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 Spearman’s Rank correlation. 05 Sampling theory |

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 Dynamic Programming Backtracking String Matching Algorithms Branch and bound |

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: University of Mumbai Computer Engineering ( Second Year – Sem III & IV) Revised Course(R2012) 32 4 Memory Organization: 5 I/O Organization and Peripherals: Introduction to parallel processing systems: |

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 : 3 Relational Model and Algebra : Introduction , Mapping the ER and EER 4 Structured Query Language (SQL) : Overview of SQL , Data Definition University of Mumbai Computer Engineering ( Second Year – Sem III & IV) Revised Course(R2012) 6 Relational–Database Design : Design guidelines for relational schema, 7 Transactions Management and Concurrency: Transaction concept, 8 Query Processing and Optimization: Overview ,Issues in Query |

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): Finite Automata: University of Mumbai Computer Engineering ( Second Year – Sem III & IV) Revised Course(R2012) 39 Regular Language (RL): Context Free Grammars (CFG): Pushdown Automata(PDA): Turing Machine (TM): Undecidability and Recursively Enumerable Languages: |

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 3.Output Primitives 4.Filled Area Primitives 5.2D Geometric Transformations 6.2D Viewing 7.3D Geometric Transformations and 3D Viewing 8.3D Geometric Transformations and 3D Viewing 9.Illumination Models and Surface Rendering 10. 11. Fractals |

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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