

Develop a comprehensive understanding of database system architecture, data models, etc.

Course Description    

This course covers database system architecture, data models, relational query languages, relational database design, query processing and optimization, storage strategies, transaction processing, and recent trends in database systems.

Course Content         

Database system architecture: Data Abstraction, Data Independence, Data Definition and Data Manipulation Languages; Data models: Entity-relationship, network, relational and object oriented data models, integrity constraints and data manipulation operations; Relational query languages: Relational algebra, tuple and domain relational calculus, SQL and QBE; Relational database design: Domain and data dependency, Armstrongs axioms, normal forms, dependency preservation, lossless design; Schema refinement; Query processing and optimization: Evaluation of relational algebra expressions, query equivalence, join strategies, query optimization algorithms; Storage strategies: Indices, B-trees, hashing; Transaction processing: Recovery and concurrency control, locking and timestamp based schedulers, multiversion and optimistic Concurrency Control schemes; Recent Trends: XML Data, XML Schema, JSON etc.

Database schema design, database creation, SQL programming and report generation using a commercial RDBMS like ORACLE/SYBASE/DB2/SQL-Server/INFORMIX. Students are to be exposed to front end development tools, ODBC and CORBA calls from application Programs, internet based access to databases and database administration.

Learning Outcome     

Students will develop a comprehensive understanding of database systems, including their architecture, design principles, query processing techniques, transaction management, and emerging trends in data management technologies

Assessment Method

Quiz /Assignment/ MSE / ESE

Course Number

MA3101 (Core)

Course Credit

(L-T-P-C)                

3-0-0-3

Course Title                  

Ordinary and Partial Differential Equations

Learning Mode           

Lectures

Learning Objectives

To get expose to the ordinary differential equations. To understand the theory and qualitative properties of solutions of differential equations. The course will also introduce students to partial differential equations and methods of solutions of some basic partial differential equations.

Course Description    

This course is meant to introduce the basic properties and solutions of both the ordinary and partial differential equations.

Course Content         

ODE: Review of ODEs, IVPs and existence and uniqueness theorems, System of ODEs: Phase plane, critical point, stability, Oscillation and Comparison theorems for second order linear equations and applications, Self-adjoint Eigenvalue problems on a finite interval, BVPs and Sturm Liouville Problems, Green’s function.

PDE: Introduction to PDE and the classification of PDEs (Linear, Nonlinear, Quasi Linear), Lagrange’s and Charpit’s Method, Second order PDEs and Their Classification, Method of Separation of Variables, Method of Characteristics, D’Alembert Solution, Duhamel’s principle. Maximum Principle and existence theorems, Fourier series, Fourier Transform, Laplace Transform and their application to solve ODEs and PDEs.

Learning Outcome     

Students will be able to identify properties of solutions of the ODEs even when explicit solutions are not possible or feasible. The solutions methods for the PDEs will be explicitly introduced.

Assessment Method

Quiz /Assignment/ MSE / ESE

Course Number

MA3102 (Core)

Course Credit

(L-T-P-C)                

3-0-0-3

Course Title                  

Complex Analysis

Learning Mode           

Lectures

Learning Objectives

The objective of the course is to train student about the fundamental properties of complex valued functions

Course Description    

Complex Analysis is a basic course for undergraduate student and is intended to discuss about important Mathematical properties of complex valued functions and enables students to solve some real-life problem.

Course Content         

Limit, Continuity, Differentiability, Analytic functions, Cauchy-Riemann Equations, Harmonic Functions, Reflection Principle, Elementary Functions, Branch point and Branch Cut, Contour Integration, Cauchy-Goursat Theorem- Simply and Multiply Connected Domains, Cauchy Integral Formula, Liouville's Theorem and the Fundamental Theorem of Algebra, Morera’s Theorem, Maximum Modulus Principle, Taylor Series, Laurent Series, Classification of Singularities, Cauchy's Residue Theorem, Residues at Poles, Zeros of Analytic Functions, Zeros and Poles, Behavior Near Isolated Singular Points, Evaluation of Improper Integrals, Jordan's Lemma, Definite integrals involving Sines and Cosines, Argument Principle, Rouche's Theorem, Bilinear Transformations,  Conformal Mapping.

Learning Outcome     

On successful completion of the course, students should be able to:

1.     Analyse the geometric behaviours of different kind of complex valued functions and use them to solve some real life problems.

2.     Behaviour of complex valued function near singular points.

3.     Use of Branch cut to solve difficult definite integrals.

Assessment Method

Quiz /Assignment/ MSE / ESE

Course Number

MA3103 (Core)

Course Credit

(L-T-P-C)                

3-0-0-3

Course Title                  

Theory of Computation

Learning Mode           

Lectures

Learning Objectives

To understand how efficiently a computational problem can be solved on a model of computation using algorithm.

Course Description    

This course is meant to introduce the fundamental but abstract areas of theoretical computer science.

Course Content         

Basic definitions, deterministic and non-deterministic finite automata.

Regular Languages, regular operations, Regular Expressions, Equivalence of DFA, NFA, Nonregular Languages and pumping lemma.

Context-Free Languages: Context-Free Grammars, Chomsky Normal Form, Pushdown Automata.

Noncontext-Free Languages and pumping lemma, Deterministic Context-Free Languages

Turing Machines: Definition of TM and its variants, Decidability, Reducibility.

Complexity Theory: Time complexity and Space Complexity.

Learning Outcome     

Students will have strong theoretical foundation to identify which computational problems are solvable which helps them to learn other areas of computer science like compiler, artificial intelligence, natural language processing and many more.

Assessment Method

Quiz /Assignment/ MSE / ESE

Course Number

MA3104 (Core)

Course Credit

(L-T-P-C)                

3-0-3-4.5

Course Title                  

Computer Networks

Learning Mode           

Lectures and Labs

Learning Objectives

Comprehend the historical development of computer networks and grasp both the theoretical and practical foundations of data communication.

Course Description    

This course provides an in-depth exploration of computer networks, covering the evolution, physical layer, medium access control, data link layer, network layer, transport layer, quality of service, and application layer protocols.

Course Content         

Evolution of computer networks; Physical Layer; transmission media and impairments, switching systems Medium Access Control Sublayer: Channel allocation Problem, multiple access protocols, Ethernet Data link layer: Framing, HDLC, PPP, sliding window protocols, error detection and correction Network Layer: Internet addressing, IP, ARP, ICMP, CIDR, routing algorithms (RIP, OSPF, BGP); Transport Layer: UDP, TCP, flow control, congestion control; Introduction to quality of service; Application Layer: DNS, Web, email, authentication, encryption.

