Discrete Structure

Course Title: Discrete Structure

Course no: CSC-152                                                                                  Full Marks: 80+20

Credit hours: 3                                                                                           Pass Marks: 32+8

Nature of course: Theory (3 Hrs.)

Course Synopsis:     This course contains the fundamental concepts of logic, reasoning                            and algorithms.

Goal:  After completing this course, the target student will gain knowledge in discrete mathematics and finite state automata in an algorithmic approach. It helps the target student in gaining fundamental and conceptual clarity in the area of Logic, Reasoning, Algorithms, Recurrence Relation, and Graph Theory.

Course Contents:

Unit 1. Logic, Induction and Reasoning                                                           12 Hrs.

Proposition and Truth function, Propositional Logic, Expressing statements in Logic Propositional Logic, The predicate Logic, Validity, Informal Deduction in Predicate Logic, Rules of Inference and Proofs, Informal Proofs and Formal Proofs, Elementary Induction, Complete Induction, Methods of Tableaux, Consistency and Completeness of the System.

Unit 2. Finite State Automata                                                                   10 Hrs.

Sequential Circuits and Finite state Machine, Finite State Automata, Language and Grammars, Non-deterministic Finite State Automata, Language and Automata, Regular Expression.

Unit 3. Recurrence Relations                                                                    8 Hrs.

Recursive Definition of Sequences, Solution of Linear recurrence relations, Solution to Nonlinear Recurrence Relations, Application to Algorithm Analysis. Combinatory, Partial Order relation.

Unit 4. Graph Theory                                                                                  15 Hrs.

Undirected and Directed Graphs, Walk Paths, Circuits, Components, Connectedness Algorithm, Shortest Path Algorithm, Bipartite Graphs, Planar Graphs, Regular Graphs, Planarity Testing Algorithms, Eulerian Graph, Hamiltonian Graph, Tree as a Directed Graph, Binary Tree, Spanning Tree, Cutsets and Cutvertices, Network Flows, Maxflow and Mincut Theorem, Data Structures Representing Trees and Graphs in Computer, Network Application of Trees and Graphs, Concept of Graph Coloring.

Text / Reference books:

1.      Kenth Rosen, Discrete Mathematical Structures with Applications to Computer Science, WCB/ McGraw Hill

2.      G. Birkhoff, T.C. Bartee, Modern Applied Algebra, CBS Publishers.

3.      R. Johnsonbaugh, Discrete Mathematics, Prentice Hall Inc.

4.      G.Chartand, B.R.Oller Mann,  Applied and Algorithmic Graph Theory, McGraw Hill

5.      Joe L. Mott, Abrahan Kandel, and Theodore P. Baker, Discrete Mathematics for Computer Scientists and Mathematicians, Prentice-Hall of India

Statistics II

Course Title: Statistics II

Course no: STA-152                                                                        Full Marks: 60+20+20

Credit hours: 3                                                                     Pass Marks: 24+8+ 8

Nature of course: Theory (3 Hrs.) + Lab (3 Hrs.)

Course Synopsis:       Concept of Sample Survey and Design, and their applications.

Goal:  This course makes students able to understand the concept of Sample Survey and             Design, and their applications in the area of Science and Technology.

Course Contents:

Unit 1: Sample Survey                                                                                   10 Hrs.

Concept of Population and Sample; Needs of Sampling; Censuses and Sample Survey; Basic Concept of Sampling; Organizational Aspect of Sample Survey; Questionnaire Design; Sample Selection and Determination of Sample Size; Sampling and Non Sampling Errors.

 

Unit 2: Sample Survey Methods                                                                   13 Hrs.

Types of Sampling; Simple Random Sampling with and without Replacement; Stratified Random Sampling; Ratio and Regression Method of Estimation under Simple and Stratified Random Sampling; Systematic Sampling; Cluster Sampling; Multistage Sampling; Probability Proportion to Size Sampling (PPS), Estimation of population total and its Variance

 

Unit 3: Design of Experiment                                                                        5 Hrs.

 

Concept of Analysis of Variance (ANOVA), F -Statistic and its Distribution, Linear Model in ANOVA, Analysis of One way, Two Way Classification (1 and m observations per cell) in Fixed Effect Model.

 

Unit 4: Simple Design                                                                                    10 Hrs.

Need for Design of Experiment, Fundamental Principles of Design, Completely Randomized Design (CRD), Randomized Block Design (RBD), Latin Square Design (LSD) and their Analysis; Missing Plot Techniques for RBD and LSD (One Observation Missing Only).

 

Unit 5: Factorial Design                                                                                7 Hrs.

2², 2³ and 3² Designs; Main Effects and Interaction Effects; Confounding in 2³ Factorial Design

Text Books:   

·        Mukhopadhyay P., Theory and Methods of Survey Sampling, Prentice Hall of India, New Delhi, 1998.

·        Montgomery Douglas C., Design and Analysis of Experiments, 5th edition, John Wiley & Sons Inc., 2001.

