**Freshman Year/First Semester**

**Nature of Course:**Theory (3 Hrs) + Lab (3 Hrs)

**Text Books:**Alexis Leon, Mathew Leon, Fundamentals of Information Technology, Leon Tech World

**Course Synopsis:**Fundamental concept of Information technology. Computer systems, Computer software, DBMS, and application of computer science.

**Goal:**This course introduces fundamental concepts of Information Technology and computer science.

**Course Contents:**

**Unit 1. Introduction to Computer Systems (10 hrs)**

Introduction to computers, Classification of digital computers systems, Anatomy of a digital Computer, Computer Architecture, Memory system, Memory Units, Auxiliary Storage devices, Input devices, Output devices.

**Unit 2. Computer Software and Software Development (6 hrs)**

Introduction to Computer Software, Operating Systems, Programming Languages, General Software Features and Trends.

**Unit 3. Database Management Systems (6 hrs)**

Data processing, Introduction to Database Management systems, Database design

**Unit 4. Telecommunications (8 hrs)**

Introduction to Telecommunication, Computer Networks, Communication Systems, Distributed systems.

**Unit 5. Internet and New Technologies in Information Technology (10 hrs)**

Internet, Multimedia tools and system, Intranets, Electronic commerce, Hypermedia, Data Warehouse and Data Marts, Data Mining, Geographical Information System.

**Unit 6. Application of Information Technology (5 hrs)**

Computers in Business and Industry, Computers in education, training, Computers in Entertainment, science, medicine and Engineering.

**Laboratory works:** The main objective is familiarizing students with operating system and desktop applications using current version of windows.

**Nature of Course:**Theory (3 Hrs) + Lab (3 Hrs)

**References:**Deitel,C : How to program,2/e (With CD), Pearson Education, Al Kelley, Ira Pohl: “A Book on c” Pearson Education, Brain W.Keringhan & Dennis M.Ritchie “The C Programming Language”, PHI, Bryons S. Gotterfried:”Programming with C” TMH, Stephen G. Kochan: “Programming in C”, CBS publishers & distributors, Yashavant Kanetkar: “Let us C”, BPB Publications.

**Course Synopsis:**This course contains the concepts of programming methodology using c.

**Goal:**This course is designed to familiarize students to the techniques of programming in C

**Course Contents:**

**Unit 1. Problem Solving with Computer (2 Hrs)**

Problem analysis, Algorithm and flowchart, Coding , Compilation and Execution, History of C, Structure of C program, Debugging, Testing and Documentation.

**Unit 2. Elements of C (4 Hrs)**

C Tokens, Escape sequence, Delimiters, Variables, Data types, Constant/Literals, Expression, Statements and Comments.

**Unit 3. Input and Output (2 Hrs)**

Conversion specification, I/O operation, Formatted I/O

**Unit 4. Operators and Expression (4 Hrs)**

Arithmetic operator, Relational operator, Logical or Boolean Operator, Assignment operator Ternary Operator, Bitwise Operator, Increment or Decrement operator, Comma operator.

**Unit 5. Control Statement (4 Hrs)**

Branching, Looping, Conditional Statements, Exit function, Difference between break and exit

**Unit 6. Arrays (6 Hrs)**

Introduction, Declaration of array, Initialization of array, Sorting, Multidimensional array

**Unit 7. Functions (5 Hrs)**

Library Functions, User defined functions, Recursion, Function declaration, Local and global variables, Use of array in function, Passing by value, Passing by Address

**Unit 8. Pointers (6 Hrs)**

Introduction, The & and * operator, Declaration of pointer, Pointer to pointer, Pointer arithmetic, Array and Pointer, Pointer and array ,Pointer with multidimensional array Pointer and strings, Array of pointer with string ,Dynamic memory allocation

**Unit 9. Structure and Union (2 Hrs)
**

Introduction, Array of structure, Passing structure to function, Passing array of structure to function, Structure within structure (Nested Structure), Union, Pointer to structure

**Unit 10. Files and file handling in C (4 Hrs)**

Concept of file, Opening and closing of file, Modes, Input/output function, Random access in

file, Printing a file.