Simulation experiments for protocol performance, configuring, testing and measuring network devices and parameters/policies; network management experiments; Exercises in network programming.

Learning Outcome     

Students will develop a comprehensive understanding of computer networks.

Assessment Method

Quiz /Assignment/ MSE / ESE

Course Number

MA3105 (Core)

Course Credit

(L-T-P-C)                

3-0-3-4.5

Course Title                  

Operating Systems

Learning Mode           

Lectures and Labs

Learning Objectives

Gain a comprehensive understanding of operating system fundamentals.

Course Description    

This course covers essential concepts in operating systems, including process management, concurrency, memory management, file systems, secondary storage, and advanced topics like distributed systems, security, and real-time systems, with practical examples drawn from Linux, Windows NT/7/8.

Course Content         

Process Management: process; thread; scheduling. Concurrency: mutual exclusion; synchronization; semaphores; monitors; Deadlocks: characterization; prevention; avoidance; detection. Memory Management: allocation; hardware support; paging; segmentation. Virtual Memory: demand paging; replacement; allocation; thrashing. File Systems and Implementation. Secondary Storage: disk structure; I/O management; device drivers; disk scheduling; disk management. (Linux will be used as a running example, while examples will draw also from Windows NT/7/8.); Advanced Topics: Distributed Systems. Security. Real-Time Systems.

Programming assignments to build different parts of an OS kernel.

Learning Outcome     

Students will develop a comprehensive understanding of operating system principles and mechanisms, enabling them to design, implement, and manage efficient and reliable computer systems.

Assessment Method

Quiz /Assignment/ MSE / ESE

Course Number

MA3201 (Core)

Course Credit

(L-T-P-C)                

3-0-0-3

Course Title                  

Number Theory and Cryptography

Learning Mode           

Lectures

Learning Objectives

Readers of this course will be well-equipped with basic concepts of numbers, their properties, and some of the standard results which are fundamental to any branch of mathematics. The course will study further properties and some advanced concept which has a lot of application in Cryptography.

Course Description    

This course introduces divisibility in integers and some knowledge of the arithmetic of congruences. The prime numbers are the building blocks of all natural numbers. The interplay between the multiplicative and additive properties of numbers and their uses in quadratic residues is particularly interesting. A few applications of these topics of number theory to modern cryptography are also introduced.

Course Content         

Integers, mathematical induction, divisibility in integers, basic algebra of infinitude of primes, Prime number theorem, Fundamental theorem of arithmetic, Dirichlet's theorem (without proof).  

Arithmetic functions, Mobius inversion formula, Structure of units modulo n, Euler's phi function. Primitive roots and indices, group of units. 

Congruences, Fermat’s theorem and Euler’s theorem, Wilson's theorem, linear congruences, Simultaneous linear congruences, Chinese Remainder Theorem, Simultaneous non-linear congruences.

Quadratic residues, law of quadratic reciprocity, binary quadratics forms, Fermat's two square theorem (without proof).

Algorithm to solve quadratic equations in Zm. Finite fields: construction and examples, factorizations of polynomials over finite fields, algorithm to determine irreducible polynomials of degree n over Zm.

Introduction to classical cryptosystems, DES-security and generalizations, Prime number generation. Public key cryptosystem (RSA).

Learning Outcome     

On successful completion of the course, students should be able to:

1. Understand the importance of integers;

2. Understand other basic courses of mathematics, like Algebra, Topology, Calculus, Analysis, Geometry and Combinatorics;

3.  Help to understand the basic techniques of Cryptography (the techniques for protecting information from unauthorized access) & Coding Theory and Information Theory (the study of the transfer of information securely) and make able to develop some new techniques too.

Assessment Method

Quiz /Assignment/ MSE / ESE

Course Number

MA3202 (Core)

Course Credit

(L-T-P-C)                

3-0-2-4

Course Title                  

Numerical Methods

Learning Mode           

Lectures and Labs

Learning Objectives

In this subject, the students will be trained with the basic available numerical methods which are required to solve applied models. This objective is required for anyone who wanted to work on computational areas.

Course Description    

This course will highlight the root finding approximation methods which are required for solving system of differential equations. In addition, the basic convergence criteria for solving ODE and PDEs will be also explained in addition to the numerical algorithms.

Course Content         

Bisection Method, Fixed Point Iteration, Secant Method, Solution of Nonlinear System based on Newton Raphson Method, Sufficient condition for convergence of Nonlinear systems, Interpolation (Lagrange’s formula, Newton’s forward and backward method, central difference, divided difference, sterling’s formula), Integration (Trapezoidal, Simpson’s 1/3^rd rule, Simpson’s 3/8^th rule, Quadrature Methods) and Differentiation.

Single step methods (Euler method and Runge Kutta Method), Multi-step methods for IVPs (Adam-Bashforth, Adam-Moulton methods), Finite difference methods for BVPs (2^nd order scalar case only), Finite difference methods for parabolic, hyperbolic and elliptic PDEs

Learning Outcome     

Students will be able to know the Mathematics behind the basic numerical algorithms

Assessment Method

Quiz /Assignment/ MSE / ESE

Course Number

MA3203 (Core)

Course Credit

(L-T-P-C)                

3-0-0-3

Course Title                  

Mathematical Statistics

Learning Mode           

Lectures

Learning Objectives

This course on mathematical statistics is aimed at the undergraduate students who are interested to learn basic concepts of statistics via mathematical approach. It gives essential background to students who further wish to learn statistics at advanced level.

Course Description    

This course is designed to cover various important methods of statistical inference. Order statistics and their join distributions are considered. Various properties of order statistics will be discussed. Then sampling from normal distribution will be discussed. Further different types of estimation problems will be described and illustrated. In this regard point and interval estimation problems will be demonstrated. Both classical and Bayesian methods of estimation will be discussed. Towards the end problem of testing will be covered.

Course Content         

Ordered Statistics, probability distributions of Sample Range, Minimum and Maximum order Statistics. Random Sampling, Sampling distributions: Chi-square, T, F distributions.

Point Estimation: Sufficiency, Factorization theorem, Consistency, Moment method of estimation, Unbiased Estimation, Minimum Variance Unbiased Estimator and their properties, Rao-Cramer lower bound, Rao-Blackwellization, Fisher Information, Maximum Likelihood Estimator and properties, Criteria for evaluating estimators: Mean squared error.

Interval Estimation:  Coverage Probabilities, Confidence level, Sample size determination, Shortest Length interval, Pivotal quantities, interval estimators for various distributions.