·         Cochran W.G., Sampling Techniques, 3rd edition, John Wiley and Sons, Inc. New York, 1977.

References:

·        Kempthorane, O., Design and Analysis of Experiments, Wiley Eastern, New York.

·        Desraj, Pramod Chandhok, Sample Survey Theory, Narosa Publishing House, 1998.

Note:      

1.                  Theory and practice should go side by side.

2.                  It is recommended 45 hours for lectures and 15 additional hours for tutorial class for   completion of the course in the semester.

3.                  SPSS Software should be used for data analysis.

4.                  Home works and assignments covering the lecture materials will be given   throughout the semester.

Geology II

Course Title: Geology II

Course no: GEO-158                                                                      Full Marks: 60+20+20

Credit hours: 3                                                                     Pass Marks: 24+8+8

Nature of course: Theory (3 Hrs.) + Lab (3 Hrs.)

Course Synopsis:     Fundamental concepts of contemporary earth and environmental                                      science and engineering with increasing computer application.

Goal:  It aims at providing students with the knowledge Earth and environmental science             and engineering

Course Contents:

Unit 1.                                                                                                             11 Hrs.

1.1 Bed load transport: mechanics and database structures.

1.2 Surface run-off: patterns and database structures

Unit 2.                                                                                                             11 Hrs.

2.1 hill slope stability: mechanics, Finite Difference Method and Finite Element Method analysis

2.2 Underground excavation: roof control and database structures

Unit 3.                                                                                                             11 Hrs.

3.1 Groundwater flow: aquifers, flow modeling and exploitation of groundwater.

3.2 Stream flow: hydrographs, time series and flood forecast techniques.

Unit 4.                                                                                                             12 Hrs.

4.1 Sediment routings; reservoir sedimentation mechanisms and routing.

4.2 Hydrological routing: reservoir and channel routing           

4.3 Universal soil Loss Equation (USLE); Components, calculations and conclusions.

Laboratory projects:         

           

            Mineral / Rock identification, Soil types, Reserve calculation, Slope stability calculation, Rock Mass Ratings, ER Mapper, ArcView, ILWIS tour, RS data analysis, Digitization, practice and Geographic locking, GIS Layers shows and illustrations, GIS assignment with digital RS data.

Practical

• To calculate the stream power of bed-load transport.
• To calculate soil erosion using universal soil loss equation (USLE).
• To calculate the roof control for an underground excavation.
• To calculate ground water flow from aquifer data.
• To calculate flood forecast form stream flow data.
• To calculate sediment routing parameters for a reservoir.
• To calculate channel routing from stream flow data.
• To design a groundwater well.
• To perform Finite difference method (FDM) analysis for slope stability (software based).
• To perform Finite Elements Method (FEM) analysis for slope stability (Software based).

Text Books:    No specific text book covering all materials but a working manual could                             be easily prepared.

Reference:               

Homework:  Homework assignments covering lecture materials and primary                                  numerical exercises.

Assignments:           Given throughout the semester.

Computer Usage: MS-WINDOWS (WINDOWS 98/XP) base PC of workstation

Prerequisites: Basic IT literacy

Category contents:
 Science Aspect: 50%
Engineering Aspect: 50%

Biology II

Course Title: Biology II

Course no: BIO-157                                                                        Full Marks: 60+20+20

Credit hours: 3                                                                                 Pass Marks: 24+8+8

Nature of course: Theory (3 Hrs.) + Lab (3 Hrs.)

Course Synopsis:     Cell Division, DNA structure and function, RNA, transcription and                               translation process, mutation, gene regulation, recombinant DNA                                         technology.

Goal:  The course is aimed at knowing the living organism at the molecular level. It also             focused on techniques for gene manipulation by using recombinant DNA technology.

Course Contents:

Unit 1.                                                                                                             5 Hrs.

Cell division: Mitosis, meiosis, mechanism of crossing over, non-disjunction, ell cycle, abnormal cell division, basis of oncology

Unit 2.                                                                                                             9 Hrs.

DNA: Structure of DNA, replication of DNA, Organization of DNA in chromosomes, forms of DNA

Unit 3.                                                                                                             11 Hrs.

3.1    RNA: Overview of gene expression, transcription-synthesis of RNA, process, structure of mRNA

3.2    Protein synthesis: Decoding the message, tRNA, ribosomal rNA, role of ribosome in protein synthesis

3.3    Genetic code: Introduction of genetic code, wooble hypothesis

Unit 4.                                                                                                             6 Hrs.

Mutation and DNA repair: Introduction, types of mutation, reversion, mechanism of DNA repair.

Unit 5.                                                                                                             6 Hrs.

5.1 Gene regulation in prokaryotes: Operon concept, transcriptional control of protein synthesis, post transcriptional gene control

5.2 Eukaryotic gene control: Control of transcription, post transcriptional gene control, splicing.

Unit 6.                                                                                                             8 Hrs.