**Unit 11. Introduction to Graphics (3 Hrs)**

Modes, Initialization, Graphics Function

**Laboratory works:**

This course require a lot of programming practices. Each topic must be followed by a

practical session. Some practical sessions include programming to:

- Create, compile and run simple c program, handle different data types available in C, perform character input and output operations.
- Perform logical operations, create decision making programs, create loops to repeat task, use different looping method.
- Create user-defined function, create recursive functions, work with automatic, global and static variables ,create manipulate arrays and matrices(single and multidimensional),work with pointers, dynamically allocate de-allocate storage space during run-time, manipulate strings (character arrays) using various string handling function
- Create and use structure an files to keep record of students, employees etc

**Text Books:**Sheldon M. Ross, Introduction to Probability and Statistics for Engineers and Scientists, 3rd Edition, India: Academic Press, 2005.

**References:**Richard A. Johnson, Miller and Freund’s probability and Statistics for Engineers, 6th Edition, Indian reprint: Pearson Education, 2001, Ronald E. Walpole, R.H. Myers, S.L. Myers, and K. Ye, Probability and Statistics for Engineers and Scientists, 7th Edition, Indian reprint: Pearson Education, 2005.

**Course Synopsis:**Concept of descriptive statistics, probability, probability distributions, inferential statistics and their applications.

**Goal:**This course enhances the ability of students in computing and understanding summary statistics; understanding the concept of probability and probability distributions with their applications in statistics. Finally, students will develop their ability of using inferential statistics in decision-making processes.

**Course Contents:**

**Unit 1. Introduction (2 Hrs)**

Scopes and limitations of statistics in empirical research; Role of probability theory in statistics; Role of computer technology in statistics

**Unit 2. Descriptive Statistics (6 Hrs)**

Measures of location: mean, median, mode, partition values and their properties; Measures of dispersion: absolute and relative measure of variation; range, quartile deviation, standard deviation; Other measures: Coefficient of variation; Measures of skewness and kurtosis.

**Unit 3. Probability (5 Hrs)**

Introduction of probability: Basic terminology in probability: sample space, events, random experiment, trial, mutually exclusive events, equally likely events, independent events; Definitions of probability: Classical, statistical, axiomatic definitions; Basic principles of counting; Laws of probability: Additive and multiplicative; Conditional probability; Bayes’ Theorem.

**Unit 4. Random Variable and Expectation (2 Hrs)**

Random Variables: Discrete and continuous random Variables; Probability distribution of random variables; Expected value of discrete & continuous random Variable.

**Unit 5. Jointly Distributed Random Variables and Probability Distributions (4 Hrs)**

Joint Probability Distribution of two random variables: Joint probability mass functions and density functions; Marginal probability mass and density functions; Mean, variance, covariance and correlation of random variables; Independent random variables; Illustrative numerical problems.

**Unit 6. Discrete Probability Distributions (5 Hrs)**

Bernoulli and binomial random variable and their distributions and moments; Computing binomial probabilities; Fitting of binomial distribution; Poisson random variable and its distribution and moments; Computing Poisson probabilities; Fitting of Poisson distribution.

**Unit 7. Continuous Probability Distributions (6 Hrs)**

Normal distribution and its moments; Standardization of normally distributed random variable; Measurement of areas under the normal curve; Negative exponential distribution and its moments; Concept of hazard rate function.

**Unit 8. Chi-square, t and F Distribution (4 Hrs) **

Characteristics function of normal random variable; Distribution of sum and mean of n independent normal random variables; Canonical definitions of chi-square, t and F random variables and their distributions; Joint distribution of and S2 in case of normal distribution.