Testing of Hypotheses: Null and Alternative Hypotheses, Simple hypothesis, Composite hypothesis, Test Statistic, Critical region, Error Probabilities, Power Function,  Level of Significance, Neyman-Pearson Lemma, One and Two Sided Tests for Mean, Variance and Proportions, One and Two Sample T-Test, Pooled T-Test, Paired T-Test, Chi-Square Test, Contingency Table Test, Maximum Likelihood Test, Duality between Confidence Intervals.

Bayesian Estimation: Prior and Posterior Distributions, Quadratic Loss Function, Posterior Mean, Bayes Estimates for well Known Distributions (Normal, Gamma, Exponential, Binomial, Poisson, Beta etc.) 

Learning Outcome     

Students will become familiar with following topics:

(1)        Distribution properties of order statistics

(2)        Desirable properties point estimators like unbiasedness, efficiency, consistency etc.

(3)        Mean squared error computations

(4)        Coverage probabilities

(5)        Posterior distributions

(6)        Error probabilities and most powerful tests

(7)        Chi-square test

Assessment Method

Quiz /Assignment/ MSE / ESE

Course Number

MA3204 (Core)

Course Credit

(L-T-P-C)                

3-0-2-4

Course Title                  

Convex Optimization

Learning Mode           

Lectures and Labs

Learning Objectives

The objective of the course is to train student about the modeling of convex programming problems and various classical and numerical optimization techniques and algorithms to solve these problems

Course Description    

Convex Optimization, as a basic subject for undergraduate students, provides the knowledge of various models of nonlinear convex optimization problems and different algorithms to solve such problems with its applications in various problems arising in economics, science and engineering.

Course Content         

Introduction to nonlinear programming, Convex Sets, Convex Functions and their properties.

Unconstrained optimization of functions of several variables: Necessary and Sufficient conditions.

Numerical methods for unconstrained optimization: Newton, LM method,  and Quasi Newton methods (DFP and BFGS methods)

Constrained optimization of functions of several variables, Lagrange Multiplier method, Karush-Kuhn-Tucker theory, Constraint Qualifications, Convex optimization, Interior point methods for inequality constrained optimization, Merit functions for constrained minimization, logarithmic barrier function for inequality constraints, A basic barrier-function algorithm, Perturbed optimality conditions.

Quadratic optimization:  Wolfe method, Beale’s Method, applications of quadratic programs in some domains like portfolio optimization and support vector machines, etc.

Practice of optimization algorithms using Software.

Learning Outcome     

On successful completion of the course, students should be able to:

1. Understand the terminology and basic concepts of various kinds of convex  optimization problems

3.  Develop the understanding about different solution methods to solve convex Programing problem. 

4. Apply and differentiate the need and importance of various algorithms to solve convex  programing problems

5.  Employ programming languages to solve convex programing problems

6. Model and solve several problems arising in science and engineering as a convex optimization problem

Assessment Method

Quiz /Assignment/ MSE / ESE

Course Number

MA3205 (Core)

Course Credit

(L-T-P-C)                

3-0-0-3

Course Title                  

Functional Analysis

Learning Mode           

Lectures

Learning Objectives

The objective of the course is to train student about the advanced concepts of metric space, normed linear spaces, Banach Space, inner product spaces, Hilbert Spaces, orthogonal sets and Lp spaces.

Course Description    

This is an advanced course for undergraduate student and is intended to discuss about important Mathematical properties of functional analysis.

Course Content         

Metric spaces, Open sets, Closed sets, Continuous functions, Completeness, Cantor intersection theorem, Baire category theorem, totally boundedness, Finite intersection property.

Normed spaces, Banach spaces, Properties of Banach spaces, Lp-spaces, Holder's inequality, Minkowski's inequality.

Linear operators, Bounded linear operators, fixed point theorems, functionals on Banach spaces, Dual space.

Inner product space, Hilbert spaces, Properties of inner product spaces, Orthogonal complements and direct sums, Orthonormal sets and sequences, Total orthonormal sets.

Learning Outcome     

On successful completion of the course, students should be able to:

1. Validate the properties of a metric space.

2. Find the norm of a bounded linear operator.

3. Construct orthogonal basis for Hilbert space.

Assessment Method

Quiz /Assignment/ MSE / ESE

Course Number

MA3206 (Core)

Course Credit

(L-T-P-C)

3 – 0 – 2 – 4

Course Title

Artificial Intelligence

Learning Mode

Lectures and Labs

Learning Objectives

This course aims to impart a deep understanding of theoretical AI concepts while equipping students for research and industry applications in artificial intelligence.

Course Description

This course offers a comprehensive overview of artificial intelligence, covering its foundation, history, and modern advancements, with a focus on uncertainty theory, learning algorithms, decision trees, neural networks, reinforcement learning, and practical machine learning applications for images and language.

Course Content

Introduction to Artificial Intelligence: Foundation, History, State-of-the-Art, Definition of AI: Thinking Vs Active and Humanly Vs Rationally, Example Tasks, Phases of AI; Uncertainty Theory and Learning: Acting under Uncertainty, Uncertain Knowledge, Bayesian Networks, Hidden Markov Models, Bayesian Learning, Bayesian Parameter Learning, Hidden Variables, The EM Algorithm for Unsupervised Learning; Learning Theory for Decision Tree: Types of Learning, Classification using Learning, Decision Tree for Discrete Input/Output Variable, Entropy, Information Gain, Overfitting, Decision Tree Pruning, Significance Test for Pruning, Extending Decision Tree for Continuous Input/Output Variable, Generalizability in Evaluation of the Learning Models, Cross-validation, Regularization, Scaling.

Computational Learning Theory: PAC, Regression Using Linear Model,

Artificial Neural Network: Structure, Perceptron, Non-Linearity, Multi-layer Architecture, Forward Propagation, Backward Propagation; Reinforcement Learning: Active Learning, Passive Learning, Adaptive Dynamic Programming, Generalization, Application of Reinforcement Learning to Game Playing;

Study of Practical Machine Learning for Images and Languages.

Learning Outcome

Students will gain a solid understanding of AI principles and techniques, enabling them to apply theoretical knowledge to real-world problems in research and industry settings.

Assessment Method

Quiz /Assignment/ MSE / ESE

Course Number          

MA4101 (DE)

Course Credit

(L-T-P-C)                

3-0-0-3

Course Title                  

Advanced Algorithms

Learning Mode           

Lectures

Learning Objectives

To learn few advanced algorithms and also to learn how to deal with the computational problems which are NP-Complete

Course Description    

This course introduces some advanced algorithms along with algorithm designing techniques in randomized and approximation algorithms.

