1.2.2 b. sc(h)mathematics - galgotiasuniversity.edu.in

1.2.2

B. Sc(H)Mathematics

Name of the School: School of Basic and Applied Sciences

Department: Basic Sciences

Year: 2019-20

Curriculum

Bachelor of Science (H) Mathematics Employability

2019-22 Skill Development

List Of Electives

Discipline Specific Electives (DSE)-I

S. No. Course Code Course L T P C

1 BSCM421 Graph Theory 4 1 0 4

2 BSCM422 Bio-Mathematics 4 1 0 4

3 BSCM423 Ring Theory 4 1 0 4

Discipline Specific Electives (DSE)-II


1 BSCM521 Formal Language and

Automata Theory

4 1 0 4

2 BSCM522 Dynamical Systems 4 1 0 4

3 BSCM523 Financial Mathematics 4 1 0 4

4 BSCM524 Differential Geometry &Tensors

4 1 0 4

Discipline Specific Electives (DSE)-III


1 BSCM621 Mathematical Modeling &

Simulation

4 1 0 4

2 BSCM622 Optimization Techniques 4 1 0 4

3 BSCM623 Cryptography and Network

Security

4 1 0 4

4 BSCM624 Applications of Algebra 4 1 0 4

Generic Electives (GE)-I


1 BSCM531 IOT 4 0 0 4

2 BSCM513 IOT Lab 0 0 2 1

3 BSCM532 Cloud computing 4 0 0 4

4 BSCM514 Cloud computing Lab 0 0 2 1

5 BSCM533 Computer Graphics 4 0 0 4

6 BSCM515 Computer Graphics Lab 0 0 2 1

Generic Electives (GE)-II


1 BSCM631 Artificial Intelligence 4 0 0 4

2 BSCM613 Artificial Intelligence Lab 0 0 2 1

3 BSCM632 Computer vision 4 0 0 4

4 BSCM614 Computer vision Lab 0 0 2 1

5 BSCM633 Neuro Computing 4 0 0 4

6 BSCM615 Neuro Computing Lab 0 0 2 1

Syllabus Discipline Electives

Name of The Course Graph Theory

Course Code BSCM421

Prerequisite Discrete Structure

Corequisite

Antirequisite

L T P C 4 1 0 4

Course Objectives: This course is aimed to cover a variety of different problems in Graph

Theory. In this course students will come across a number of theorems and proofs. Theorems will

be stated and proved formally using various techniques. Various graphs algorithms will also be

taught along with its analysis. After the course the student will have a strong background of graph

theory which has diverse applications in the areas of computer science, biology, chemistry,

physics, sociology, and engineering. Topics include: Basic concepts of graph theory, Trees,

Bipartite graphs and matching, Connectivity, Eulerian circuits, Degree Sequences, Planarity.

Course Outcomes:

CO1 Define basic notions in graph theory including bi-partite graphs and matching,

Network and flow, some basic algorithms for graphs and discuss travelling

salesman’s problem.

CO2 Discuss degree sequences including tree and path, then using it in some algorithms

for graphs.

CO3 Explain the basic operations on Graphs and subgraphs, and determine whether

graphs are Hamiltonian and/or Eulerian. Also, discuss the application of trees.

CO4 Solve problems involving Eulerian circuits, and found the matrix representation of

graph.

CO5 Solve problems involving vertex and edge, connectivity, planarity and crossing

numbers. CO6 Understand the concept of networking using graph theory

Text Book (s)

1. N Deo – Graph theory with applications to Engineering and Computer Science, Prentice Hall of

India, 1987.

2. K R Parthasarathy – Basic Graph theory, Tata McGraw-Hill, New Delhi, 1994.

3. Edgar G. Goodaire and Michael M. Parmenter, Discrete Mathematics with Graph Theory 2nd Ed.,

Pearson Education (Singapore) P. Ltd., Indian Reprint, 2003.

4. Rudolf Lidl and Günter Pilz, Applied Abstract Algebra, 2nd Ed., Undergraduate Texts in

Mathematics, Springer (SIE), Indian Sreprint, 2004.

Reference Book (s)

1. C.L. Liu – Elements of discrete mathematics, McGraw-Hill, 1986.

2. Kenneth H. Rosen – Discrete Mathematics and its applications, McGraw-Hill, 2002.

3. F Harary – Graph theory, Addison Wesley, Reading Mass, 1969.

4. J A Bondy and U S R Murthy – Graph theory with applications, Elsevier, 1976.

Unit-1 Introduction 10 Hours

Definition, examples and basic properties of graphs, pseudographs, complete graphs, bi‐

partite graphs, isomorphism of graphs, paths and circuits, Eulerian circuits, Hamiltonian

cycles, the adjacency matrix, weighted graph, travelling salesman’s problem, shortest path,

Dijkstra’s algorithm, Floyd‐Warshall algorithm. Unit-2 8 Hours

Degree Sequences – Graphic Sequences, Travelling salesman’s problem, shortest path,

Tree and their properties, spanning tree, Dijkstra’s algorithm, Warshall algorithm. Unit-3 10 Hours

Basic Definitions, Isomorphism, Subgraphs, Operations on graphs, Walks, Paths, Circuits,

Connected and disconnected graphs, Euler graphs, Hamiltonian graphs, Some

Applications, Trees and Basic properties, Distance, Eccentricity, centre, Spanning trees,

Minimal spanning tree. Unit-4 10 Hours

Eulerian circuits, Eulerian graph, semi-Eulerian graph, theorems, Hamiltonian

cycles,theorems Representation of a graph by matrix, the adjacency matrix, incidence

matrix, weighted graph.

Unit-5 10 Hours

Cut- sets, Fundamental circuits; fundamental cut-sets, Connectivity, Separability,

cutvertex, Network flows, 1- and 2- Isomorphisms. Planar and non planar graphs, Euler’s

formula, Detection of planarity. Matrix representation of Graphs – Adjacency matrix of a

graph, Incidence matrix of a graph. Unit-6 3 Hours

Network Analysis using graph theory

Continuous Assessment Pattern

Internal Assessment

(IA)

Mid Term Test

(MTE)

End Term Test

(ETE)

Total Marks

20 30 50 100

Name of The Course Bio- Mathematics

Course Code BSCM 422

Prerequisite

Corequisite

Antirequisite

L T P C 4 1 0 4

Course Objectives: The aim of the course is to describe the application of mathematical

models to biological phenomena. A variety of contexts in human biology and diseases are

considered, as well as problems typical of particular organisms and environments.

Course Outcomes:

CO1 Discuss various Mathematical modeling process for Biological phenomena like

bacterial growth in a Chemostat, harvesting a single natural population, Populations

in competitions, Epidemic Models (SI, SIR, SIRS, SIC).

CO2 Find numerical and graphical solutions of continuous models like Insect Outbreak

Model, multiple species communities and Routh-Hurwitz Criteria, Phase plane

methods etc

CO3 Demonstrate spatial models for spreading colonies of microorganisms, blood flow

in circulatory system, Spread of genes in a population etc.

CO4 Discuss Discrete Models for Growth models, Decay models, Drug Delivery

Problem, Discrete Prey-Predator models, Density dependent growth models with

harvesting.

CO5 Discuss Case Studies for Optimal Exploitation models, Models in Genetics, Stage

Structure Models, Age Structure Models. CO6 Apply Statistical Thermodynamics Dynamics in Biology

Text Book (s)

1. L.E. Keshet, Mathematical Models in Biology, SIAM, 1988.

2. J. D. Murray, Mathematical Biology, Springer, 1993.

3. Y.C. Fung, Biomechanics, Springer-Verlag, 1990.

Reference Book (s)

1. F. Brauer, P.V.D. Driessche and J. Wu, Mathematical Epidemiology, Springer, 2008.

2. M. Kot, Elements of Mathematical Ecology, Cambridge University Press, 2001.

Unit-1 11 Hours

Mathematical Biology and the modeling process: an overview. Continuous models:

Malthus model, logistic growth, Allee effect, Gompertz growth, Michaelis-Menten

Kinetics, Holling type growth, Bacterial growth in a Chemostat, Harvesting a single natural

population, Prey predator systems and Lotka Volterra equations, Populations in

competitions, Epidemic Models (SI, SIR, SIRS, SIC) Unit-2 11 Hours

Activator-Inhibitor system, Insect Outbreak Model: Spruce Budworm, Numerical solution

of the models and its graphical representation. Qualitative analysis of continuous models:

Steady state solutions, stability and linearization, multiple species communities and Routh-

Hurwitz Criteria, Phase plane methods and qualitative solutions, bifurcations and limit cycles with examples in the context of biological scenario.

