Computer Engineering Semester 4


Applied Mathaematics IV
Complex Integration
1.1 Complex Integration – Line Integral, Cauchy’s Integral theorem for simply
connected regions, Cauchy’s Integral formula(without proof)
1.2 Taylor’s and Laurent’s series ( without proof)
1.3 Zeros, poles of f(z), Residues, Cauchy’s Residue theorem
1.4 Applications of Residue theorem to evaluate Integrals of the type
02 Matrices:-
2.1 Eigen values and eigen vectors
2.2 Cayley-Hamilton theorem(without proof)
2.3 Similar matrices, diagonalisable of matrix.
2.4 Derogatory and non-derogatory matrices ,functions of square matrix.

03 Correlation
3.1Scattered diagrams, Karl Pearson’s coefficient of correlation, covariance,

Spearman’s Rank correlation.
3.2 Regression Lines.
04 Probability
4.1 Baye’s Theorem,
4.2 Random Variables:- discrete & continuous random variables, expectation,
Variance, Probability Density Function & Cumulative Density Function.
4.3 Moments, Moment Generating Function.
4.4 Probability distribution: binomial distribution, Poisson & normal distribution.
(For detail study)

05 Sampling theory
5.1 Test of Hypothesis, Level of significance, Critical region, One Tailed and two
Tailed test, Test of significant for Large Samples:-Means of the samples and test of
significant of means of two large samples.
5.2 Test of significant of small samples:- Students t- distribution for dependent and
independent samples.
5.3 Chi square test:- Test of goodness of fit and independence of attributes,
Contingency table.
Mathematical Programming
6.1 Types of solution, Standard and Canonical form of LPP, Basic and feasible
solutions, simplex method.
6.2 Artificial variables, Big –M method (method of penalty).
6.3 Duality, Dual simplex method.
6.4 Non Linear Programming:-Problems with equality constrains and inequality
constrains
(No formulation, No Graphical method).

Term work:
Term work shall consist of minimum four SCILAB practicals and six tutorials.
SCILAB practicals : 10 marks
Tutorials : 10 marks
Attendance : 05 marks
Total : 25 marks
University of Mumbai Computer Engineering ( Second Year – Sem III & IV) Revised Course(R2012) 26
Text Books:
1. Higher Engineering Mathematics by Grewal B. S. 38th edition, Khanna Publication 2005.
2. Operation Research by Hira & Gupta,S Chand.
3. A Text Book of Applied Mathematics Vol. I & II by P.N.Wartilar &
4. J.N.Wartikar, Pune, Vidyarthi Griha Prakashan., Pune.
5. Probability and Statistics for Engineering, Dr. J Ravichandran, Wiley-India.Theory Examination:
1. Question paper will comprise of total 6 questions, each of 20 Marks.
2. Only 4 questions need to be solved.
3. Question 1 will be compulsory and based on maximum part of the syllabus.
4. Remaining questions will be mixed in nature (for example suppose Q.2 has part (a) from module 3 then part (b) will
be from any module other than module 3)
In question paper, weightage of each module will be proportional to number of respective lecture hours as
mentioned in the syllabus.
Analysis of Algorithm
Introduction to analysis of algorithm
• Decision and analysis fundamentals
• Performance analysis , space and time complexity
• Growth of function – Big –Oh ,Omega , Theta notation
• Mathematical background for algorithm analysis
• Analysis of selection sort , insertion sort
• Randomized algorithms
• Recursive algorithms
• The substitution method
• Recursion tree method
• – Master methodDivide and Conquer
• General method
• Binary search
• Finding minimum and maximum
• Merge sort analysis
• Quick sort analysis
• Strassen’s matrix multiplication
• The problem of multiplying long integers

• – constructing Tennis tournament

Greedy Method
• General Method
• Knapsack problem
• Job sequencing with deadlines
• Minimum cost spanning trees-Kruskal and prim’s algorithm
• Optimal storage on tapes
• Single source shortest path

Dynamic Programming
• General Method
• Multistage graphs
• all pair shortest path
• single source shortest path
• Optimal binary search tree
• 0/1 knapsack
• Travelling salesman problem
• – Flow shop scheduling

Backtracking
• General Method
• 8 queen problem( N-queen problem)
• Sum of subsets
• Graph coloring