Course Outline         

Graph algorithms: Maximum bipartite matching, Maximum weighted bipartite matching, Matching in general graphs.

Fast Fourier transformation and its applications. String Matching: Rabin-Karp algorithm, Knuth-Morris-Pratt algorithm.

Randomized algorithm: Randomized Min-Cut algorithm, Coupon collector’s problem, Median finding, Randomized quick sort, Markov-Chebyshev, Chernoff bound, Load balancing, Hashing revisited, Probabilistic methods: Basic counting, Expectation arguments, Sample and Modify, Application of Lovasz Local Lemma

Introduction to approximation algorithms.

Learning Outcome     

Students will learn few advanced algorithms and also learn how to design randomized algorithms, approximation algorithms for different computational problems.

Assessment Method

Quiz /Assignment/ Project / MSE / ESE

Course Number          

MA4102 (DE)

Course Credit

(L-T-P-C)                

3-0-0-3

Course Title                  

Cryptography and Network Security

Learning Mode           

Lectures

Learning Objectives

The objective of the course is to present an introduction to Cryptography, with an emphasis on how to protect information security from unauthorized users and is to understand the basics of Network vulnerability and Security Protection.

Course Description    

The aim of this course is to introduce the student to the areas of cryptography and cryptanalysis. This course develops a basic understanding of the algorithms used to protect users online and to understand some of the design choices behind these algorithms.

Course Outline         

Security goals and attacks, Cryptography  and cryptanalysis basics, Mathematics behind cryptography, Traditional and modern symmetric-key ciphers, DES, AES,  Asymmetric-key ciphers, One-way function, Trapdoor one-way function, RSA cryptosystem, Elgamal Cryptosystem, Diffie-Hellman key exchange algorithm, Cryptographic hash function, Message authentication, Digital signature, RSA digital signature,  IPSec, SSL/TLS, PGP and Email security

Learning Outcome     

Students will be familiar with the significance of information security in the digital era. Also, they can identify various threats and vulnerabilities in networking.

Assessment Method

Quiz /Assignment/ Project / MSE / ESE

Course Number          

MA4103 (DE)

Course Credit

(L-T-P-C)                

3-0-0-3

Course Title                  

Rings and Modules

Learning Mode           

Lectures/ Tutorials

Learning Objectives

Readers of this course will be well-equipped with basic concepts of Rings & Modules which are prerequisites to the courses on Fields and Galois Theory, Coding Theory, Cryptography, Homological Algebra, Noncommutative Algebra, Algebraic Geometry, and advanced courses on Analysis.

Course Description    

It gives a foundation for further studies in algebra by discussing several classes of rings and modules. This course includes structure theorems for modules over PID, Artinian, and Noetherian rings and modules, and their radicals.

Course Outline         

Rings, Ring of Endomorphisms, Ideal, Prime Ideals, Maximal Ideal, Principal Ideal Domain, Nilpotent Ideal, Nil Ideal, UFD, Field of Fractions.

Modules, submodules, quotient modules and module homomorphisms, Generation of modules, direct sums and free modules, simple modules 

Finitely generated modules over principal ideal domains.

Ascending Chain Condition and Descending Chain Condition, Artinian and Noetherian rings and modules, Hilbert basis theorem, Primary decomposition of ideals in Noetherian rings.

 Radicals: Nil radical, Jacobson radical and prime radical, the relation of radicals in the case of Artinian and Noetherian rings.

Learning Outcome     

On successful completion of the course, students should be able to:

1.         Understand, apply and analyze the notion of rings, ideals, and modules in related concepts required for advanced courses and research in Algebra.

2.         Familiar with the key properties and examples of Artinian and Noetherian rings and modules and their generalization;

3.         Decide whether a given ring or module, or a class of rings or modules, is Noetherian/Artinian, by applying the characterizations discussed in the course;

4.         Able to use this concept for research in Information Circuits (Coding Theory, Cryptography, Image Processing, etc.

Assessment Method

Quiz /Assignment/ Project / MSE / ESE

Course Number          

MA4104 (DE)

Course Credit

(L-T-P-C)                

2 – 0 – 2 – 3

Course Title                  

Deep Learning

Learning Mode           

Lectures and Labs

Learning Objectives

Gain expertise in artificial neural networks, covering fundamentals, feedforward and deep neural networks, convolutional networks, recurrent neural networks, and popular deep learning architectures, to proficiently tackle pattern recognition tasks and real-world challenges.

Course Description    

Explore the foundations and applications of deep learning, covering artificial neural networks, convolutional networks, recurrent neural networks, and popular architectures like VAE, and GANs for solving real-world tasks.

Course Outline         

Basics of artificial neural networks (ANN); Feedforward neural networks: Pattern classification using perceprton, Multilayer feedforward neural networks, Backpropagation learning,  Normalization; Deep neural networks (DNNs): Difficulty of training DNNs, Optimization for training DNNs, Optimization methods for neural networks (AdaGrad, RMSProp, Adam etc.), Regularization methods.

Convolutional Networks (CNNs): Introduction to CNNs – convolution, pooling, Deep CNNs, Deep CNN architectures (AlexNet, VGG, GoogLeNet, ResNet), Other Recent CNN architectures.

Recurrent neural networks (RNNs), Long Short Term Memory (LSTM), Other Recent Sequential Networks; Some popular Architectures/concepts in Deep Learning: Object Detection and Localization, Siamese Networks, Autoencoders & VAE, Generative Adversarial Networks (GANs), Other Recent Topics.

Learning Outcome     

Students will acquire a thorough grasp of both foundational and advanced concepts in deep learning, along with practical proficiency in utilizing these methods to address real-world challenges.

Assessment Method

Quiz /Assignment/ Project / MSE / ESE

Course Number

MA4105 (DE)

Course Credit

(L-T-P-C)                

3-0-0-3

Course Title                  

Fields and Galois Theory

Learning Mode           

Lectures

Learning Objectives

To get exposed to the classical journey of solving polynomial equations,  the theoretical ways to look at it, particularly when numerical methods have its limitations.

Course Description    

This course will cover the basics of field theory and its extensions from the perspective of the existence of solutions of polynomial equations.

Course Content         

Review of Rings, Ring homomorphisms, Ideals, prime and maximal ideals

Fields, basic theory of field extensions: field automorphisms, Algebraic extension, splitting fields, algebraic closure, separable and inseparable extensions, finite fields, cyclotomic polynomials, normal extensions.