Unit-3 08 Hours

Spatial Models: One species model with diffusion, Two species model with diffusion.

Conditions for diffusive instability, Spreading colonies of microorganisms, Blood flow in

circulatory system, Travelling wave solutions, Spread of genes in a population Unit-4 9 Hours

Discrete Models: Overview of difference equations, steady state solution and linear

stability analysis. Introduction to Discrete Models, Linear Models, Growth models, Decay

models, Drug Delivery Problem, Discrete Prey-Predator models, Density dependent growth

models with harvesting.

Unit-5 9 Hours

Host-Parasitoid systems (Nicholson-Bailey model), Numerical solution of the models and

its graphical representation. Case Studies: Optimal Exploitation models, Models in

Genetics, Stage Structure Models, Age Structure Models. Unit-6 6 Hours

Statistical Thermodynamics Dynamics in Biology: Temperature, energy and Entropy,

Partition function and free energy, Bending fluctuation of DNA and spring like protein,

Thermodynamics of protein organization along DNA


Internal Assessment

(IA)

Mid Term Test

(MTE)

End Term Test

(ETE)

Total Marks

20 30 50 100

Name of The Course Ring Theory

Course Code BSCM423

Prerequisite

Corequisite

Antirequisite

L T P C 4 1 0 4

Course Objectives: Objective of this course is to introduce basic concepts of Ring, subring ,

their homomorphism and related properties.

Course Outcomes:

CO1 Apply methods to find Ring Sub ring and Ideal.

CO2 Apply methods to find Homomorphism, Isomorphism and Kernel.

CO3 Explain the concept of Polynomial rings, Division algorithm and Factorization of

polynomials.

CO4 Apply the concept of Principal Ideal Domain, Euclidean Domain, Unique

Factorization Domain. CO5 Explain Ring embedding and quotient field .

CO6 Understand field extension, algebraic extension and finite field.

Text Book (s)

1. Surjeet Singh and QaziZameeruddin: Modern Algebra, Vikas Publication.

2. J.A. Gallian: Contemporary Abstract Algebra, Narosa Publication.

Reference Book (s)

1. I. N. Herstein: Topics in Algebra, Wiley Eastern Ltd., New Delhi.

2. N. Jacobson: Basic Algebra, Volume I and II. W. H. Freeman and Co.

Unit-1 10 Hours

Rings and their properties, Boolean Ring, Integral domain, Division ring and Field,

Subrings, Ideals and their properties, Operations on ideals, Ideal generated by a subset of a

ring, Quotient rings Unit-2 9 Hours

Homomorphism of rings and its properties, Kernel of a homomorphism, Natural

homomorphism, Isomorphism and related theorems, Field of quotients Unit-3 10 Hours

Polynomial rings over commutative rings, Properties of R[X], Division algorithm and its

consequences, Factorization of polynomials, Irreducibility test, Eisenstein’s criterion for irreducibility

Unit-4 11 Hours

Factorization in integral domains, prime and irreducible element, Principal Ideal Domain,

Euclidean Domain, Unique Factorization Domain and its properties Unit-5 8 Hours

Ring embedding and quotient field, regular rings and their examples, properties of regular

ring, ideals in regular rings Unit-6 5 Hours

Field, Field extension, splitting field, algebraic extension, Finite fields and their properties.


Internal Assessment

(IA)

Mid Term Test

(MTE)

End Term Test

(ETE)

Total Marks

20 30 50 100

Name of The Course Formal Languages and Automata Theory


Prerequisite Discrete Mathematics

Corequisite

Antirequisite

L T P C 4 1 0 4

Course Objectives:

1. To focus on the study of abstract models of computation. These abstract models allow the students

to assess via formal reasoning what could be achieved through computing when they are using it to

solve problems in science and engineering.

2. The course exposes students to the computability theory, as well as to the complexity theory. The

goal is to allow them to answer fundamental questions about problems, such as whether they can or not

be computed, and if they can, how efficiently.

3. The course introduces basic computation models and their properties, and the necessary

mathematical techniques to prove more advanced attributes of these models.

Course Outcomes:

CO1 Demonstrate an ability to apply the knowledge for solving real world problems.

CO2 Relate practical problems to languages and automata.

CO3 Design an appropriate abstract machine to solve a problem.

CO4 Design a grammar for a given formal language.

CO5 Develop a clear understanding of undecidability and computational efficiency.

CO6 To learn codes for different language and its application

Text Book (s)

1. K.L.P. Misra – et.al. - Theory of Computer Science, 2nd Edn. PHI, New Delhi, 2000.

2. J.E. Hopcroft , et.al. - Introduction to Automata Theory, Languages and Computation, 2nd

Edn. Pearson Education , New Delhi 2001.

Reference Book (s)

1. J.C. Martin - Introduction to Languages and the Theory of Computation 2nd Edn, TMH, New

Delhi, 2000.

Unit-I: Introduction to Automata 10 Hours

Study and Central concepts of automata theory, An informal picture of finite automata,

deterministic and non-deterministic finite automatas, applications of finite automata, finite

automata with epsilon – transitions.

Unit-2: Regular expression and languages & Properties of Regular Languages 12 Hours

Regular expressions, finite automata and regular expressions, applications of regular

expressions, algebraic laws of regular expressions.

Properties of Regular Languages: Proving languages not to be regular, closure properties of

regular languages, equivalence and minimization of automata. Unit-3: Context – free Grammars and Languages 10 Hours

Parse trees, Applications of context free grammars, Ambiguity in grammars and languages.

Properties of Context – Free Languages: Normal forms of context free grammars, pumping

lemma for context free languages, close properties of context free languages.

Unit-4: Pushdown Automata 8 Hours

Pushdown automation (PDA), the language of PDA, equivalence of PDA’s and CFG’s,

Deterministic Pushdown Automata. Unit-5: Introduction to Turing Machine 8 Hours

The Turing machine, programming techniques for Turing machine, extensions to the basic

Turing machine, restricted Turing Machines, Turing Machines and Computers. Unit: 6 4 Hours

Recursive languages, Some properties of recursive and recursively enumerable languages,

Codes for TMs. A language that is not recursively enumerable (the diagonalization

language). The universal language, Undecidability of the universal language, The Halting

problem, Undecidable problems about TMs.


Internal Assessment

(IA)

Mid Term Test

(MTE)

End Term Test

(ETE)

Total Marks

20 30 50 100

Name of The Course Dynamical System

Course Code BSCM522

Prerequisite Differential equations

Corequisite NA

Antirequisite NA L T P C 4 1 0 4

Course Objectives: The course objectives to introduce the main features of dynamical

systems, particularly as they arise from systems of ordinary differential equations as models in

applied mathematics. The topics presented will include phase space, fixed points and stability

analysis, bifurcations, Hamiltonian systems and dissipative systems. Discrete dynamical

systems will also be discussed briefly, leading to the idea of a ‘chaotic’ dynamical system.

Course Outcomes:

CO1 Explain the main features of dynamical systems and their realisation as systems of

ordinary differential equations

CO2 identify fixed points of simple dynamical systems, and study the local dynamics

around these fixed points, in particular to discuss their stability and bifurcations

CO3 Make use of a range of specialised analytical techniques which are required in the

study of dynamical systems CO4 Explain and predict the occurrence and consequences of bifurcations

CO5 Find fixed points and period orbits of discrete dynamical systems, and find their

stability CO6 Analyze the chaotic behaviour of any dynamical system.