**Unit 9. Inferential Statistics (7 Hrs)**

Simple random sampling method and random sample; Sampling distribution and standard error; Distinction between descriptive and inferential statistics; General concept of point and interval estimation; Criteria for good estimator; Maximum likelihood method of estimation; Estimation of mean and variance in normal distribution; Estimation of proportion in binomial distribution; Confidential interval of mean in normal distribution; Concept of hypothesis testing; Level of significance and power of a test; Tests concerning the mean of a normal distribution case – when variance is known (Z-test) and unknown (t-test)

**Unit 10. Correlation and Linear Regression (4 Hrs)**

Simple Correlation: Scatter diagram; Karl Pearson’s correlation coefficient and its properties, Simple Linear Regression: Model and assumptions of simple linear regression; Least square estimators of regression coefficients; Tests of significance of regression coefficients; Coefficient of determination

**Note:**

- 1Theory and practice should go side by side.
- It is recommended 45 hours for lectures and 15 additional hours for tutorial class for completion of the course in the semester.
- SPSS software should be used for data analysis.
- Students should have intermediate knowledge of Mathematics.
- Home works and assignments covering the lecture materials will be given throughout the semester.

**Text Books**Thomas and Fenns: Calculus and Analytical Geometry, 9th Edition, 2004. (Thomas, Jr. G. B., and Finney, Ross L. Publisher: Pearson Education Pvt. Ltd, Kreyszig, Erwin, Advanced Engineering Mathematics, John- Wiley & Sons (1991). 5th Edition.

**References**E.W. Swokowski, Calculus with Analytical Geometry, Second Alter Edition. Sneddan Ian- Elements of Partial Differential Equations.

**Course Synopsis:**Preliminaries revision of differentiation and integration; Techniques of integration infinite series; Vectors and analytical geometry in space (differential geometry). Vector valued functions. Multi variable functions and partial derivatives. Multiple integrals and integration in vector fields. Partial derivatives; Equations of First Partial Derivatives.

**Goal:**This course aims at providing students with some advanced topics in undergraduate calculus and fundamental concepts of partial differentiation and P.D.E of second order. It is assured that a student who has done Certificate Level papers in mathematics will be able to study this course.

**Course Contents:**

**Unit 1. Topics in Differential Calculus and Integral Calculus (8 Hrs)**

1.1 Functions and Graphs

1.2 Extreme values of functions; graphing of derivatives

1.3 Mean value integers

1.4 Definite integers, Properties and application, Mean value theory for definite integers

1.5 Fundamental theory of Integral Calculus and application, Improper integrals

**Unit 2. Infinite Series (5 Hrs) **

2.1 Infinite sequence and sequence of convergence and divergence

2.2 Integral test, comparison test, ratio and root test

2.3 Absolute and conditional convergence

2.4 Power series, Taylor and Maclaurin series, convergence of Taylor series

**Unit 3. Conic Section (3 Hrs)**

3.1 Classifying conic sections by eccentricity

3.2 Plane curves, parametric and polar equations, integration in polar coordinates

**Unit 4. Vectors and Vectors Valued Functions (6 Hrs)**

4.1 Vectors in the space

4.2 Lines and planes in space

4.3 Cylinders and Quadric surfaces

4.4 Cylindrical and Spherical Coordinates

4.5 Vector valued functions and space curves

4.6 Unit tangent vector, curvature and torsion and TNB system

**Unit 5. Multiple Integrals (5 Hrs)**

5.1 Double integrals in rectangular polar coordinates

5.2 Finding areas, moments and center of mass

5.3 Triple integrals in rectangular coordinates and application

5.4 Substitutes in multiple integrals

**Unit 6. Multivariate Calculus (9 Hrs)**

6.1 Functions, limits and continuity of two or more variables

6.2 Partial derivatives

6.3 Differentiability, Differentials, Total Differential Coefficients

6.4 Directional derivatives and gradient vectors

6.5 Extreme values

6.6 Lagrange Multiplies

**Unit 7. Partial Differential Equations (9 Hrs)**

7.1 Review of Ordinary Differential Equations

7.2 Analysis of P.D.E of 1st and 2nd order

7.3 Linear equations of the 1st order and the general solutions

7.4 P.D.E of 2nd order, its derivation and basic concepts

7.5 Solution of general P.D.E with constant coefficients, complimentary solution and integral solution

7.6 Wave equations and heat equations and their solutions (Chapter II, Section 11.1, 11.2, 11.4, 11.5). Erwin and Kreyszig. 8th edition, John-Wiley Publications.