Galois extension, Galois group of a field extension, The fundamental theorem of Galois theory, Galois closure, theory of symmetric polynomials, the fundamental theorem of Algebra, solvable extensions, radical extensions, solution of polynomial equations by radicals, insolvability of the quintic, transcendence of e and pi

Learning Outcome     

The students will know algebraically closed field, splitting fields, Fundamental theorems of Algebra and of Galois theory. Students will understand why it is not possible to have a formula for solving a polynomial equation of degree five.

Assessment Method

Quiz /Assignment/ Project / MSE / ESE

Course Number          

MA4106 (DE)

Course Credit

(L-T-P-C)                

3-0-0-3

Course Title                  

Mathematical Finance

Learning Mode           

Lectures

Learning Objectives

The main objective of the course is to introduce the students to the broader area of mathematical finance from a theoretical and computational perspective.

Course Description    

Mathematical Finance, as an interdisciplinary subject, focuses on relations between fundamentals of Mathematics and concepts of financial markets along with the other economic activities.

Course Outline         

Financial markets and instruments, risk-free and risky assets; Interest rates, present and future values of cash flows, term structure of interest rates, spot rate, forward rate; Bonds, bond pricing, yields, duration, term structure of interest rates; Asset pricing models, no-arbitrage principle; Cox-Ross-Rubinstein binomial model, geometric Brownian motion model; Financial derivatives, Forward and futures contracts and their pricing, hedging strategies using futures, interest rate and index futures; Swaps and its valuation, interest rate swaps, currency swaps; Options, general properties of options, trading strategies involving options; Discrete time pricing of European and American derivative securities by replication; Continuous time pricing of European and American derivate securities by risk-neutral valuation.

Learning Outcome     

On successful completion of the course, students should be able to:

1. Understand the fundamentals of quantitative finance.

2. Grasp the concept of time value of money and interest rates.

3. Comprehend ideas of pricing through the application of basic mathematical concepts.

Assessment Method

Quiz /Assignment/ Project / MSE / ESE

Course Number          

MA4206 (DE)

Course Credit                

3-0-0-3

Course Title                  

Control Theory

Learning Mode           

Lectures

Learning Objectives

The objective of the course is to train student about the fundamental principles of control theory to analyze and design control systems.

Course Description    

Control theory is a basic course for undergraduate student and is intended to discuss about important mathematical properties of control systems and enables students to solve some optimal control problems.

Course Outline         

Mathematical models of control systems, State space representation, Autonomous and non-autonomous systems, State transition matrix, Solution of linear dynamical system.

Transfer function, Realization, Controllability, Kalman theorem, Controllability Grammian, Control computation using Grammian matrix, Observability, Duality theorems, Discrete control systems, Controllability and Observability results for discrete systems.

Companion form, Feedback control, State observer, Liapunov stability, Stability analysis for linear systems, Liapunov theorems for stability and instability for nonlinear systems, Stability analysis through Linearization, Routh criterion, Nyquist criterion, Stabilizability and detachability.

State feedback of multivariable system, Riccatti equation, Introduction to Calculus of variation, Euler- Hamiltonian equations, Computation of optimal control for linear systems.

Learning Outcome     

By the end of the course, students will be able to describe the fundamental components of control systems, including controllability, observability and stability. They should be able to explain how these components interact to achieve desired system behavior.

Assessment Method

Quiz /Assignment/ Project / MSE / ESE

Course Number

MA4208 (DE)

Course Credit

(L-T-P-C)                

3-0-0-3

Course Title                  

Introduction to Coding Theory

Learning Mode           

Lectures/ Tutorials

Learning Objectives

Readers of this course will be well-equipped with the application of the basics of mathematics, specially, Algebra, Number Theory and Probability Theory in Information Theory.

Course Description    

It gives a foundation for further studies in information communications. This course includes different codes such as binary codes, Hamming codes, linear codes (cyclic codes in detail), and nonlinear codes, with different bounds by using mathematical tools, which are essential to understand an information communication system.

Course Content         

Polynomial rings over fields, Extension of fields, Computation in GF(q), n-th roots of unity, Vector space over finite fields.

Error Detection, correction and decoding.

Linear block codes: Hamming weight, Generator and Parity-check matrix Encoding and Decoding of linear codes, Bounds: Sphere-covering bound, Gilbert-Varshamov bound, Hamming bound, Singleton bound.

Hamming codes, Simplex codes, Golay codes, First and Second order Reed-Muller codes. Nonlinear codes: Hadamard codes, Preparata codes, Kerdock codes, Nordstorm-Robinson code, Weight distribution of codes.

The structure of cyclic codes, roots of cyclic codes, Decoding of cyclic codes, Burst-error-correcting codes, Quadratic residue codes, BCH codes, Reed-Solomon (RS) codes, GRS codes, Convolutional codes, LDPC codes, Turbo codes.

Learning Outcome     

On successful completion of the course, students should be able to:

1. Understand the primary information communication circuits;

2. Able to understand the importance of better codes in communication channels;

3.  Help to develop some MDS, and better new codes using the concept of number theory and algebra;

4. Capable of analyzing the capacity of a code based on studied bounds and results.

Assessment Method

Quiz /Assignment/ Project / MSE / ESE

Course Number          

MA4209 (DE)

Course Credit

(L-T-P-C)                

3-0-0-3

Course Title                  

Portfolio Theory and Risk Management

Learning Mode           

Lectures

Learning Objectives

The goal of this course are two-folds, namely design of portfolios and the identification as well as risk management of such portfolios.

Course Description    

Portfolio theory involves the usage of techniques of probability theory and statistics in the design and analysis of a financial portfolios (such as mutual funds). On the other hand, risk management involves tools from Mathematics and Statistics in the identification of financial risks to portfolios.

Course Outline         

Return and risk of a portfolio, mean-variance portfolio theory, efficient frontier, Capital Asset Pricing Model, Arbitrage Pricing Theory; Utility theory, risk attitude of investors; Non-mean-variance portfolio theory, safety first models, semi-deviation, stochastic dominance; Bond portfolios, duration and convexity of a bond. Fundamentals of financial risk management, credit risk, market risk, operational risk, Basel and Solvency regulations; Market risk, Value-at-Risk (VaR), computation of VaR, coherent measures of risk.

Learning Outcome     

On successful completion of the course, students should be able to:

1. Understand the fundamentals of portfolio theory from asset picking to asset allocation and performance analysis of the portfolio.