Text Book (s)

1. M. W. Hirsch & S. Smale – Differential Equations, Dynamical Systems and Linear Algebra

(Academic Press 1974)

2. L. Perko – Differential Equations and Dynamical Systems (Springer – 1991)

Reference Book (s)

1. Lawrence Perko, Differential equations and dynamical systems, Springer-Verlag, 2001.

2. F. Verhulst, Non-linear Differential Equations and Dynamical Systems, Springer, 1990.

Unit-1 10 Hours

An Introduction to Dynamical Systems: Background and examples, dynamical systems,

attractors and invariant sets. Phase Portraits: Phase portraits in 1D, topological equivalence. Unit-2 10 Hours

linear systems, linear 2D systems, stability and linearization of non-linear systems,

Lyapunov stability, drawing global phase portraits. Unit-3 9 Hours

Non-linear dynamical systems: solutions to initial value problem, existence and uniqueness

ofsolutions, linearization, phase space, classification of critical points. Unit-4 10 Hours

Bifurcations: Introductions, Saddle-Node Bifurcations, Transcritical Bifurcation,

Pitchfork Bifurcation, Imperfect Bifurcations and Catastrophes. Unit-5 9 Hours

Definition of a discrete dynamical system, graphical analysis of 1D discrete dynamical

systems, stability of fixed points and periodic orbits, chaotic orbits – definition and

examples. Unit-6 6 Hours

Higher-dimensional dynamical system: Lorenz and Rossler equations, chaos, strange

attractors and fractals


Internal Assessment

(IA)

Mid Term Test

(MTE)

End Term Test

(ETE)

Total Marks

30 20 50 100

Name of The Course Financial Mathematics


Prerequisite

Corequisite

Antirequisite

L T P C 4 1 0 4

Course Objectives: The key objectives of financial mathematics are also to understand how

to construct the best investment strategies that minimizes risks in the real world.

Course Outcomes:

CO1 Summarize the concepts of time value of money using interest rates and discounting

CO2 Explain concepts related to complex rate functions and annuities.

CO3 Apply discounted cash flow techniques in different project appraisal

CO4 Explain concepts of Internal rate of return and securities

CO5 Estimate the price of a future and forward contract

CO6 Able to hedge for the asset.

Text Book (s)

1. Suresh Chandra, S. Dharmaraja, Aparna Mehra, R. Khemchandani, Financial

Mathematics: An Introduction, Narosa Publication House, 2012.

Reference Book (s)

1. D.G. Luenberger, Investment Science, Oxford University Press, Oxford, 1998.

2. J.C. Hull, Options, Futures and Other Derivatives, 4th ed., Prentice-Hall, New York,

2000.

3. J.C. Cox and M. Rubinstein, Options Market, Englewood Cliffs, N.J.: Prentice Hall,

1985.

Unit-1 10 Hours

Interest rates, Simple interest rates, Compound interest rates, Present value of a single

future payment. Discount factors, effective and nominal interest rates. Unit-2 11 Hours

Relation between the time periods for compound interest rates and the discount factor.

Compound interest functions. Annuities and perpetuities.

Unit-3 10 Hours

loan schedule, Investment project appraisal, Cash flow, present value of a cash flow

Unit-4 9 Hours

Equation of value, Inte rnal rate of return, securities, fixed income securities, types of markets.

Unit-5 8 hours

Forward and futures contracts, options, properties of stock option prices, trading strategies

involving options Unit-6 4 hours

Hedging strategy, Black-Scholes option pricing formula


Internal Assessment

(IA)

Mid Term Test

(MTE)

End Term Test

(ETE)

Total Marks

20 30 50 100

Name of The Course Differential Geometry & Tensors


Prerequisite Linear algebra, Calculus in several variables, Vector calculus.

Corequisite

Antirequisite

L T P C 4 1 0 4

Course Objectives: The aim of the course is to provide knowledge of the geometry of

curves and surfaces. The course integrates concepts from different parts of mathematics, such

as linear algebra, calculus and differential equations. It also provides intuitive examples for

many concepts in linear algebra, calculus and differential equations. These examples are

fundamental to physics and mechanics: they play a role in our understanding of the movements

of particles and the theory of relativity.

Course Outcomes:

CO1 Apply method to find the parametric representations and tangent, Evolute and

Envolute of curve. CO2 Apply methods of theory of surfaces

CO3 Explain the theory of Geodesics.

CO4 Find the tensor product of vector spaces and its associated vectors.

CO5 Elobrate the knowledge about tensor analysis and tensor differentiation.

CO6 Understand Manifolds

Recommended Books:

1. Tensor Calculus, Zafar Ahsan, Anamaya Publication, New Delhi.

2. Differential Geometry of manifolds, U.C.De&A.A.Shaikh, Narosa Publishing House Pvt. Ltd,

2007.

3. Schaum’s Outlines of Tensor Calculus.

4. Tensor Calculus & Riemannian Geometry, D.C. Agarwal, Krishna Publications.

Reference Book (s):

1- J. A. Schouten, Ricci-Calculus. An introduction to tensor analysis and its geometrical

applications, 2d ed. Berlin, Springer, 1954.

2- Introduction to Tensor Calculus: Kees Dullemond & Kasper Peeters,

Lecture Notes series.

Unit-1: Theory of Space Curves 9 Hours

Space curves, Planer curves, Curvature, torsion and Serret-Frenet formulae. Osculating

circles, Osculating circles and spheres. Existence of space curves. Evolutes and involutes

of curves.

Unit-2: Theory of Surfaces 11 Hours

Parametric curves on surfaces. Direction coefficients. First and second Fundamental forms.

Principal and Gaussian curvatures. Lines of curvature, Euler’s theorem. Rodrigue’s formula,

Conjugate and Asymptotic lines. Developables: Developable associated with space curves

and curves on surfaces, Minimal surfaces.

Unit-3 10 Hours

Canonical geodesic equations. Nature of geodesics on a surface of revolution. Clairaut’s

theorem. Normal property of geodesics. Torsion of a geodesic. Geodesic curvature. Gauss-

Bonnet theorem. Surfaces of constant curvature. Conformal mapping. Geodesic mapping.

Tissot’s theorem.

Unit-4: Tensor algebra 08 Hours

Vector spaces, the dual spaces, tensor product of vector spaces, transformation formulae,

contraction, special tensor, inner product, associated tensor.

Unit-5: Tensor Analysis 10 Hours

Contravariant and covariant vectors and tensors, Mixed tensors, Symmetric and skew-

symmetric tensors, Algebra of tensors, Contraction and inner product, Quotient theorem,

Reciprocal tensors, Christoffel’s symbols, Covariant differentiation, Gradient, divergence

and curl in tensor notation. Unit-6: Manifolds 4 Hours

Manifolds, Tangent Spaces, Sub-Manifolds and Its Applications.


Internal Assessment

(IA)

Mid Term Test

(MTE)

End Term Test

(ETE)

Total Marks

20 30 50 100

Name of The Course Mathematical Modeling & Simulation

Course Code BSCM621

Prerequisite Linear algebra & Calculus

Corequisite NA

Antirequisite NA L T P C 4 1 0 4

Course Objectives: The overall objectives of this course is to enable students to build

mathematical models of real-world systems, analyze them and make predictions about behaviour

of these systems. Variety of modelling techniques will be discussed with examples taken from

physics, biology, chemistry, economics and other fields. The focus of the course will be on

seeking the connections between mathematics and physical systems, studying and applying

various modelling techniques to creating mathematical description of these systems, and using

this analysis to make predictions about the system’s behavior.

Course Outcomes:

CO1 Assess and articulate what type of modelling techniques are appropriate for a given

real world system CO2 Construct a mathematical model of a given real world system and analyze it,

CO3 Discuss predictions of the behaviour of a given real world system based on the

analysis of its mathematical model.

CO4 Demonstrate the power of mathematical modelling and analysis and be able to

apply their understanding to their further studies. CO5 Apply network modelling in some relevant situation

CO6 Understand the impact of infectious diseases in prey-predator system.

Text Books:

1. Kapur , J.N.,”Mathematical Modelling”,New Age international publisher, 1988.

2. Burghes D.N , “Modelling with differential equations”, Ellis Horwood and

John Wiley, 1991

Reference Books:

1. Burghes, D.N.,” Mathematical Modelling in the Social Management and Life

Science”,Ellie Herwood and John Wiley.

2. Charlton, F.,” Ordinary Differential and Difference Equations”, Van Nostrand.

3. Brauer, Castillo-Chavez,”Mathematical Models in Population Biology and Epidemiology”.

Unit-1 10 Hours

Introduction to compartmental models, lake pollution model, exponential growth of

population, limited growth of population, limited growth with harvesting, discrete

population growth , logistic equation with time lag. Unit-2 9 Hours

Linear homogeneous and non-homogeneous equations of higher order with constant

coefficients, Euler’s equation, method of undetermined coefficients, method of variation of

parameters, application to projectile motion. Unit-3 9 Hours

Equilibrium points, interpretation of the phase plane, predator-prey model and its

analysis, competing species and its analysis, epidemic model of influenza and its analysis,

battle model and its analysis. Unit-4 10 Hours

Mathematical modeling of vibrating string, vibrating membrane, conduction of heat in

solids, gravitational potential, conservation laws and Burger’s equations, classification of

second order PDE, reduction to canonical forms, equations with constant coefficients,

general solution. Unit-5 10 Hours

Graphs, diagraphs, networks and subgraphs, vertex degree, paths and cycles, regular and

bipartite graphs, four cube problem, social networks, exploring and traveling, Eulerian and

Hamiltonian graphs, applications to dominoes, diagram tracing puzzles, Knight’s tour

problem, gray codes. Unit-6 6 Hours

Prey-predator model with infectious disease in any one of the species, Ecological models,

Role of time delay in various mathematical modeling.