String Matching Algorithms
• The naïve string matching Algorithms
• The Rabin Karp algorithm
• String matching with finite automata
• The knuth-Morris-Pratt algorithm
• Longest common subsequence algorithm

Branch and bound
• General method
• 15 puzzle problem
• Travelling salesman problem

Text Books:
1. Ellis horowitz , sartaj Sahni , s. Rajsekaran. “Fundamentals of computer algorithms” University Press.
2. T.H.coreman , C.E. Leiserson,R.L. Rivest, and C. Stein, “Introduction to algorithms”, 2nd edition , PHI publication
2005.
3. Alfred v. Aho , John E. Hopcroft , Jeffrey D. Ullman , “Data structures and Algorithm” Pearson education , fourth
impression 2009
Termwork:
Total experiments to be performed are 12 = ( 9 + 3 ) 9 Experiments marked * are mandatory.
For additional 3 experiments teacher can choose experiments from suggested list.
The final certification and acceptance of term work ensures that satisfactory performance of laboratory work and
minimum passing marks in term work.
Termwork: 25 Marks ( total marks ) = 15 Marks Experiments + 05 Marks Assignment + 5 (Attendance
(theory+practical))
Practical Exam will be based on above syllabus
Theory Examination:
1. Question paper will comprise of total 6 questions, each of 20 Marks.
2. Only 4 questions need to be solved.
3. Question 1 will be compulsory and based on maximum part of the syllabus.
4. Remaining questions will be mixed in nature (for example suppose Q.2 has part (a) from module 3 then part (b) will
be from any module other than module 3)
In question paper, weightage of each module will be proportional to number of respective lecture hours as
mentioned in the syllabus.
Computer Organization and Architecture*
1 Overview of Computer Architecture & Organization:
• Introduction of Computer Organization and Architecture.
• Basic organization of computer and block level description of
the functional units.
• Evolution of Computers, Von Neumann model.
• Performance measure of Computer Architecture.
• Introduction to buses and connecting I/O devices to CPU and
Memory, bus structure.

2 Data Representation and Arithmetic Algorithms:
• Number representation: Binary Data representation, two’s
complement representation and Floating-point
representation. IEEE 754 floating point number
representation.
• Integer Data computation: Addition, Subtraction.
Multiplication: Signed multiplication, Booth’s algorithm.

University of Mumbai Computer Engineering ( Second Year – Sem III & IV) Revised Course(R2012) 32
• Division of integers: Restoring and non-restoring division
• Floating point arithmetic: Addition, subtraction
3 Processor Organization and Architecture:
• CPU Architecture, Register Organization , Instruction
formats, basic instruction cycle. Instruction interpretation and
sequencing.
• Control Unit: Soft wired (Micro-programmed) and
hardwired control unit design methods. Microinstruction
sequencing and execution. Micro operations, concepts of
nano programming.
• Introduction to RISC and CISC architectures and design
issues.
• Case study on 8085 microprocessor: Features, architecture,
pin configuration and addressing modes.

4 Memory Organization:
• Introduction to Memory and Memory parameters.
Classifications of primary and secondary memories. Types of
RAM and ROM, Allocation policies, Memory hierarchy and
characteristics.
• Cache memory: Concept, architecture (L1, L2, L3), mapping
techniques. Cache Coherency, Interleaved and Associative
memory.
• Virtual Memory: Concept, Segmentation and Paging , Page
replacement policies.

5 I/O Organization and Peripherals:
• Input/output systems, I/O modules and 8089 IO processor.
• Types of data transfer techniques: Programmed I/O,
Interrupt driven I/O and DMA.
• Peripheral Devices: Introduction to peripheral devices,
scanner, plotter, joysticks, touch pad.

Introduction to parallel processing systems:
• Introduction to parallel processing concepts
• Flynn’s classifications
• pipeline processing
• instruction pipelining,
• pipeline stages
• pipeline hazards.