2. Identification and quantification of risk of financial portfolios using mathematical and statistical tools.

3. Determination of robust techniques to mitigate the identified financial risks.

Assessment Method

Quiz /Assignment/ Project / MSE / ESE

Course Number

MA4210 (DE)

Course Credit

(L-T-P-C)                

3-0-0-3

Course Title                  

Differential Geometry

Learning Mode           

Lectures

Learning Objectives

Same as Learning Outcome

Course Description    

It is a basic course in classical differential geometry of curves and surfaces.

Course Content         

Curve theory: Regular curves, arc-length parametrization, curvature, torsion, Frenet formula, isoperimetric inequality

Surface theory: Regular surfaces, Curvatures: Gauss and Mean, Surfaces of revolution, Constant mean curvature surfaces: minimal surfaces, Weierstrass-Enneper representation,  Geodesics: The geodesic equations, Isometries and conformal maps. The Gauss-Bonnet theorem.

Learning Outcome     

At the end of this course, students will learn:

- to compute curvature and torsion of curves

- to compute Gauss and mean curvature of surfaces

- to compute the complex representation formula for a minimal surface given in isothermal parametrization.

- the relation between Euler characteristic of a surface and the Gaussian curvature of a surface through Gauss-Bonnet theorem.

Assessment Method

Quiz /Assignment/ Project / MSE / ESE

Course Number          

MA4211 (DE)

Course Credit

(L-T-P-C)                

3-0-0-3

Course Title                  

Introduction to Mathematical Biology

Learning Mode           

Lectures

Learning Objectives

To learn application of Mathematics in Biology. To comprehend

mathematical analysis and to correlate the outcome of mathematical system into biological system. To learn and understand the bridge between mathematical and biological worlds.

Course Description    

This course is meant to expose the candidate to mathematical modeling

biological systems and then apply it to various systems and analyse these models and obtain biological inferences from models.

Course Outline         

Motivation. Introduction to biological systems and their mathematical representation. Basic mathematical tools such as Linearization, qualitative solution of difference and differential equations, stability, nonlinear dynamics.

Mathematical modeling in ecology: Single species models (continuous and discrete), multispecies models: Prey-predator models, Competition models, cooperation models, harvesting in population, fisheries models, optimal harvest.

Mathematical modeling of infectious diseases: Introduction to disease modeling, compartmental models, Basic models- SI, SIS, SIR, SIRS etc. Models with demography, Vaccination models, Ross Malaria Model.

Mathematical models in cellular biology such as HIV in vivo dynamics, Models in immunology.

Stochastic models. Parameter estimation.

Learning Outcome     

Students will be able to apply the mathematical knowledge on a biological system, analyse it and interpret it in terms of the biological systems.

Assessment Method

Quiz /Assignment/ Project / MSE / ESE

Course Number          

MA4212 (DE)

Course Credit

(L-T-P-C)                

3-0-0-3

Course Title                  

Statistical Decision Theory

Learning Mode           

Lectures

Learning Objectives

This course provides an in-depth content for understanding useful fundamentals concepts of statistical decision theory. Several inference problems under this framework will be discussed.

Course Description    

Most of inference problems are described under faily general setup of statistical decision theory. Efficient estimation procedures will be discussed under different parametric restrictions.

Course Outline         

Decision theoretic estimation problems, Classical risk functions, Bayes risk, Bayes and minimax estimators, Admissible Bayes estimators, essentially complete class rules, minimal complete class, illustrations, Ancillarity, UMVUE, truncated parameter space estimation problems, equivariance of decision rules, location-scale groups of transformations, minimum risk equivariant estimators, highest posterior density intervals.

Learning Outcome     

Students will learn basic concepts of statistical decision problems with a focus on deriving efficient estimators for various parametric functions.

Assessment Method

Quiz /Assignment/ Project / MSE / ESE

Course Number          

MA4213 (DE)

Course Credit

(L-T-P-C)                

3 – 0 – 0 – 3

Course Title                  

Applied Computational Techniques

Learning Mode           

Lectures

Learning Objectives

In this subject, the students will be informed about numerical analysis and computational schemes for solving ordinary and partial differential equations.

Course Description    

This course involves basic parts of computing approaches involving numerical analysis and how to solve differential equations

Course Outline         

Introduction to floating point arithmetic, Machine precision, Approximation errors, Truncation and roundoff errors, Condition number of function

Generation of finite differences schemes by interpolating data, Finite-difference schemes for various derivatives, Smoothness, Rate of accuracy

Introduction of system of linear IVP's and BVP's, Euler's Explicit and Implicit Method, Runge-Kutta Methods, Linear Multistep Methods, Nonlinear Two-Point BVPs and its discretization.

PDEs, Initial and Boundary Conditions, Finite difference method for elliptic PDE.

Approximations of parabolic and hyperbolic PDEs by FTCS and BTCS, Crank-Nicolson schemes, ADI methods, Lax Friedrich method, Upwind scheme; CFL conditions.

Consistency, Stability analysis by matrix method and/or von Neumann analysis, Convergence by Lax's equivalence theorem.

Learning Outcome     

Through this course, students will learn the basic ideas of computations and their convergence analysis. They will also learn solving differential equations numerically.

Assessment Method

Quiz /Assignment/ Project / MSE / ESE

Course Number          

MA4214 (DE)

Course Credit

(L-T-P-C)                

2 – 0 – 2 – 3

Course Title                  

Deep Learning for Computer Vision

Learning Mode           

Lectures and Labs

Learning Objectives

This is an advanced course on Computer Vision. This will enable the students to learn concepts of image processing, computer vision and utilize these techniques to implement vision algorithms efficiently for use in research or industry.

Course Description    

This course provides a comprehensive exploration of computer vision fundamentals, covering image formation, deep learning techniques, and advanced topics such as object detection, segmentation, and 3D computer vision.

Course Outline         

Introduction and Overview: Course Overview and Motivation; Introduction to Image Formation, Capture and Representation; Linear Filtering, Correlation, Convolution; Visual Features and Representations: Edge, Blobs, Corner Detection; SIFT, SURF; HoG, LBP; Review of Deep Learning (DL): Multi-layer Perceptrons, Backpropagation, CNN, RNN, Transfomer, AE, VAE, GANs, Diffusion Models etc.

Deep Learning for Computer Vision; Image Classification and Action/Activity Recognition; Object Detection; Segmentation: FCN, SegNet, U-Net, Other Recent Models; Visualizing CNN features, DeepDream, Style Transfer.