Internal Assessment

(IA)

Mid Term Test

(MTE)

End Term Test

(ETE)

Total Marks

20 30 50 100

Name of The Course Optimization Techniques

Course Code BSCM622

Prerequisite Operation Research-1

Corequisite

Antirequisite

L T P C 4 1 0 4

Course Objectives: To impart knowledge in concepts and tools of Operations Research .To

understand mathematical models and numerical techniques in Operations Research .To apply

these techniques constructively to make effective business decisions

Course Outcomes:

CO1 Solve Non-linear and dynamic programming problems.

CO2 Explain networking analysis.

CO3 Interpret the simulation methods.

CO4 Interpret the Information theory.

CO5 Solve constrained and unconstrained optimization problems with numerical

optimization techniques. CO6 Demonstrate various methods of Forecasting.

Text Book (s)

1. M.S. Bazaraa, H.D. Sherali, C.M. Shetty, Nonlinear Programming, J. Wiley & Sons.

2. G. Hadley, Nonlinear and Dynamic Programming, Addison-Wesley, 1972.

3. I.C. Hu, Integer Programming and Network Flows, Addison-Wesley, 1970.

Reference Book (s)

1. Hillier, Lieberman, Introduction to Operations Research, McGraw Hill Book Company, 1989.

2. Mangasarian O.L., Non-linear Programming, McGraw Hill, New York.

Unit-1: Nonlinear Programming & Dynamic Programming 9 Hours

Nonlinear programming, Karush-Kuhn-Tucker necessary and sufficient conditions of

optimality, Quadratic programming , Wolfe's method, Beale's method.

Dynamic programming, Bellman's principle of optimality, Recursive relations, System

with more than one constraint, Solution of LPP using dynamic Programming. Unit-2: Network Analysis 12 Hours

Analysis of a project thorough network diagram, Network scheduling by CPM, PERT,

Financial planning through network, Network crashing. Network flow problems, Max-

flow-min-cut theorem, Integral flow theorem, Maximum flow algorithms, Linear

programming interpretation of Max-flow-mincut theorem. The out-of-Kilter formulation of

minimal cost network flow problem, Labeling procedure for the Out-of-Kilter algorithm, Insight into changes in Primal and Dual function values. Sequencing Problem.

Unit-3: Simulation 8 Hours

Basic concepts, Monte Carlo method, Random number generation, Waiting the simulation

model, New process planning through simulation, Capital budgeting through simulation Unit-4: Information Theory 9 Hours

Shannon theory, Measure of information, Entropy – the expected information, Entropy as a

measure of uncertainty, Memoryless channel, Conditional entropies, Mutual information,

Information process by a channel, Channel capacity, Encoding, Shannon-Fanno encoding

procedure.

Unit-5: Unconstrained Optimization 10 Hours

Search Methods-Fibonacci search, Golden section search. Gradient Methods- Method of

steepest descent, Damped Newtown’s Method, Davidson-Fletcher-Powell Method, Line

search derivatives, Projection Methods. Constrained Optimization: Methods of feasible

direction, Cutting hyperplane Method. Unit-6: Forecasting 8 Hours

Introduction, Forecasting Methods, component of Time series, Smoothing methods in

Forecasting, Trend Projection in Forecasting, Seasonal Components in Forecasting


Internal Assessment

(IA)

Mid Term Test

(MTE)

End Term Test

(ETE)

Total Marks

20 30 50 100

Name of The Course Cryptography and Network Security


Prerequisite

Corequisite

Antirequisite

L T P C 4 1 0 4

Course Objectives: This Course focuses towards the introduction of network security using

various cryptographic algorithms. Underlying network security applications. It also focuses on

the practical applications that have been implemented and are in use to provide email and web

security.

Course Outcomes:

CO1 Explain the fundamentals of Cryptography and Network Security, including data

and advanced encryption CO2 Analyse about different types of attacks.

CO3 Develop security networks and its usages.

CO4 Improve the knowledge of standard algorithms that can be used to provide

confidentiality, integrity and authentication of data. CO5 Design firewall characteristics.

CO6 Understand the bitcoin

Text Book (s)

1. TCP/IPProtocolSuite,BehrouzA.Forouzan,DataCommunicationandNetworking,Tata McGraw

Hill.

Reference Book (s)

3. W.Stallings,CryptographyandNetworkSecurity,PrinciplesandPractice,Pearson Education,

2000.


Public Key Cryptography Principles & Applications, Algorithms: RSA, Message

Authentication: One way Hash Functions: Message Digest, MD5, SHA1.Public Key

Infrastructure: Digital Signatures, Digital Certificates, Certificate Authorities. Unit-2 10 Hours

NetworkAttacks:BufferOverflow,IPSpoofing,TCPSessionHijacking,SequenceGuessing,

NetworkScanning:ICMP,TCPsweeps,BasicPortScans;DenialofServiceAttacks:SYN

Flood, Teardrop attacks, land, Smurf Attacks Unit-3 9 Hours

IP security Architecture: Overview, Authentication header, Encapsulating Security Pay Load,

combining Security Associations, Key Management. Virtual Private Network Technology:

Tunneling using IPSEC Unit-4 9 Hours

Requirements, Secure Socket Layer, and Secure Electronic Transactions, Network

Management Security: Overview of SNMP Architecture-SNMPV1, SNMPV3. Unit-5 9 Hours

Firewall Characteristics& Design Principles, Types of Firewalls: Packet Filtering

Router, Application Level Gate way or Proxy, Content Filters, Bastion Host. Unit-6 4 Hours

Crypto Currency (BitCoin), Password based Cryptography, Secret Sharing.


Internal Assessment

(IA)

Mid Term Test

(MTE)

End Term Test

(ETE)

Total Marks

20 30 50 100

Name of The Course Applications of Algebra

Course Code BSCM624

Prerequisite

Corequisite

Antirequisite

L T P C 4 1 0 4

Course Objectives: The objective of this course is to provide knowledge about applications

of both abstract and linear algebra. The aim is to study about the codes that deal with error

detection and correction in any technological devices that allows communication. Also, the

course focus on the key concepts of image processing.

Course Outcomes:

CO1 Construct of Balanced incomplete block designs (BIBD).

CO2 Define and illustrate main concepts and prove fundamental theorems concerning

error-correcting codes CO3 Understand the symmetry groups and coloring patterns.

CO4 Elobrate anatomy of special types of matrices and applications of image processing

CO5 Analyze the applications of Linear Transformations.

CO6 To learn about inner product space and spectral theory

Text Book (s)

1. I. N. Herstein and D. J. Winter, Primer on Linear Algebra, Macmillan Publishing Company,

New York,1990.

2. S. R. Nagpaul and S. K. Jain, Topics in Applied Abstract Algebra, Thomson Brooks and Cole,

Belmont, 2005.

3. Richard E. Klima, Neil Sigmon, Ernest Stitzinger, Applications of Abstract Algebra with Maple,

CRC Press LLC, Boca Raton,2000.

Reference Book (s)

1. David C. Lay, Linear Algebra and its Applications. 3rd Ed., Pearson Education Asia, Indian

Reprint,2007. 2. Fuzhen Zhang, Matrix theory, Springer-Verlag New York, Inc., New York,1999.

Unit-1 10 Hours

Balanced incomplete block designs (BIBD): definitions and results, incidence matrix of a

BIBD, construction of BIBD from difference sets, construction of BIBD using quadratic

residues, difference set families, construction of BIBD from finite fields. Unit-2 9 Hours

Coding Theory: introduction to error correcting codes, linear cods, generator and parity

check matrices, minimum distance, Hamming Codes, decoding and cyclic codes. Unit-3 9 Hours

Symmetry groups and color patterns: review of permutation groups, groups of symmetry

and action of a group on a set; colouring and colouring patterns, Polya theorem and pattern inventory, generating functions for non-isomorphic graphs.