Recombinant DNA technology; introduction, tools for cloning, vectors and restriction endonucleases, gene cloning and expression, application of recombinant DNA in healthcare and agriculture industry

Laboratory Assignments:

1. Observation of stages of mitosis by cytological slide preparation from root tip of onion.
2. Observation of stages of meiosis by cytological slide preparation from anthers.
3. Preparation of models of DNA, RNA and protein synthesis
4. Testing for DNA with Geulgen stain.
5. Testing fro DNA and RNA with Methyl Green Pyronin stain.
6. Counting of WBC and RBC in human blood.

Text Books:    Biology by Villee, Solomon, Martin, Martion, Gerg, Davis 2^nd Edition,                             Saunders college publishing, USA.

Reference Book:     Concepts in Biology by E.D. Enger & F.C. Ross, 9^th Ed. Tata                                               McGraw Hill

                                   

                                   Biology by P.H. Reven, 5^th Ed. WBC McGraw Hill.

Laboratory Manual:          Biology; A functional approach; Student's Manual / By M.B.V.

                                    Roberts and T.J. King (second edition - ELBS / Nelson, 1988)

Physics II

Course Title: Physics II

Course no: PHY-156                                                                       Full Marks: 60+20+20

Credit hours: 3                                                                                Pass Marks: 24+8+8

Nature of course: Theory (3 Hrs.) + Lab (3 Hrs.)

Course Synopsis:     (a)      Basic concepts of probability, entropy, classical and quantum                                                 statistics.

(b)            Simple concepts of quantum mechanics leading to Schrödinger equation and its application to simple cases.

(c) Methods of solid state physics - crystal structure, band theory of solids, free electron theory of metals and band theory of semiconductors.

Goal:  The course aims at providing fundamental physical concepts needed to understand information processing and related devices,

Unit 1. Statistical Physics                                                                            9 Hrs.

1.1             Macroscopic and microscopic description of a thermodynamic system; ensemble, phase space.

1.2             Thermodynamic probability, fundamental postulates of stat. physics.

1.3             Entropy and probability Bolltzmann theorem, statistical equilibrium

1.4             Maxwell-Boltzmann distribution for ideal gas

1.5             Quantum Statistics:

1.5.1   Bose-Einstein statistics-Photon Gas, Planck's law for Black Body             Radiation

1.5.2   Fermi - Dirac statistics- application to electron gas

Unit 2. Modern Physics                                                                              23 Hrs.

2.1       Introduction to Quantum mechanics

2.1.1   Wave particle duality, de Broglie's matter

            Waves, phase-velocity and group velocity

2.1.2   Heisenberg's uncertainty principle. 

2.1.3   Basic postulates of q m

-     dynamical variable - linear operator

-     eigen values of linear hermitian operator

-     measurement of a dynamical variable

-     Schrödinger equation

-     interpretation of wave function

                        2.1.4   Simple applications of Schrödinger equation

-           particle in a box, infinite potential well

-           barrier penetration

-           square potential well

-           linear harmonic oscillator

-           hydrogen atom

-           rigid rotator

2.2       Band Theory of Solids

2.2.1   Crystalline structure of solids, Bravais lattice miller indices, reciprocal lattice, examples

2.2.2   Band theory of solids: origin of Bands

2.2.3   Classification of solid conductor, insulator and semi conductors

2.2.4   Free electron theory of metal: Fermi energy, electron energy distribution, thermo ionic emission Schottky effect, contact potential.

Unit 3. Semi Conductors                                                                           13 Hrs.

3.1       Band structure of semiconductors, energy gap

3.2       Electrons and holes, electric conduction in semiconductors, effective mass, extrinsic and extrinsic semiconductors

3.3       n-type and p-type semiconductors, carrier concentration, mobility, temperature dependence.

3.4       p-n junction

3.5       Metal semiconductor junction, Schottky junction, Ohmic contact.

Laboratory works:

1. To determine inter planer spacing of given crystal by electron diffraction method.
2. To determine the band gap of given sample
3. To determine the nature of charge carrier of a given simple by hall apparatus
4. Study NOT, AND, OR, NAND, NOR, EX-OR, EX-NOR gates
5. To study the temperature dependency of a given sample.
6. To study the characteristic of simple and zener diode
7. To construct and study CE amplifier
8. To construct and study CC amplifier
9. To construct and study CB amplifier
10. To study output input and transfer characteristics of NPN transistor.

Text books:

(1)       Thermal physics: C. Kittel

(2) Modern Physics: Murgeshan

(3) Introduction to solid state physics: C. Kittel.

References books:

Elementary Solid State Physics - M.A. Omar Addison-Wesley

Heat, Thermodynamics and Statistical Physics:- Singhal, Agrawal and Satya Prakash, Pragati Prakashan, Meerut, India

Home work:       Several problems every week.

Prerequisites:     Calculus based introductory physics and physics I