DL for Pose Estimation, Optical Flow, Object Tracking, Depth Estimation, Image Matching, Image Editing, Image Inpainting, and Image Super-resolution; 3D computer vision: 3D scene understanding and segmentation, 3D shape synthesis; Other Recent Topics.

Learning Outcome     

At the end of the course, the students will be able to:

1. Implement fundamental image processing techniques required for computer vision

2. Understand Image formation process

3. Develop computer vision applications

Assessment Method

Quiz /Assignment/ Project / MSE / ESE

Course Number

MA4215 (DE)

Course Credit

(L-T-P-C)                

3-0-0-3

Course Title                  

Discrete Differential Geometry

Learning Mode           

Lectures

Learning Objectives

Same as Learning Outcome

Course Description    

The aim of this course is to discretize. The classical differential geometric object. This course also finds its application in design, graphics and architectural engineering.

Course Content         

Brief introduction to Differential geometry of curves and surfaces (smooth).

Exterior calculus: Vectors and 1-forms, differential forms and the wedge product, differential operators and Stoke’s theorem.

Curvature of discrete surfaces: Vector area, Area gradient, Volume gradient, Gauss-Bonnet theorem.

The Laplacian: Discretization via finite element method and via discrete exterior calculus.

Learning Outcome     

At the end of this course, students should be able to:

-discretize classical geometric objects such as curves, surfaces.

-discretize the Laplacian operator

Assessment Method

Quiz /Assignment/ Project / MSE / ESE

Course Number

MA4216 (DE)

Course Credit

(L-T-P-C)                

3-0-0-3

Course Title                  

Integral Equations and Calculus of Variations

Learning Mode           

Lectures

Learning Objectives

In  this  subject,  the  students  will  learn the mathematical methods for solving integral equations and integro differential equations and their convergence analysis.

Course Description    

This course is on the existing approaches for solving integral equations and integro differential equations with their convergence analysis.

Course Content         

Introduction of Integral Equation, Correlation between integral and differential Equations, Classification of integral equations - Volterra and Fredholm equations, Green's function. Iterative methods for solving equations of the second kind, Neumann series and Fredholm theory, Singular integral equations.

Calculus of Variation: Variational problem with functionals containing first order derivatives and Euler equations. Variational problem with moving boundaries. Boundaries with constraints. Higher order necessary conditions, Existence of solutions of variational problem

Learning Outcome     

Main focus will be on how to solve integral equations and integro differential equations and their convergence analysis

Assessment Method

Quiz /Assignment/ Project / MSE / ESE

­­Course Number

MA2206 (IDE)

Course Credit

(L-T-P-C)                

3-0-0-3

Course Title                  

Introduction To Numerical Methods

Learning Mode           

Lectures

Learning Objectives

To learn basics of computation, errors, and how to manage error during computation.

Course Description    

Course starts with definition of number representation and errors. It focuses on solutions of nonlinear equations, system of nonlinear equations, quadrature, finite differences, their applications to solve ODEs and PDEs.

Course Content         

Number Representation and Errors: Numerical Errors; Floating Point Representation; Finite Single and Double Precision Differences; Machine Epsilon; Significant Digits.

Numerical Methods for Solving Nonlinear Equations: Method of Bisection, Secant Method, False Position, Newton‐Raphson's Method, Multidimensional Newton's Method, Fixed Point Method and their convergence.

Numerical Methods for Solving System of Linear Equations: Norms; Condition Numbers, Forward Gaussian Elimination and Backward Substitution; Gauss‐Jordan Elimination; FGE with Partial Pivoting and Row Scaling; LU Decomposition; Iterative Methods: Jacobi, Gauss Siedal; Power method and QR method for Eigen Value and Eigen vector.

Interpolation and Curve Fitting: Introduction to Interpolation; Calculus of Finite Differences; Finite Difference and Divided Difference Tables; Newton‐Gregory Polynomial Form; Lagrange Polynomial Interpolation; Theoretical Errors in Interpolation; Spline Interpolation; Approximation by Least Square Method.

Numerical Differentiation and Integration: Discrete Approximation of Derivatives: Forward, Backward and Central Finite Difference Forms, Numerical Integration, Simple Newton‐Cotes Rules: Trapezoidal and Simpson's (1/3) Rules; Gaussian Quadrature Rules: Gauss‐Legendre, Gauss‐Laguerre, Gauss‐Hermite, Gauss‐Chebychev.

Numerical Solution of ODE & PDE: Euler's Method for Numerical Solution of ODE; Modified Euler's Method; Runge‐Kutta Method (RK2, RK4), Error estimate; Multistep Methods: Predictor‐Corrector method, Adams‐Moulton Method; Boundary Value Problems and Shooting Method; finite difference methods, numerical solutions of elliptic, parabolic, and hyperbolic partial differential equations.

Exposure to software package MATLAB.

Learning Outcome     

Students should be able to write Program in MATLAB and solve some real life problems based the techniques learned during the course.

Assessment Method

Quiz /Assignment/ Project / MSE / ESE

Course Number          

MA2207 (IDE)

Course Credit

(L-T-P-C)                

3-0-0-3

Course Title                  

Complex Analysis

Learning Mode           

Lectures

Learning Objectives

This course involves necessity of complex analysis over basic real analysis and its use to approximate indefinite integrals and for other purposes.

Course Description    

This course mainly involves theory and applications of complex analysis with several mathematical examples.

Course Outline         

Complex Analysis: Complex numbers, Geometric representation, Applications of complex numbers in geometry, Powers and roots of complex numbers. Functions of a complex variable: Limit, Continuity, Differentiability, Analytic functions, Cauchy-Riemann equations, Laplace equation, Harmonic functions, Harmonic conjugates. Elementary Analytic functions (polynomials, exponential function, trigonometric functions), Complex logarithm function, Branches and Branch cuts of multiple valued functions. Complex integration, Cauchy's integral theorem, Cauchy's integral formula. Liouville’s Theorem and Maximum-Modulus theorem, Power series and convergence, Taylor series and Laurent series. Zeros, Singularities and its classifications, Residues, Rouches theorem (without proof), Argument principle (without proof), Residue theorem and its applications to evaluating real integrals and improper integrals. Conformal mappings, Mobius transformation, Schwarz-Christoffel transformation.

Learning Outcome     

Upon the finishing of this course, students will be able to incline on higher mathematics and to obtain analytical understanding. It will also help them to move towards research.

Assessment Method

Quiz /Assignment/ Project / MSE / ESE

Course Number

MA3106 (IDE)

Course Credit

(L-T-P-C)                

3-0-0-3

Course Title                  

An Introduction to Computational Commutative Algebra

Learning Mode           

Lectures

Learning Objectives

To expose students with the basic computational techniques in Commutative Algebra and its applications in engineering problems

Course Description    

This course covers the classical theory of Grobner basis and some of its first applications.