Unit-4 12 Hours

Special types of matrices: idempotent, nilpotent, involution, and projection tri diagonal

matrices, circulant matrices, Vandermonde matrices, Hadamard matrices, permutation and

doubly stochastic matrices, Frobenius- König theorem, Birkhoff theorem. Positive Semi-

definite matrices: positive semi-definite matrices, square root of a positive semi-definite

matrix, a pair of positive semi-definite matrices, and their simultaneous diagonalization.

Symmetric matrices and quadratic forms: diagonalization of symmetric matrices, quadratic

forms, constrained optimization, singular value decomposition, and applications to image

processing and statistics.

Unit-5 10 Hours

Applications of linear transformations: Fibonacci numbers, incidence models, and

differential equations. Least squares methods: Approximate solutions of system of linear

equations, approximate inverse of an m×n matrix, solving a matrix equation using its

normal equation, finding functions that approximate data. Linear algorithms: LDU

factorization, the row reduction algorithm and its inverse, backward and forward

substitution, approximate inverse and projection algorithms.

Unit-6 3 Hours

Inner product space and examples, self adjoint operators, self normal operators ,Spectrum

of eigen value, Spectral Theorem for Normal Maps (real and complex).


Internal Assessment

(IA)

Mid Term Test

(MTE)

End Term Test

(ETE)

Total Marks

20 30 50 100

Syllabus Generic Electives

Name of The Course Internet of Things (IOT)

Course Code BSCM531

Prerequisite Programming language like python

Corequisite

Antirequisite

L T P C 4 0 0 4

Course Objectives: Students will understand the concepts of Internet of Things and can able to build IoT

applications.

Course Outcomes:

CO1 Understand the concepts of Internet of Things

CO2 Analyze basic perspective and difference between IOT and M2M

CO3 Develop understanding of state-of-the-artIoT architecture

CO4 Design IoT applications in different domain and be able to analyze their

performance

CO5 Demonstrate competence in implementing Internet of Things privacy, security and

governance CO6 Analyze of advance features in C using pointers & structures

Text Book (s)

1. Vijay Madisetti, ArshdeepBahga, “Internet of Things: A Hands-On Approach”

2. Peter Waher, 'Learning Internet of Things', Packt Publishing, 2015

Reference Book (s)

1. Stackowiak, R., Licht, A., Mantha, V., Nagode, L.,” Big Data and The Internet of Things Enterprise

Information Architecture for A New Age”, Apress, 2015.

2. Dr. John Bates , “Thingalytics - Smart Big Data Analytics for the Internet of Things”, john Bates,

2015


Defining IoT, characteristics of IoT, physical design of IoT, logical design of IoT,

functional blocks of IoT, networks and communication, communication models & APIs.,

processes, data Management, IoT Related Standardization. Unit-2: M2M 9 Hours

Introduction, some definitions, M2M value chains, IoT value chains, difference between

IoT and M2M, an emerging industrial structure for IoT, the international driven, global

value chain and global information monopolies. Unit-3 : IOT Architecture 9 Hours

Introduction, state–of-the art, architecture reference model and architecture, IoT reference

model, IoT reference architecture- introduction, functional view, information view,

deployment and operational View, other relevant architectural views. Unit-4: IOT Applications for Value Creations 10 Hours

Introduction, IoT applications for industry: future Factory concepts, Brownfield IoT, smart

objects, smart Applications, four aspects in your Business to master IoT, value, creation

from big aata and serialization, IoT for retailing industry, IoT for oil and gas industry, opinions on IoT Application and value for Industry, home management, eHealth.

Unit-5: Internet of Things Privacy, Security and Governance 10 Hours

Introduction, overview of governance, privacy and security Issues, contribution from FP7

Projects, security, privacy and trust in IoTData-Platforms for smart Cities, first Steps

towards a secure platform, smartie approach.. Unit-6: Advanced features in C 6 Hours

Advanced features in C Pointers, relationship between arrays and pointers Argument

passing using pointers, Array of pointers. Passing arrays as arguments. Strings and C string

library. Structure and Union. Defining C structures, Giving values to members, Array of

structure, Nested structure, passing strings as arguments. File Handling.


Internal Assessment

(IA)

Mid Term Test

(MTE)

End Term Test

(ETE)

Total Marks

20 30 50 100

Name of The Course Internet of Things (IOT) Lab

Course Code BSCM513

Prerequisite Programming language like C, Java, Python

Corequisite AWS

Antirequisite

L T P C 0 0 2 1

Course Objectives: In this course students will be able to develop simple IOT applications using

open source IoT Toolkits like Arduino, Raspberry Pi, Eclipse IoT Project etc.

Course Outcomes:

CO1 Revision of the concepts of Internet of Things

CO2 Understand the application of IoT

CO3 Use of Devices, Gateways and Data Management in IoT.

CO4 Design IoT applications in different domain and be able to analyze their

performance

CO5 Application of IoT in Industrial and Commercial Building Automation and Real

World Design Constraints

Text Book (s)

1. Vijay Madisetti, Arshdeep Bahga, “Internet of Things: A Hands-On Approach”

2. Peter Waher, 'Learning Internet of Things', Packt Publishing, 2015

Reference Book (s)

1. Stackowiak, R., Licht, A., Mantha, V., Nagode, L.,” Big Data and The Internet of Things Enterprise

Information Architecture for A New Age”, Apress, 2015.

2. Dr. John Bates , “Thingalytics - Smart Big Data Analytics for the Internet of Things”, john Bates,

2015

List of Experiments:

Experiment

No

Experiment

1 Define and Explain Eclipse IoT Project

2 List and summarize few Eclipse IoT Projects

3 Sketch the architecture of IoT Toolkit and explain each entity in

brief.

4 Demonstrate a smart object API gateway service reference

implementation in IoT toolkit

5 Write and explain working of an HTTP- to-CoAP semantic

mapping proxy in IoT toolkit 6 Describe gateway-as-a-service deployment in IoT toolkit.

7 Explain application framework and embedded software agents for

IoT toolkit

8 Explain working of Raspberry Pi

9 Connect Raspberry Pi with your existing system components.

10 Give overview of Zetta

11 Develop s simple IOT application for eHealth

Major Equipment:

Raspberry pi, Arduino

List of Open Source Software/learning website:

https://github.com/connectIOT/iottoolkit

https://www.arduino.cc/

http://www.zettajs.org/

• Contiki (Open source IoT operating system)

• Arduino (open source IoT project)

• IoT Toolkit (smart object API gateway service reference implementation)

• Zetta (Based on Node.js, Zetta can create IoT servers that link to various devices and sensors)


Internal Assessment

(IA)

Mid Term Test

(MTE)

End Term Test

(ETE)

Total Marks

50 0 50 100

https://github.com/connectIOT/iottoolkit

https://www.arduino.cc/

http://www.zettajs.org/

Name of The Course Cloud Computing

Course Code BSCM532

Prerequisite Data Structures and algorithms

Corequisite Graph Theory

Antirequisite

L T P C 4 0 0 4

Course Objectives: The main purpose of this course is to provide the most fundamental

knowledge to the students so that they can understand cloud computing technology and its

application.

Course Outcomes:

CO1 Understand cloud computing and service models.

CO2 Develop in depth understanding of Virtualization

CO3 Learn cloud Architecture, services and storage

CO4 Understand the notions of resource management and security in Cloud

CO5 Demonstrate competence in implementing cloud.

CO6 Elaborate the concept of Cloud Simulators.

Text Book (s)

1. Kai Hwang, Geoffrey C. Fox, Jack G. Dongarra, “Distributed and Cloud Computing, From

Parallel Processing to theInternet of Things”, Morgan Kaufmann Publishers, 2012.

2. Rittinghouse, John W., and James F. Ransome, ―Cloud Computing: Implementation,

Management and Security,CRC Press, 2017.

Reference Book (s)

1. RajkumarBuyya, Christian Vecchiola, S. ThamaraiSelvi, ―Mastering Cloud Computing,

Tata Mcgraw Hill, 2013.

2. Toby Velte, Anthony Velte, Robert Elsenpeter, “Cloud Computing – A Practical Approach,


3. George Reese, “Cloud Application Architectures: Building Applications and Infrastructure

in the Cloud:Transactional Systems for EC2 and Beyond (Theory in Practice), O’Reilly,

2009.