**Elective**

**Nature of Course:**Theory (3 Hrs) + Lab (3 Hrs)

**Text Books: **Draper, N. and H. Smith, Applied Regression Analysis, 2nd edition, New York: John Wiley & Sons, 1981, Hogg & Tanis, Probability & Statistical Inference, 6th edition, First Indian Reprint, 2002, Gujaratii, D. Basic Econometrics, International edition, 1995, Gibbons, J.D, Nonparametric Statistical Inference. International Student Edition, Siegel, S. Nonparametric Statistics for the Behavioural Sciences. McGraw-Hill, New York.

**References:**Hollander, M. & Wolfe, Nonparametric Statistical Methods. Johns Wiley & Sons, New York

**Course Synopsis:** Concept of Applied Statistical Techniques and its Applications

**Goal:** This course makes students able to understand Applied Statistical Techniques and their applications in the allied areas.

**Course Contents:**

**Unit 1: Sampling Techniques (10 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; Multistage Sampling; Estimation of population total and its Variance.

**Unit 2: Non Parametric Test (16 Hrs)**

Chi-square test: Test of goodness of fit; Test for independence (Categorical Data). Definition of Order Statistics; Run Test; Sign Test; Wilcoxon Matched Pairs Signed Ranks Test; Mann-Whitney U Test; Median Test; Kolmogorov Smirnov Test (One Sample Case); Cochran Q Test; Kruskl Wallis One way ANOVA Test; Friedman Two way ANOVA Test.

**Unit 3: Correlation and Regression Analysis (19 Hrs)**

Partial and Multiple Correlations; Multiple Linear Regressions: Assumptions; Coefficient Estimation, and Significance Test; Coefficient of Determination; Cobb-Dauglas Production Function; Growth Model; Logistic Regression; Autoregressive Model of order One, and Appraisal of Linear Models (Heteroscedasticity, Multicolinearity, Autocorrelation).

**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.

**Freshman Year/Second Semester**

**Nature of Course:**Theory (3 Hrs) + Lab (3 Hrs)

**Text/ Reference book**M.Morris Mao, “Logic & Computer Design Fundamentals”, Pearson Education.

**Course Synopsis:**General concepts to be used in the design and analysis of digital systems and introduces the principles of digital computer organization and design.

**Goals:**

• Introduce fundamental digital logic and switching networks. Exposure of Boolean algebra and its application for circuit analysis.

• Introduction to multilevel gates networks, flip-lops, counters and logic devices.

**Course Contents:**

**Unit 1: Binary Systems (7 Hrs)**

Digital Systems, Binary numbers, Number base conversion, Octal and hexadecimal numbers, Binary Systems, Integrated Circuits

**Unit 2: Boolean algebra and Logic Gates (6 Hrs)**

Basic definitions of Boolean algebra, basic Theory of Boolean Algebra, Boolean Function, Logic Operations, Logic Gates, IC Digital Logic Families

**Unit 3: Simplification of Boolean Functions (6 Hrs)**

K-map, Two and Three variable maps, Four variable maps, product of sums, sum of product simplification, NAND and NOR implementation

**Unit 4: Combinational Logic (6 Hrs)**

Design Procedure, Adders, Subtractors, Code Conversions, Analysis Procedure, NAND Circuits, NOR Circuits, Exclusive –OR Circuits