Text Books:
1. Carl Hamacher, Zvonko Vranesic and Safwat Zaky, “Computer Organization”, Fifth Edition, Tata
McGraw-Hill.
2. John P. Hayes, “Computer Architecture and Organization”, Third Edition.
3. William Stallings, “Computer Organization and Architecture: Designing for Performance”, Eighth
Edition, Pearson.
4. B. Govindarajulu, “Computer Architecture and Organization: Design Principles and Applications”,
Second Edition, Tata McGraw-Hill.
Termwork:
Term work should consist of at least 08 experiments.
Journal must include at least 2 assignments.
The final certification and acceptance of term work ensures that satisfactory performance of laboratory work and
minimum passing marks in term work.
Term Work: 25 Marks ( total marks ) = 15 Marks ( Experiment ) + 5 Marks ( Assignment ) + 5 (Attendance
(theory+practical))
oral exam will be based on the above syllabus.
Note:
1. The faculty should conduct eight programming practical / experiments based on the above syllabus including
two case studies on recent developments covering the above contents.
All the programs should be implemented in C/C++/Java under Windows or Linux environment.
Experiments can also be conducted using available open source tools.
2. 8085 microprocessor should be included only as a sample case study to visualize the concepts. No questions
in University Exams / Class Tests should be asked on 8085 microprocessor.
Theory Examination:
1. Question paper will comprise of total 6 questions, each of 20 Marks.
2. Only 4 questions need to be solved.
3. Question 1 will be compulsory and based on maximum part of the syllabus.
4. Remaining questions will be mixed in nature (for example suppose Q.2 has part (a) from module 3 then part (b) will
be from any module other than module 3)
In question paper, weightage of each module will be proportional to number of respective lecture hours as
mentioned in the syllabus.
Database Management System
1 Introduction Database Concepts: Introduction, Characteristics of
databases, File system V/s Database system, Users of Database system,
Concerns when using an enterprise database, Data Independence, DBMS
system architecture, Database Administrator,

2 Entity–Relationship Data Model :
Introduction, Benefits of Data Modeling, Types of Models, Phases of
Database Modeling, The Entity-Relationship (ER) Model, Generalization,
Specialization and Aggregation, Extended Entity-Relationship (EER)
Model.

3 Relational Model and Algebra : Introduction , Mapping the ER and EER
Model to the Relational Model , Data Manipulation , Data Integrity
,Advantages of the Relational Model, Relational Algebra , Relational
Algebra Queries, Relational Calculus.

4 Structured Query Language (SQL) : Overview of SQL , Data Definition
Commands, Set operations , aggregate function , null values, , Data
Manipulation commands, Data Control commands , Views in SQL, Nested

University of Mumbai Computer Engineering ( Second Year – Sem III & IV) Revised Course(R2012) 
and complex queries .
5 Integrity and Security in Database: Domain Constraints, Referential
integrity, Assertions, Trigger, Security, and authorization in SQL

6 Relational–Database Design : Design guidelines for relational schema,
Function dependencies, Normal Forms- 1NF, 2 NF, 3NF, BCNF and 4NF

7 Transactions Management and Concurrency: Transaction concept,
Transaction states, ACID properties, Implementation of atomicity and
durability, Concurrent Executions, Serializability, Recoverability,
Implementation of isolation, Concurrency Control: Lock-based ,
Timestamp-based , Validation-based protocols, Deadlock handling,
Recovery System: Failure Classification, Storage structure, Recovery &
atomicity, Log based recovery, Shadow paging.

8 Query Processing and Optimization: Overview ,Issues in Query
Optimization ,Steps in Query Processing , System Catalog or Metadata,
Query Parsing , Query Optimization, Access Paths , Query Code
Generation , Query Execution , Algorithms for Computing Selection and
Projection , Algorithms for Computing a Join , Computing Aggregation
Functions , Cost Based Query Optimization .