Introduction to Cloud Computing – Definition of Cloud – Evolution of Cloud Computing –

Underlying Principles of Parallel and Distributed Computing – Cloud Characteristics –

Elasticity in, Cloud – On-demand Provisioning. Unit-2: Cloud Enabling Technologies 10 Hours

Service Oriented Architecture – REST and Systems of Systems – Web Services – Publish-

Subscribe Model – Basics of Virtualization – Types of Virtualization – Implementation

Levels ofVirtualization – Virtualization Structures – Tools and Mechanisms –

Virtualization of CPU –Memory – I/O Devices –Virtualization Support and Disaster

Recovery Unit-3 : Cloud Architecture, Services and Storage 9 Hours

Layered Cloud Architecture Design – NIST Cloud Computing Reference Architecture –

Public,Private and Hybrid Clouds – laaS – PaaS – SaaS – Architectural Design Challenges

– CloudStorage – Storage-as-a-Service – Advantages of Cloud Storage – Cloud Storage

Providers – S3. Unit-4: Resource Management and Security in Cloud 10 Hours

Inter Cloud Resource Management – Resource Provisioning and Resource Provisioning

Methods –Global Exchange of Cloud Resources – Security Overview – Cloud Security

Challenges –Software-as-a-Service Security – Security Governance – Virtual Machine

Security – IAM –Security Standards..

Unit-5: Cloud Technologies and Advancements 10 Hours

Hadoop – MapReduce – Virtual Box — Google App Engine – Programming Environment

forGoogle App Engine –– Open Stack – Federation in the Cloud – Four Levels of

Federation –Federated Services and Applications – Future of Federation. Unit-6: Cloud Simulators- Cloud Sim and Green Cloud 4 Hours

Introduction to Simulator, understanding Cloud Sim simulator, CloudSim

Architecture(User code, CloudSim, GridSim, SimJava) Understanding Working platform

for CloudSim, Introduction to GreenCloud.


Internal Assessment

(IA)

Mid Term Test

(MTE)

End Term Test

(ETE)

Total Marks

20 30 50 100

Name of The Course Cloud Computing Lab

Course Code BSCM514

Prerequisite Programming language

Corequisite

Antirequisite

L T P C 0 0 2 1

Course Objectives:The main purpose of this laboratory is to provide hands on knowledge to the students

so that they can develop web base applications in cloud by learning the design and development process

involved in creating a cloud based applications.

Course Outcomes

CO1 Configure various virtualization tools such as Virtual Box, VMware workstation.

CO2 Deployment and Configuration options in Google Cloud

CO3 Deployment and Configuration options in Microsoft Azure

CO4 Install and use a generic cloud environment that can be used as a private cloud.

CO5 Deployment and Configuration options in Amazon (AWS)

Text Book (s)

1. Kai Hwang, Geoffrey C. Fox, Jack G. Dongarra, “Distributed and Cloud Computing, From

Parallel Processing to the Internet of Things”, Morgan Kaufmann Publishers, 2012.

2. Ritting house, John W., and James F. Ransome, ―Cloud Computing: Implementation,

Management and Security, CRC Press, 2017.

Reference Book (s)

1. Rajkumar Buyya, Christian Vecchiola, S. ThamaraiSelvi, ―Mastering Cloud Computing,


2. Toby Velte, Anthony Velte, Robert Elsenpeter, “Cloud Computing – A Practical Approach,


3. George Reese, “Cloud Application Architectures: Building Applications and Infrastructure

in the Cloud: Transactional Systems for EC2 and Beyond (Theory in Practice), O’Reilly,

2009.

List of Experiments

Experiment

No

Experiments

1 Hands on virtualization using XenServer

2 Hands on containerisation using Docker

3 Deployment and Configuration options in Amazon (AWS)

4 Deployment and Configuration options in Google Cloud

5 Deployment and Configuration options in Microsoft Azure

6 Install Google App Engine. Create hello world app and other

simple web applications using python

7 Install Hadoop single node cluster and run simple applications like

wordcount. 8 Use GAE launcher to launch the web applications.

9 Find a procedure to transfer the files from one virtual machine to

another virtual machine.

10 Find a procedure to launch virtual machine using trystack (Online

Openstack Demo Version)

11 Simulate a cloud scenario using CloudSim and run a scheduling

algorithm that is not present in CloudSim.


Internal Assessment

(IA)

Mid Term Test

(MTE)

End Term Test

(ETE)

Total Marks

50 0 50 100

Name of The Course Computer Graphics

Course Code BSCM533

Prerequisite Corequisite Antirequisite

L T P C

4 0 0 4

Course Objectives:

This course focuses on 2D and 3D interactive and non-interactive graphics. This course studies the

principles underlying the generation and display of 2D and 3D computer graphics. In this course topics

include geometric modeling, 3D viewing and projection, lighting and shading, color, and the use of

one or more technologies and packages such as OpenGL, and Blender. Course requirements usually

include exam and several programming or written homework assignments.

Course Outcomes:

CO1 To understand the principles, commonly used paradigms and techniques of computer

graphics. e.g. the graphics pipeline, and Bresenham’s algorithm for speedy line and

circle generation.

CO2 Be able to understand 2D graphics concepts in the development of computer games,

information visualization, and business applications.

CO3 To develop a facility with the relevant mathematics of 3D graphics like projection,

clipping and transformation

CO4 Be able to understand the representation of non linear shapes. E. g. Curves, hidden

surfaces.

CO5 Be able to develop animations like motion sequence, morphing and illustrating

models for lighting/shading. CO6 Elaborate visible surface detection concepts and different color model.

Text Book (s)

1 Donald Hearn and M Pauline Baker, “Computer Graphics C Version”, Pearson

Education, India; 2 edition 2002.

2

Computer Graphics Principles and Practice, Second Edition in C, James D.Foley,

Andries Van Dam, Steven K.Feiner, JhonF.Hughes, Addison Wesley, Third Edition,

2014.

Reference Book (s)

1 Steven Harrington, “Computer Graphics: A Programming Approach” , McGraw-Hill

Inc.,US; 2nd Revised edition edition, 1983.

2 David Rogers, “ Procedural Elements of Computer Graphics”, McGraw Hill

Education; 2 edition, 2017.

Unit-1: Introduction 10 Hours

Types of computer graphics, Graphic Displays- Random scan displays, Raster scan

displays, Frame buffer and video controller, Points and lines, Line drawing algorithms,

Circle generating algorithms, Midpoint circle generating algorithm, and parallel version of

these algorithms. Unit-2: Transformations 10 Hours

Basic transformation, Matrix representations and homogenous coordinates, Composite

transformations, Reflections and shearing. Windowing and Clipping: Viewing pipeline,

Viewing transformations, 2-D Clipping algorithms-Line clipping algorithms such as Cohen

Sutherland line clipping algorithm, Liang Barsky algorithm, Line clipping against non

rectangular clip windows; Polygon clipping – Sutherland Hodgeman polygon clipping, Weiler and Atherton polygon clipping, Curve clipping, Text clipping.

Unit-3: Three Dimensional 9 Hours

3-D geometric primitives, 3-D Object representation, 3-D Transformation, 3-D viewing,

projections, 3-D Clipping. Unit-4: Curves and Surfaces 9 Hours

Quadric surfaces, Spheres, Ellipsoid, Blobby objects, Introductory concepts of Spline,

Bspline and Bezier curves and surfaces. Unit-5: Hidden Lines and Illumination models 10 Hours

Hidden Lines and Surfaces: Back Face Detection algorithm, Depth buffer method, A-buffer

method, Scan line method, basic illumination models – Ambient light, Diffuse reflection,

Specular reflection and Phong model, Combined approach, Warn model, Intensity Attenuation, Color consideration, Transparency and Shadows.

Unit-6: Advance topics: 6 Hours

Visible surface detection concepts, back-face detection, depth buffer method, illumination,

light sources, illumination methods (ambient, diffuse reflection, specular reflection), Color

models: properties of light, XYZ, RGB, YIQ and CMY color models.


Internal Assessment

(IA)

Mid Term Test

(MTE)

End Term Test

(ETE)

Total Marks

20 30 50 100

Name of The Course Computer Graphics Lab


Prerequisite Programming language like C, Java, Python

Corequisite Antirequisite

L T P C

0 0 2 1

Course Objectives:

• Understand graphics programming.

• Be exposed to creation of 3D graphical scenes using open graphics library suits.

• Be familiar with image manipulation, enhancement.

• Learn to create animations.

• To create a multimedia presentation/Game/Project.

Course Outcomes:

CO1 Understand the application of computer graphics.