**Unit 5: Combinational Logic with MSI and LSI (6 Hrs)**

Binary Parallel Adder, Decimal Adder, Magnitude Comparator, Decoders, Multiplexers, Read-only-Memory (ROM), Programmable Logic Array (PLA)

**Unit 6: Sequential Logic (8 Hrs)**

Flip-Flops, Triggering of flip-flops, Design procedure, Design with state equations and state reduction table

**Unit 7: Registers and Counters (6 Hrs)**

Registers, Shift registers, Ripple Counters, Synchronous Counters, Timing Sequences, the memory Unit

**Laboratory works:**

1. Familiarizations with logic gates

2. Encodes and decodes

3. Multiplexer and de-multiplexer

4. Design of simple combination circuits

5. Design of adder/subtractor

6. Design of flip- flop

7. Clock driven sequential circuits

8. Conversion of parallel data into serial format

9. Generation of timing signal for sequential system

**Nature of course:**Theory (3 Hrs)

**Text/ References**Kenth Rosen, Discrete Mathematical Structures with Applications in Computer Science, WCB/McGraw Hill, G.Birkhoff, T.C. Bartee, Modern Applied Algebra, CBS Publishers.R. Johnsonbaugh, Discrete Mathematics, Prentice Hall Inc , G. Chartand, B.r. Oller mann, Applied and Algorithmic Graph Theory, McGraw Hill,

*Discrete mathematics for Computer Scientists and Mathematicians*, Prentices-Hall of India.

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

**Goals:**After completing this course, the largest 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.

**Unit2 : 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.

**Unit3: Recurrence Relations (8 Hrs)**

Recursive Definition of Sequences, Solutions 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 Graph, Planarity Testing Algorithms, Eulerian Graph , Hamiltonian Graph, Tree as a Directed Graph, Binary Tree, Spanning Tree, Cutsets and cutvertices, Network Flows, maxflow and Minflow Theorem, Data Structures Representing Trees and Graphs in computer, Network Application of Tree and Graphs, Concepts of Graph Coloring.

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

**Text / Reference books:**Ramesh S.Gaonkar, Microprocessor Architecture, Programming, and Applications with 8085, Prentice Hall, A.P.Malvino and J.A.Brown, Digital Computer Electronics, 3rd Edition, Tata McGraw Hill, D.V.Hall, Microprocessors and Interfacingv – Programming and Hardware, McGraw Hill, 8000 to 8085 Introduction to 8085 Microprocessor for Engineers and Scientists, A.K.Gosh, Prentice Hall.

**Course Synopsis:**This course contains of fundamental concepts of computer organization, basic I/O interfaces and Interrupts operations.

**Goals:**The course objective is to introduce the operation, programming and application of microprocessor.

**Course Contents:**

**Unit1: Introduction (3 Hrs)**

Introduction to Microprocessors, Basic organization

**Unit 2: Basic Computer Architecture (10 Hrs)**

SAP Architectures, Instructions, Microprogram; 8-bits “W” bus, 4-bits program counter, 4-bits Memory Address Register (MAR), 16×8-bit memory, 8-bit instruction register (IR), 6-cycle controller with 12- bit micro-instruction word, 8-bit accumulator, 8-bit B register, 8-bit adder-subtractor, 8-bit output register,SAP-1 Instructions, Fetch & Execution, microprogram, fetch cycle, execution cycle, microprogram, controller implementations, SAP 2 Architecture, architectural differences with SAP-1 , bi-directional registers, instruction set, flags.

**Unit 3: Instruction Cycle (3 Hrs)**

Fetch Operation and Timing Diagram; Execute Operation and Timing Diagram, Machine Cycle and States.

**Unit 4: Intel 808580868088 (8 Hrs)**

Functional Block Diagram and Pin configuration, Timing and Control Unit, Registers, Data and Address Bus, Instructions, Operation Code and Operands, Addressing Modes, Interrupts, Flags, Instructions and Data Flow.