Course Content         

Ring, Ideals, Ring homorphisms, polynomial rings, Unique factorization, polynomials and affine space, affine varieties, parametrization of affine varieties, monomial ordering: Lexicographic order, graded lex order, graded rev lex order, inverse lexicographic order etc,  division algorithm for polynomials in n variables, monomial ideals, Dickson’s Lemma, Hilbert basis theorem, Grobner bases and its properties, Buchberger’s algorithm, reduced Grobner basis,

Applications of Grobner basis: Ideal description problem, Ideal membership problem, Solving polynomial equations, Implicitization problem, integer programming problem.

Learning Outcome     

Students will learn the basic theory of Grobner basis, Hilbert basis theorem, a division algorithm for polynomials in n variables etc. students will be exposed to various applications of Grobner basis in engineering and math problems.

Assessment Method

Quiz /Assignment/ Project / MSE / ESE

Course Number          

MA3107 (IDE)

Course Credit

(L-T-P-C)                

3-0-0-3

Course Title                  

Partial Differential Equations

Learning Mode           

Lectures

Learning Objectives

To understand the basic concepts of the Partial Differential Equations, how they arise and what are the main methods to solve them. In addition to build conceptual understanding of properties of the solutions.

Course Description    

The course will introduce the students about Fourier Series and Fourier Transform and further introduce them to the first and second order partial differential equations and their solutions.

Course Outline         

Fourier series: Fourier Integral, Fourier series of 2π periodic functions, Fourier series of odd and even functions, Half-range series, Convergence of Fourier series, Gibb’s phenomenon, Differentiation and Integration of Fourier series, Complex form of Fourier series.

Fourier Transformation: Fourier Integral Theorem, Fourier Transforms, Properties of Fourier Transform, Convolution and its physical interpretation, Statement of Fubini’s theorem, Convolution theorems, Inversion theorem.

Partial Differential Equations: Introduction and motivation, basic concepts, Linear and quasi-linear first order PDE, Lagrange’s Method of solution and its geometrical interpretation, compatibility condition, Charpits method, special types of first order equations.

Derivations of Heat and Wave equations in one-dimension and interpretation of different types of conditions. Second order PDE and classification of second order semi-linear PDE, Canonical form. Cauchy problems. D’ Alemberts formula and Duhamel’s principle for one dimensional wave equation, Fourier series method for IBV problem for wave and heat equation in 1-D, rectangular region. Uniqueness of solutions for IBVPs for heat and wave equations. Laplace and Poisson equations, Maximum principle with application, Fourier series method for Laplace equation in two and three dimensions. Fourier transform method to solve PDEs.

Learning Outcome     

The students will be able to understand what are PDEs and how to find their solutions, when they exist. They will also understand tools to find these solutions for standard cases.

Assessment Method

Quiz /Assignment/ Project / MSE / ESE

Course Number

MA4112 (IDE)

Course Credit

(L-T-P-C)                

3-0-0-3

Course Title                  

Number Theory and Algebra

Learning Mode           

Lectures

Learning Objectives

This course aims to help the students:

(1)   well-equipped with basic concepts of numbers, their properties, and some of the standard results that are fundamental to any branch of mathematics;

(2)   gain a comprehensive understanding of algebraic structures as groups and rings;

(3)   help to understand the advanced algebraic structures and their applications;

(4)   properties of these topics and some advanced concept have a lot of applications in Cryptography, Coding Theory, Networking etc

Course Description    

It covers basic topics of number theory, groups and rings. Besides the many examples of groups, rings, this course includes applications of Sylow’s theorems, Isomorphism theorems for groups and rings, Euclidean domain, UFD, quotient fields, and finite field extensions with several examples. On the other hand, this course also presents quadratic residue and Gauss quadratic reciprocity law and its applications.

Course Content         

Number Theory: Divisibility, primes, fundamental theorem of arithmetic. Congruences, solution of congruences, Euler's Theorem, Fermat's Little Theorem, Wilson's Theorem, Chinese remainder theorem, primitive roots and power residues. Arithmetical functions (Φ(n), μ(n), d(n), σ(n)). Quadratic residues, quadratic reciprocity. Diophantine equations.

Semigroups, groups, subgroups, normal subgroups, homomorphisms, quotient groups, isomorphisms. Examples: group of integers modulo m, permutation groups, cyclic groups, dihedral groups, matrix groups. Sylow's theorems (without proof) and applications. Basic properties of rings, units, ideals, homomorphisms, Isomorphism theorems, quotient rings, prime and maximal ideals, fields of fractions, Euclidean domains, principal ideal domains and unique factorization domains, polynomial rings.

Learning Outcome     

On successful completion of the course, students should be able to:

1.  Understand the importance of integers and their properties;

2. Understand, apply, and analyze the notion of groups, rings, and ideals in related concepts required for advanced courses;

3. Familiar with the basic properties and examples of different notions of algebra and their generalization;

4. Help to understand the basic techniques of Cryptography (the techniques for protecting information from unauthorized access) & Coding Theory and Information Theory (the study of the transfer of information securely) and make able to develop some new techniques too. 

Assessment Method

Quiz /Assignment/ Project / MSE / ESE

Course Number

MA4113 (IDE)

Course Credit

(L-T-P-C)                

3-0-0-3

Course Title                  

Mathematical Relativity Theory of Relativity

Learning Mode           

Lectures

Learning Objectives

The students would learn the singularity theorems of Hawking and Penrose, the positive mass theorem, and the theorems on black hole uniqueness and black hole thermodynamics.

Course Description    

To introduce the students to some of the most important mathematical results of general relativity.

Course Content         

Minkowski spacetime, Penrose diagrams, The Schwarzschild solution, Causality, Singularity theorems: Geodesic congruences, Hawking’s Singukarity theorem, Penrose’s singularity theorem, Cauchy Problem: Klein-Gordon equation, Maxwell’s equation, Einstein’s equations, Mass in General relativity: Komar mass, Field theory, Einstein-Hilbert action, Gravitational waves, Positive mass theorem, Penrose inequality, Black holes: The Kerr solution, Black hole thermodynamics and Hawking radiation.

Learning Outcome     

The students would learn the singularity theorems of Hawking and Penrose, the positive mass theorem, and the theorems on black hole uniqueness and black hole thermodynamics.

Assessment Method

Quiz /Assignment/ Project / MSE / ESE