CO2 Create 2D mathematical figures using tools.

CO3 Create 2D animations using tools.

CO4 Implement image manipulation and enhancement.

CO5 Create 3D graphical scenes using open graphics library suits.

Text Book (s)

Reference Book (s)


Experiment

No

Experiment

1 To implement DDA algorithms for line and circle.

2 To implement Bresenham’s algorithms for line, circle and ellipse

drawing. 3 To implement Mid Point Circle algorithm using Python .

4 To implement Mid Point Ellipse algorithm using Python .

5 To perform 2D Transformations such as translation, rotation,

scaling, reflection and sharing.

6 To implement Cohen–Sutherland 2D clipping and window–

viewport mapping. 7 To implement Liang Barksy Line Clipping Algorithm.

8 To perform 3D Transformations such as translation, rotation and

scaling.

9 To convert between color models.

10 To perform animation using any Animation software.

11 To perform basic operations on image using any image editing

software. 12 To draw different shapes such as hut, face, kite, fish etc.

Major Equipment:

C, C++, Java, python,OpenGL

List of Open Source Software/learning website:

1. spoken-tutorial.org


Internal Assessment

(IA)

Mid Term Test

(MTE)

End Term Test

(ETE)

Total Marks

50 0 50 100

Name of The Course Artificial Intelligence

Course Code BSCM631

Prerequisite Linear Algebra & Statistics


L T P C

4 0 0 4

Course Objectives: The main purpose of this course is to provide the most fundamental

knowledge to the students so that they can understand AI.

Course Outcomes:

CO1 Identify problems where artificial intelligence techniques are applicable

CO2 Learn different knowledge representation techniques

CO3 Participate in the design of systems that act intelligently and learn from experience

CO4 Understand the notions of state space representation, exhaustive search, heuristic

search along with the time and space complexities

CO5 Possess the ability to apply AI techniques to solve problems of Game Playing,

Expert Systems, Machine Learning and Natural Language Processing

CO6 Overview of Explainable Artificial Intelligence

Text Book (s)

1. Stuart Russell, Peter Norvig, “Artificial Intelligence – A Modern

Approach”, Pearson Education

2. Elaine Rich and Kevin Knight, “Artificial Intelligence”, McGraw-Hill

Reference Book (s)

1. E Charniak and D McDermott, “Introduction to Artificial Intelligence”, Pearson Education

2. Dan W. Patterson, “Artificial Intelligence and Expert Systems”, Prentice Hall of India

3. Expert Systems: Principles and Programming- Fourth Edn, Giarrantana/ Riley, Thomson.

4. PROLOG Programming for Artificial Intelligence. Ivan Bratka- Third Edition – Pearson

Education.

5. Neural Networks Simon Haykin PHI


Introduction to Artificial Intelligence, Foundations and History of Artificial Intelligence,

Applications of Artificial Intelligence, Intelligent Agents, Structure of Intelligent Agents.

Computer vision, Natural Language Possessing. Unit-2: Search 9 Hours

Searching for solutions, Uniformed search strategies, Informed search strategies, Local

search algorithms and optimistic problems, Adversarial Search, Search for games, Alpha -

Beta pruning Unit-3 : Knowledge Representation and Reasoning 10 Hours

Propositional logic, Theory of first order logic, Inference in First order logic, Forward &

Backward chaining, Resolution, Probabilistic reasoning, Utility theory, Hidden Markov

Models (HMM), Bayesian Networks. Unit-4: PATTERN RECOGNITION 11 Hours

Concept and concept learning, Pattern classification and recognition, Feature vector

representation of patterns, Nearest neighbor based learning, Discriminant function and decision boundary, Multi-class pattern recognition, General formulation of machine

learning, The k-means algorithm.

Unit-5: Neural network 10 Hours

Neural network, Model of one neuron, Learning rules for one neuron, Feature

extraction/selection, Self-organizing neural network, Winner-take-all learning strategy,

Learning vector quantization, R4-rule, Layered neural network, Unit 6- Overview of Explainable Artificial Intelligence 4 Hours

Overview of Explanation Methods and Transparent Machine Learning Algorithms:

Reflection, Global vs. local explainability, Ante-hoc vs. Post-hoc interpretability, Ante-

hoc: GAM, S-AOG, Hybrid models, iML


Internal Assessment

(IA)

Mid Term Test

(MTE)

End Term Test

(ETE)

Total Marks

20 30 50 100

Name of The Course Artificial Intelligence Lab

Course Code BSCM613

Prerequisite Linear Algebra & Statistics, programming language


L T P C

0 0 2 1

Course Objectives:

The laboratory will emphasize the use of PROLOG and LISP tools from public domain. The main

purpose of this course is to provide the most fundamental knowledge to the students so that they can

built simple AI applications.

Course Outcomes:

CO1 Exposure to PROLOG

CO2 Exposure to LISP

CO3 Learn logic programming using PROLOG

CO4 Learn logic programming using LISP

CO5 Develop simple AI applications

Text Book (s)

1. Stuart Russell, Peter Norvig, “Artificial Intelligence – A Modern Approach”, Pearson

Education

2. Elaine Rich and Kevin Knight, “Artificial Intelligence”, McGraw-Hill

Reference Book (s)

1. E Charniak and D McDermott, “Introduction to Artificial Intelligence”, Pearson Education

2. Dan W. Patterson, “Artificial Intelligence and Expert Systems”, Prentice Hall of India

3. Expert Systems: Principles and Programming- Fourth Edn, Giarrantana/ Riley, Thomson.

4. PROLOG Programming for Artificial Intelligence. Ivan Bratka- Third Edition – Pearson Education.

5. Neural Networks Simon Haykin PHI


Experiment

No

Experiment

1 Introduction to Prolog

2 Introduction to Prolog. Continued

3 Write simple fact for the statements using PROLOG.

4 Write predicates for one converts centigrade temperatures to

Fahrenheit, the other checks if a temperature is below freezing 5 Write a program to solve the Monkey Banana problem.

6 WAP in turbo Prolog for medical diagnosis and show the

advantage and disadvantage of green and red cuts 7 WAP to implement factorial, fibonacci of a given number.

8 Write a program to solve 4-Queen problem.

9 Write a program to solve traveling salesman problem.

10 Give overview of Zetta

11 Write a program to solve water jug problem using LISP


Internal Assessment

(IA)

Mid Term Test

(MTE)

End Term Test

(ETE)

Total Marks

50 0 50 100

Name of The Course Computer Vision

Course Code BSCM632

Prerequisite Linea Algebra, Probability & Statistics


L T P C

4 0 0 4

Course Objectives: Computer Vision focuses on development of algorithms and

techniques to analyze and interpret the visible world around us. This requires understanding of

the fundamental concepts related to multi- dimensional signal processing, feature extraction,

pattern analysis visual geometric modeling, stochastic optimization etc. Knowledge of these

concepts is necessary in this field, to explore and contribute to research and further developments

in the field of computer vision. Applications range from Biometrics, Medical diagnosis,

document processing, mining of visual content, to surveillance, advanced rendering etc. Course Outcomes:

CO1 Develop an overview of computer vision and image processing.

CO2 Understand fundamental data structures for image processing

CO3 Apply feature detection and matching algorithms for image processing

CO4 Develop knowledge of image recognition

CO5 Explain deep learning in image processing

CO6 Motion analysis and Activity Recognition

Text Book (s)

1. Rafael C. Gonzales, Richard E. Woods, “Digital Image Processing”, Third

Edition, Pearson Education, 2010.

2. Anil Jain K. “Fundamentals of Digital Image Processing”, PHI Learning Pvt. Ltd., 2011.

Reference Book (s)

1. Willliam K Pratt, “Digital Image Processing”, John Willey, 2002.

2. Malay K. Pakhira, “Digital Image Processing and Pattern Recognition”, First Edition, PHI Learning

Pvt. Ltd., 2011.

Unit-1: 9 Hours

Introduction to Computer Vision, Cameras and Optics, Light and Color, computer imaging

systems, lenses, Image analysis, preprocessing, Image Filtering

Unit – II 10 Hours

Levels of Image Data Representation, Traditional Image Data Structures: Matrices, 2

Chains, Topological Data Structures, Relational Structures, Hierarchical Data Structures,

Pyramids, Quadtrees.