**Unit 5: Assembly Language Programming (9 Hrs)**

Assembly instruction format, Instruction Types, Mnemonics, Operands, Macro assemblers, Linking, Assembler directives, Simple sequence programs, Flags, Branch, Jumps, While-Do, Repeat-Until, If-Then-Else and Multiple If-then Programs, Debugging.

**Unit 6: Basic I/O, Memory R/W and Interrupt Operations (6 Hrs) **

Memory Read, Memory Write, I/O Read, I/O Write, Direct Memory Access, Interrupt, Types, Interrupt Masking, 8259 operation.

**Unit 7: Input/ Output Interfaces (6 Hrs)**

Parallel communication, Serial communication, Data transfer wait operation, 8255A working, 8255A Modes, RS-232 interface, Keyboard and display controller.

**Laboratory works: **

Assembly language programming using 8085/8086/8088 trainer kit. The programming should include: Arithmetic operation, base conversion, conditional branching etc.

**Sample Lab work list may include:**

1. Assembly language program using 8085 microprocessor kit.

2. Program should comprise the use of all types of instructions and addressing modes.

3. The programming should include the concept of Arrays and the concept of Multiplications and Division operations on Microprocessor.

4. Assembly language programming, using any types of Assembler, which should include the different functions of Int 10h, and 12h

**Nature of Course:**Theory (3 Hrs)+ Lab (3 Hrs)

**Text books:**Data Structure Using C & C++, Langsam Yedidyah, Augenstein Moshe J., Tennenbaum Aaron M., PHI

**Reference:**The Design and Analysis of algorithm, Nitin Upadhyaya, SK Kataria & Sons.

**Course of Synopsis:** Study of basic data structure vocabulary, the concept of an algorithm.

**Goal: ** To provide the Concept of data structure and implementation using programming techniques.

**Course Contents:**

**Unit 1: (14 Hrs)**

1.1 Introduction to Data Structure: Information and its meaning, Array in C++: The array as an ADT, Using one dimensional array, Two dimensional array, Multi dimensional array, Structure, Union, Classes in C++.

1.2 The Stack: Introduction, definition, primitive operation, the stack as an abstract data type, implementing the POP operation, testing for exceptional condition, implementing the PUSH operation.

1.3 The Infix, Postfix, & Prefix: Introduction, evaluating the postfix operation, program to evaluate the postfix operation, limitation of program, converting from one to another.

1.4 Recursion: Introduction, factorial functions, multiplication of natural numbers, Fibonacci sequence, binary search, the tower of Hanoi problem, translation from prefix to postfix using recursion.

**Unit 2: (31 Hrs)**

2.1 Queues: Introduction the queue and its sequential representation: The queue as an abstract data type, implementation of queue, inserts operation, priority queue.

2.2 Linked Lists: Introduction, inserting and deleting the nodes from a list, linked implementation of stack, get node and free node operation, linked implementation of queue .Linked list as a data structure, circular lists, stack as a circular list, and queue as a circular list.

2.3 Tree: Introduction, Binary Trees: Operation on Binary Trees, application on BinaryTrees. Binary Tree Representation: node representation of binary tree, internal and external nodes, implicit array representation of binary tree, binary tree traversal, threaded binary tree, heterogonous binary tree. The Huffman algorithm. Representing lists as binary trees. Trees and their application.

2.4 Sorting: Introduction, O notation, efficiency of sorting, exchange sort: bubble sort, quick sort.

2.5 Selection and Tree Sorting: Introduction, straight selection sort, binary tree sort, heapsort, insertion sort, merge and radix sort.

2.6 Searching: Introduction, sequential searching, binary search, interpolation search, tree search, general search tree, hashing.

2.7 Graphs: Introduction, linked representation of graphs.

2.8 Algorithm: Introduction, design of algorithm, algorithm validation, analysis of algorithm, algorithm testing, subalgorithm.