Text Books:
1. G. K. Gupta :”Database Management Systems”, McGraw – Hill.
2. Korth, Slberchatz,Sudarshan, :”Database System Concepts”, 6th Edition, McGraw – Hill
3. Elmasri and Navathe, “ Fundamentals of Database Systems”, 5thEdition, PEARSON Education.
4. Peter Rob and Carlos Coronel, “ Database Systems Design, Implementation and Management”, Thomson
Learning, 5th Edition.
Termwork:
Term work should consist of at least 12 experiments.
Journal must include at least 2 assignments.
The final certification and acceptance of term work ensures that satisfactory performance of laboratory work and
minimum passing marks in term work.
Term Work: 25 Marks ( total marks ) = 15 Marks ( Experiment ) + 5 Marks ( Assignment ) + 5 (Attendance
(theory+practical))
practical exam will be based on the above syllabus.
Theory Examination:
1. Question paper will comprise of total 6 questions, each of 20 Marks.
2. Only 4 questions need to be solved.
3. Question 1 will be compulsory and based on maximum part of the syllabus.
4. Remaining questions will be mixed in nature (for example suppose Q.2 has part (a) from module 3 then part (b) will
be from any module other than module 3)
In question paper, weightage of each module will be proportional to number of respective lecture hours as
mentioned in the syllabus.
Theoretical Computer Science
Introduction:
• Alphabets, Strings and Languages
• Chomskey hierarchy and Grammars.
• Finite Automata (FA) and Finite State machine (FSM).

Regular Grammar (RG):
• Regular Grammar and Regular Expression (RE): Definition,
Equivalence and Conversion from RE to RG and RG to RE.
• Equivalence of RG and FA, Converting RG to FA and FA to RG.
• Equivalence of RE and FA, Converting RE to FA and FA to RE.

Finite Automata:
• Deterministic and Nondeterministic Finite Automata ( DFA and NFA ):
Definitions, Languages, Transitions ( Diagrams, Functions and Tables).
• Eliminating epsilon-transitions from NFA.

University of Mumbai Computer Engineering ( Second Year – Sem III & IV) Revised Course(R2012) 39
• DFA, NFA: Reductions and Equivalence.
• FSM with output: Moore and Mealy machines.

Regular Language (RL):
• Decision properties: Emptiness, Finiteness and Membership.
• Pumping lemma for regular languages and its applications.
• Closure properties.
• Myhill-Nerode Theorem and An application: Text Search.

Context Free Grammars (CFG):
• Definition, Sentential forms, Leftmost and Rightmost derivations.
• Context Free languages (CFL): Parsing and Ambiguity.
• CFLs: Simplification and Applications.
• Normal Forms: CNF and GNF.
• Pumping lemma for CFLs and its applications.
• Closure properties and Kleene’s closure.

Pushdown Automata(PDA):
• Definition, Transitions ( Diagrams, Functions and Tables), Graphical
Notation and Instantaneous Descriptions.
• Language of PDA, Pushdown Stack Machine ( PSM ) as a machine with
stack, Start and Final state of PSM.
• PDA/PSM as generator, decider and acceptor of CFG
• Deterministic PDA (DPDA) and Multi-stack DPDA.

Turing Machine (TM):
• Definition, Transitions ( Diagrams, Functions and Tables).
• Design of TM as generator, decider and acceptor.
• Variants of TM: Multitrack, Multitape and Universal TM.
• Equivalence of Single and Multi Tape TMs.
• Power and Limitations of TMs.
• Design of Single and Multi Tape TMs as a computer of simple
functions: Unary, Binary ( Logical and Arithmetic ), String operations (
Length, Concat, Match, Substring Check, etc )

Undecidability and Recursively Enumerable Languages:
• Recursive and Recursively Enumerable Languages.
• Properties of Recursive and Recursively Enumerable Languages.
• Decidability and Undecidability, Halting Problem, Rice’s Theorem,
Grebach’s Theorem, Post Correspondence Problem,
• Context Sensitivity and Linear Bound Automata.
Comparison of scope of languages and machines:
• Subset and Superset relation between FSM, PSM and TM.
• Subset and Superset relation between RL, CFL and Context Sensitive
Language.

Text Books:
1. Michael Sipser, “ Theory of Computation”, Cengage learning.
2. John E. Hopcroft, Rajeev Motwani, Jeffery D. Ullman, “ Introduction to Automata Theory, Languages and
Computation”, Pearson Education
Theory Examination:
1. Question paper will comprise of total 6 questions, each of 20 Marks.
2. Only 4 questions need to be solved.
3. Question 1 will be compulsory and based on maximum part of the syllabus.
4. Remaining questions will be mixed in nature (for example suppose Q.2 has part (a) from module 3 then part (b) will
be from any module other than module 3)
In question paper, weightage of each module will be proportional to number of respective lecture hours as
mentioned in the syllabus.
 Theoretical Computer Science
 Introduction to Computer Graphics
(a) What is Computer Graphics?
(b) Where Computer Generated pictures are used
(c) Elements of Pictures created in Computer Graphics
(d) Graphics display devices
(e) Graphics input primitives and Devices