Unit – III 9 Hours

Interest points and corners, Local image features, Model fitting, Hough Transform,

RANSAC and transformations

Unit – IV 10 Hours

Machine learning and recognition overview, Recognition and Bag of Words, Large-scale

retrieval: Spatial Verification, TF-IDF, Query Expansion, feature encoding, Detection with

sliding windows: Viola Jones, Detection with sliding windows

Unit – V 10 Hours

Neural networks Basics and Convolutional Networks, Object Detectors Emerge in Deep

Scene CNNs and Deeper Deep Architectures, Structured Output from Deep Networks,

Unsupervised" Learning and Colorization

Unit-VI 4 Hours

Motion detection and tracking, Inference of human activity from image sequences


Internal Assessment

(IA)

Mid Term Test

(MTE)

End Term Test

(ETE)

Total Marks

20 30 50 100

Name of The Course Computer Vision Lab


Prerequisite Basic Knowledge of Digital Images, Linear Algebra, Partial

Differential Equations and Python. Corequisite Antirequisite

L T P C

0 0 2 1

Course Objectives: To introduce basic principles of Image Processing techniques and to lay

the theoretical foundation of image processing theory for developing applications involving image

processing. Students successfully completing this course will be able to apply a variety of computer

techniques for the design of efficient algorithms for real-world applications.

Course Outcomes:

CO1 Design, implement, and evaluate a computer-based system, process, component, or

program to meet desired needs.

CO2 Analyze the local and global impact of computing on individuals, organizations,

and society. CO3 Utility of current techniques, skills, and tools necessary for computing practice.

CO4 Apply design and development principles in the construction of software systems of

varying complexity. CO5 Create generating noise PDFs for uniform, Rayleigh and exponential noise.

Text Book (s)

1. Rafael C. Gonzalez & Richard E. Woods, “Digital Image Processing”, 2nd edition, Pearson

Education.

2. David A. Forsyth, Jean Ponce, “Computer Vision: A Modern Approach”, Prentice Hall.

3. A.K. Jain, “Fundamental of Digital Image Processing”, PHI.

Reference Book (s)

1. W.K. Pratt, “Digital Image Processing”,


Experiment

No

Experiment

1 Write a Program to display the Negative of a digital Image.

2 Write a Program to perform thresholding on an input Image.

3 Write a Program to perform gray level slicing without background.

4 Write a Program to perform gray level slicing with background.

5 Write a Program to perform bit-plane slicing.

6 Write a Program to display Histogram of an image.

7 Write a Program to perform Log Transformation of an image.

8 Write a Program to implement Ideal low pass filter.

9 Write a Program to implement Butterworth low pass filter.

10 Write a Program to implement Gaussian low pass filter.

11 Write a Program for generating noise PDFs for uniform, Rayleigh

and exponential noise. 12 Write a Program to implement various edge detection operators.


Internal Assessment

(IA)

Mid Term Test

(MTE)

End Term Test

(ETE)

Total Marks

50 0 50 100

Name of The Course Neuro Computing

Course Code BSCM633

Prerequisite Engineering Mathematics


L T P C

4 0 0 4

Course Objectives: To learn the fundamentals of ANN and its application to engineering system.

Course Outcomes:

CO1 Describe the neurons & artificial neural network.

CO2 Explain the perceptron architecture and its types.

CO3 Demonstrate the variety of unsupervised learning process.

CO4 Describe neural network of different algorithm and rules of particular processes.

CO5 Apply the concept of neural network in different engineering problems.

CO6 Apply the concept self-organizing networks to solve real life problems

Text Book (s)

1. Simon O. Haykin , “Neural Networks and Learning Machines”, 3rd Edition,Pearson,2009.

2. Hagan, Demuth, Beale, ‘Neural Network Design’, PWS Publishing Company, 1st Edition, 2002.

3. Freeman, J.A and Skapura, D.M., ‘Neural networks - Algorithms, applications and programming

techniques’, Addison Wesley Publications, Digitized Reprint(2007), 1991.

Reference Book (s)

1. Satish Kumar, ‘Neural Networks–A classroom approach’, Tata McGraw-Hill Publishing Company

Limited, 2013

Unit-1 10 Hours

History-Biological Inspiration- Neuron Model- Single-Input Neuron-Multi- Input Neuron-

Network Architectures- A Layer of Neurons-Multiple Layers of Neurons. Unit-2 9 Hours

Perceptron Architecture- Single-Neuron Perceptron- Multi-Neuron Perceptron- Perceptron

Learning Rule- Constructing Learning Rules-Training Multiple-Neuron Perceptron.

Unit-3 10 Hours

Simple Associative Networks-Unsupervised Hebb Rule- Hebb Rule with Decay-Instar

Rule- Outstar Rule ,Kohonen Rule. Unit-4 10 Hours

Adaline Network – Madaline Network – Mean Square Error- LMS Algorithm- Back

Propagational Neural networks–Hopfield Networks. Unit-5 9 Hours

Adaptive Filtering-Adaptive Noise Cancellation-Forecasting–Neural control applications–

Character recognition. Unit-6 4 Hours

Unsupervised learning of clusters, winner-take-all learning, recall mode, Initialization of

weights, separability limitations


Internal Assessment

(IA)

Mid Term Test

(MTE)

End Term Test

(ETE)

Total Marks

20 30 50 100

Name of The Course Neuro Computing Lab

Course Code BSCM615

Prerequisite Basic Knowledge of Python/ MatLab


L T P C

0 0 2 1

Course Objectives: The objective of this course is to:

1. make students familiar with basic concepts and tool used in neural networks

2. teach students structure of a neuron including biological and artificial

3. teach learning in network (Supervised and Unsupervised)

4. teach concepts of learning rules.

Course Outcomes:

CO1 Familiarization of MatLab/Python

CO2 Develop knowledge of Perceptron and it various activation function

CO3 Design linearly separable and non- separable vectors

CO4 Understand supervised and unsupervised learning concepts & understand

unsupervised learning using Kohonen networks. CO5 Design single and multi-layer feed-forward neural networks

Text Book (s)

1. Simon O. Haykin , “Neural Networks and Learning Machines”, 3rd Edition,Pearson,2009.

2. Hagan, Demuth, Beale, ‘Neural Network Design’, PWS Publishing Company, 1st Edition, 2002.

3. Freeman, J.A and Skapura, D.M., ‘Neural networks - Algorithms, applications and programming

techniques’, Addison Wesley Publications, Digitized Reprint(2007), 1991.

4. Mohamad H. Hassoun, Foundamentals of Artificial Neural Networks, The MIT Press, 1995.

5. Laurene Fausett, Fundamentals of Neural Networks: Architectures, Algorithms, and Applications,

Prentice Hall International, Inc., 1994.

6. B. D. Ripley, Pattern Recognition and Neural Networks, Cambridge University Press., 1996.

Reference Book (s)

1. Satish Kumar, ‘Neural Networks–A classroom approach’, Tata McGraw-Hill Publishing Company

Limited, 2013

1

Experiment

No

Experiment

1 (i) To perform matrix operations in Matlab/Python

(ii) Write a program to calculate the factorial of a number by

creating a script file by using while loop

(iii) Write a program in Matlab/Python to find the factorial by

creating a function file by using for loop

2 (i) Write a program in Matlab/Python to plot multiple curves in

single plot by creating a script file

(ii) Write a program in Matlab/Python for plotting multiple curves

in single figure

3 Write a program to solve 4-Queen problem in Matlab/Python

4 Write a program in Matlab/Python to plot piecewise continuous

activation function (threshold and signum function in neural

network) in Matlab/Python

5 To write a program to implement AND and OR gates using

Perceptron in Matlab/Python

To design and train a perceptron training for EX-OR gate in

Matlab/Python

6 (i) Write a program to create the Perceptron using GUI in

Matlab/Python

(ii) Write a program in Matlab/Python to create `Perceptron using

commands

7 (i) Write a program in Matlab/Python to classify the Classes using

Perceptron

(ii) Write a program in Matlab/Python for Pattern Classification

using Perceptron network

8 Write a program in Matlab/Python for creating a Back Propagation

Feed-forward neural network

9 To design a Hopfield Network which stores 4 vectors in

Matlab/Python

10 Write a program to implement classification of linearly separable

Data with a perceptron in Matlab/Python

12 Write a program to illustrate Linearly non-separable vectors in Matlab/Python


Internal Assessment

(IA)

Mid Term Test

(MTE)

End Term Test

(ETE)

Total Marks

50 - 50 100

1.2.2 b. sc(h)mathematics - galgotiasuniversity.edu.in

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