**Laboratory works:**

1. Write a code to multiply two matrixes and get the transpose of the third one.

2. Write a code to implement the stack that should check overflow and underflow also.

3. Write a code to convert any prefix number to postfix.

4. Write a code to convert any infix number to postfix.

5. Write a code to convert any postfix number to prefix.

6. Implement tower of Hanoi.

7. Write a code to implement different sorting techniques.

8. Write a code to demonstrate the binary search.

9. Write a code to implement the queue.

10. Write a code to convert stack operation to queue operation.

**Homework**

**Assignment:** Assignment should be given from the above units in throughout the semester.

**Computer usage:** No specific

**Prerequisite:** C, C++

**Category content:**

Science Aspect: 40%

Design Aspect 60%

**Nature of Course: Theory**

**Text books:**David c. lay: Linear Algebra and its applications, 3rd edition, Pearson Education.

**References:**Kolman, Bernard, Introductory Linear Algebra with Application. 7th edition. Pearson, Gilbert Strang; linear Algebra and its Application. 3rd edition, Kreszig, E. “advanced Engineering Mathematics.” 5th edition, . Wiley

**Course synopsis:** Linear equations in linear algebra, matrix algebra, Determinants, Vector spaces, Eigen values and Eigen vectors. Orthogonality and least squares. Symmetric matrices and quadratic forms.

**Goal:** This course provides students with the knowledge of fundamental linear algebra and the theory of matrices. On completion of this course the student will master the basic concepts and acquires skills in solving problems in linearbalgebra.

**Course Contents:**

**Unit 1: Linear equations in linear Algebra (10 Hrs)**

1.1 Systems of linear equations

1.2 Row reduction and Echelon Forms

1.3 Vector equations

1.4 The matrix equations Ax = b

1.5 Solution sets of linear systems

1.6 Linear independence

1.7 Introduction Liner Transformation

1.8 The matrix of the Linear Transformation

**Unit 2: Matrix Algebra (8 Hrs)**

2.1 Matrix operations

2.2 The inverse of matrix

2.3 Characterization of invertible matrices

2.4 Partitioned Matrices

2.5 The Leontief Input- output models

2.6 Application to Computer graphics

**Unit 3: Determinants (4 Hrs)**

3.3 Introduction of determinants

3.2 Properties of determinants

3.3 Cramer’s rule value and linear transformations

**Unit 4: Vector spaces (8 Hrs)**

4.1 Vector spaces and sub polar

4.2 Null spaces, Column spaces and linear transformation

4.3 Linearly Independent sets; Bases

4.4 Coordinate system

4.5 The dimension of a vector space

4.6 Rank

4.7 Change of basis

**Unit 5: Eigen values and Eigen vectors (7 Hrs)**

5.1 Eigen vectors and Eigen values

5.2 The characteristics equations

5.3 Diagonolization

5.4 Eigen vectors and Linear Transformation

5.5 complex Eigen values

5.6 Discrete Dynamical values

**Unit 6: Orthogonality and Least squares (8 Hrs)**

6.1 Linear products, length and Orthogonality

6.2 Orthogonal sets

6.3 orthogonal Projections

6.4. The Gram- Schmidt process

6.5 Least square problems

6.6 Applications to Linear models

**Nature of Course:**Theory (3 Hrs) + Lab (3 Hrs)

**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. 2011 , Cochran W.G. sampling Techniques, 3rd edition, John Wiley & Sons, Inc. New York, 1997.

**References:**Kempthorane o design and analysis of experiments, Wiley Eastern, New York , Desraj, Pramod Chandhok, sample survey Theory, Narosa Publishing House, 1998.

**Course of 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 application in the area of science and Technology.

**Course Contents:****Unit 1: Sample Survey (10 Hrs) **

**Unit 1: **Concept of population and sample; Needs of Sampling; Censuses and sample Survey; Basic concepts 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; sampling 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 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)**

2^{2}, 2^{3}, and 3^{2} Design; Main effects and Interactions Effects; Confounding in 2^{3} Factorial Design

**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 courses I 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.