2. Introduction to openGL
(a) Getting started Making pictures (02)
University of Mumbai Computer Engineering ( Second Year – Sem III & IV) Revised Course(R2012) 42
(b) Drawing basic primitives
(c) Simple interaction with mouse and keyboard
(For implementation use openGL programming)

3.Output Primitives
(a) Points and Lines, Antialiasing
(b) Line Drawing algorithms
• DDA line drawing algorithm
• Bresenham’s drawing algorithm
• Parallel drawing algorithm
(c) Circle and Ellipse generating algorithms
• Mid-point Circle algorithm
• Mid-point Ellipse algorithm
(d) Parametric Cubic Curves
• Bezier curves
• B-Spline curves

4.Filled Area Primitives
(a) Scan line polygon fill algorithm
(b) Pattern fill algorithm
(c) Inside-Outside Tests
(d) Boundary fill algorithms
(e) Flood fill algorithms

5.2D Geometric Transformations
(a) Basic transformations
(b) Matrix representation and Homogeneous Coordinates
(c) Composite transformation
(d) Other transformations
(e) Transformation between coordinated systems

6.2D Viewing
(a) Window to Viewport coordinate transformation
(b) Clipping operations – Point clipping
(c) Line clipping
• Cohen – Sutherland line clipping
• Liang – Barsky line clipping
• Midpoint subdivision
(d) Polygon Clipping
• Sutherland – Hodgeman polygon clipping
• Weiler – Atherton polygon clipping

7.3D Geometric Transformations and 3D Viewing
(a) 3D object representation methods
B-REP , sweep representations , CSG
(b) Basic transformations
• Translation
• Rotation
• Scaling
(c) Other transformations
1. Reflection
2. Rotation about an arbitrary axis
(d) Composite transformations
(e) Projections – Parallel and Perspective
(f) 3D clipping

8.3D Geometric Transformations and 3D Viewing
(a) Classification of Visible Surface Detection algorithm
(b) Back Surface detection method
(c) Depth Buffer method
(d) Scan line method
(e) BSP tree method
(f) Area Subdivision method

9.Illumination Models and Surface Rendering
(a) Basic Illumination Models
(b) Halftone and Dithering techniques
(c) Polygon Rendering
Constant shading , Goraud Shading , Phong Shading

10. 11. Fractals
(a) Introduction
(b) Fractals and self similarity
Successive refinement of curves, Koch curve,
Fractional Dimension,
(c) String production and peano curves
(For implementation use C Programming)

 Termwork:
The final certification and acceptance of term work ensures that satisfactory performance of laboratory work and
minimum passing marks in term work.
Term Work: 25 Marks ( total marks ) = 15 Marks ( Experiment ) + 5 Marks ( Assignment ) + 5 (Attendance
(theory+practical))
Practical Exam will be based on above syllabus
 TEXT BOOKS
1. Donald D. Hearn & M. Pauline Baker, “ Computer Graphics-C Version”, 2nd Edition, Pearson Education,
2002, ISBN 81-7808-794-4
2. F.S.Hill , Jr. , “Computer Graphics using OpenGL” , second edition PHI publication.
3. James D. Foley, Andries van Dam, Steven K Feiner, John F. Hughes, “Computer Graphics Principles and
Practice, 2nd Edition in C, Audison Wesley, ISBN – 981-235-974-5
4. William M. Newman, Roberet F. Sproull, “ Principles of Interactive Computer Graphics”, Second Edition,
Tata McGraw-Hill Edition
 Theory Examination:
1. Question paper will comprise of total 6 questions, each of 20 Marks.
2. Only 4 questions need to be solved.
3. Question 1 will be compulsory and based on maximum part of the syllabus.
4. Remaining questions will be mixed in nature (for example suppose Q.2 has part (a) from module 3 then part (b) will
be from any module other than module 3)
In question paper, weightage of each module will be proportional to number of respective lecture hours as
mentioned in the syllabus.

 

 

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